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Essays on consumer returns in online retail and sustainable operations
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Essays on consumer returns in online retail and sustainable operations
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ESSAYS ON CONSUMER RETURNS IN ONLINE RETAIL AND SUSTAINABLE OPERATIONS by Hailong Cui A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BUSINESS ADMINISTRATION) May 2020 Copyright 2020 Hailong Cui Dedication To My Jesus — My Savior My Mum —DäDtÉÝDÌàXàX´8È@xØØ My Ashu — My Better Half ii Acknowledgments My past few years in the Ph.D. program has been the most intellectually challenging and rewarding ex- perience that I have ever had. I want to take this opportunity to acknowledge the University of Southern California, Marshall School of Business, and Department of Data Sciences and Operations for providing a nurturing environment in which I could grow academically and for providing financial support. Most importantly, however, I want to express my sincere gratitude to my advisors — Professor Greys Soˇ si´ c, Professor Sampath Rajagopalan and Professor Amy R. Ward who advised me and supported me through the ups and downs I have had during the course of Ph.D. study. It has been an honor and privilege to have an opportunity to work with them, which in fact has been the best part of my entire Ph.D. study. I am also indebted to Professor Sha Yang for serving on my dissertation committee, and Professor Xin Tong and Professor Paul Adler for serving on my qualifying exam committee. I want to thank the following faculty with whom I took courses which laid a foundation for my Ph.D. dissertation (last names in alphabetical order): Jinchi Lv, Greys Soˇ si´ c, Sampath Rajagopalan, Ramandeep Randhawa, Paat Rusmevichientong, Xin Tong, Amy R. Ward, Leon Zhu (Data Sciences and Operations); Anthony M. Marino, Kevin J. Murphy (Finance and Business Economics); Lee Cerling (Business Commu- nication); Quentin Berger, Jianfeng Zhang (Mathematics); John Gunnar Carlsson, Phebe Vayanos (Industrial and Systems Engineering); Gillian Hadfield, Scott Malzahn (Law School), as well as Professor Gareth James (Data Sciences and Operations) who organized statistics reading courses that helped me in my research. iii Table of Contents Dedication ii Acknowledgments iii Contents iv List of Tables vi List of Figures viii Abstract ix 1 Impact of Task-Level Worker Specialization, Workload, and Product Personalization on Con- sumer Returns 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Empirical Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Hypotheses and Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 Return Rate Estimation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2 Predicting Product Return Volume Using Machine Learning Methods 46 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3 Empirical Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4 Main Effects Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 2.5 Incorporating Interaction Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.6 Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 iv 3 Recycling Common Materials: Effectiveness, Optimal Decisions, and Coordination Mecha- nisms 88 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.4 Recycling Effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.5 Centralized Recycling Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.6 Decentralized Recycling Decisions and Coordination Mechanisms . . . . . . . . . . . . . . 114 3.7 A Case Study: Minimum Recycled Content Requirement . . . . . . . . . . . . . . . . . . . 121 3.8 Some Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 3.9 Concluding Remarks and Managerial Insights . . . . . . . . . . . . . . . . . . . . . . . . . 125 4 Technical Details 127 4.1 Technical Details Related to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.2 Technical Details Related to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 4.3 Technical Details Related to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 References 154 v List of Tables 1.1 A Sample Operational Data Set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 Summary Statistics of Production Related Variables . . . . . . . . . . . . . . . . . . . . . . . . 29 1.3 Correlation Matrix of Production Related Variables . . . . . . . . . . . . . . . . . . . . . . . . 29 1.4 Effect of Worker Specialization, Workload and Personalization on Return Rate y . . . . . . . . . . . 36 1.5 Robustness Checks on Effect of Worker Specialization, Workload and Personalization on Return Rate y 40 2.1 A sample operational data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.2 Definition of response and predictor variables fort = 1; ;39;i = 1;2;3;j = 1; ;13: . . . . . 57 2.3 Summary statistics of response and predictor variables. Data size N total = 1;360 represents the number of data points in our model because we model the return volume per product type, per retailer, per time period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.4 Prediction performance of 6 main effects models trained on 33 periods and tested on 6 periods. . . . 64 2.5 OLS results for main effects models in the training set. Standard errors are shown in parentheses. ***, **, and * denote statistical significance at the 0.001, 0.01 and 0.05 confidence levels respectively. 66 2.6 2-way and 3-way interaction terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.7 Prediction performance of 2 LASSO models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.8 Prediction performance of three models (trained on periods 1 to 33) for each of the 6 future periods. . 72 2.9 Prediction performance for each of the 6 future periods with models updated every period. . . . . . 72 2.10 Predictors and coefficients selected by LASSO w.r.t. 1se . . . . . . . . . . . . . . . . . . . . . 73 2.11 Prediction performance of alternative methods against LASSO. Note y : Optimal Elastic Net is reduced to LASSO (see details on the next page.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.12 Comparison of 4 cases of random test periods against the main analysis for models 5 and 6. . . . . . 82 2.13 Comparison of 4 cases of random test periods against the main analysis for the LASSO model. . . . 83 2.14 Comparison of 5 and 7 test periods against the main analysis (6 periods) for three models. . . . . . . 84 3.1 Notation for' (per unit of product) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.2 Minimum Yield Rates With Respect to Emissions. . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.3 Minimum Yield Rates With Respect to Operational Costs . . . . . . . . . . . . . . . . . . . . . 104 vi 3.4 Minimum Yield Rates With Respect to Aggregate Costs . . . . . . . . . . . . . . . . . . . . . . 105 3.5 Emissions, Operational Cost, and Aggregate Cost (per unit of product) . . . . . . . . . . . . . . . 106 3.6 A summary of definitions for centralized recycling. . . . . . . . . . . . . . . . . . . . . . . . . 106 3.7 A summary of notations for decentralized recycling. . . . . . . . . . . . . . . . . . . . . . . . . 116 4.1 Sewing-Stage Task Name and Description, Applicable Product Types, and Material Codes . . . . . 127 4.2 Return Policies of Online Retailers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.3 Summary Statistics of Consumer Socio-Economic and Demographic Characteristics at Shipping ZIP5 128 4.4 Average Marginal Effect vs. Worker Specialization (WS) . . . . . . . . . . . . . . . . . . . . . . 130 4.5 Robustness Checks on Effect of Worker Specialization, Workload and Personalization on Return Rate y When Worker Specialization is Measured During the Past 1 Week to 6 Months (1 month = 30 days) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.6 Robustness Checks on Effect of Worker Specialization, Workload and Personalization on Return Rate y When Worker Specialization is Measured During the Past 1 Week to 6 Months (1 month = 30 days) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 4.7 Effect of Worker Specialization, Workload and Personalization on Return Rate y using IV . . . . . . 133 4.8 Prediction performance using original data (trained on 33 periods and tested on 6 periods). . . . . . 135 4.9 Prediction performance using de-trended and de-seaonslized data (trained on 33 periods and tested on 6 periods). Note: y Model 2.2 is reduced to Model 2.1 because trend and month variables are not used in this data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.10 A comparison of prediction performance between models using actual returns y in the test periods and models using predicted returns z in the test periods to derive the predictor variable LaggedReturns. 136 4.11 Prediction performance with respect to different values of the minimum node size forB = 500. . . . 136 4.12 Prediction performance with different values ofB for the minimum node size = 5. . . . . . . . . . 136 4.13 Gradient Boosting model performance by tuning learning rate with default subsampling rate 0.5. Note y :, learning rate, is also referred to as the shrinkage parameter. Note z :B , early stopping, is also called the optimal number of iterations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.14 Gradient Boosting model performance using grid-search through tuning parameter space (;). . . . 137 4.15 Emissions from primary materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4.16 Emissions from Transportation of secondary materials . . . . . . . . . . . . . . . . . . . . . . . 147 4.17 Emissions from secondary materials ande r . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.18 Virgin Material Manufacturing and Transportation Costs . . . . . . . . . . . . . . . . . . . . . . 149 4.19 Cost for Transportation of secondary materials to Product Manufacturing Facility . . . . . . . . . . 151 4.20 Cost of secondary materials ands r for Each Material . . . . . . . . . . . . . . . . . . . . . . . . 152 4.21 Minimum Yield Rates vs. Actual Yield and collection rates . . . . . . . . . . . . . . . . . . . . 153 vii List of Figures 1.1 Factors Driving Consumer Product Returns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1 Sales, returns and return rates over 39 months, between July 2012 and September 2015. . . . . . . . 54 2.2 Sales, returns and return rates by product type (left) and by retailer (right) over all periods. . . . . . 54 2.3 A histogram of days to return for products returned within a year. . . . . . . . . . . . . . . . . . . 60 2.4 Selecting based on 10-fold CV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 2.5 Observed vs. predicted returns for some retailer product pairs (see colors online.) . . . . . . . . . . 75 3.1 A simplified product life cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.2 An illustration of optimal collection and yield rates in the social planner’s problem. . . . . . . . . . 108 4.1 Average Marginal Effect (vertical) vs. Worker Specialization (horizontal) . . . . . . . . . . . . . . 130 4.2 Observed vs. predicted returns by models 5, 6 and LASSO for 6 future periods. Missing data indicate no sales, e.g., (Retailer 1, Product 3) for all test periods. . . . . . . . . . . . . . . . . . . . . . . 138 viii Abstract With the emergence of the big-data era, there has been an explosion in the amount of private and public data. How can businesses use such data more effectively to improve operational decisions that impact financial outcomes? How can policy makers learn from such data to design environmental policies for long-term sus- tainability? These are some of the challenging questions that numerous business leaders and policy makers face today and are the motivation for my Ph.D. dissertation in which I specifically address the following three questions that I explain in more detail in the next two subsections. Can a Manufacturer Reduce Consumer Returns Using its Operational Levers? (Chapter 1) 1 Can a Manufacturer Predict Return V olume Using Machine Learning Methods? (Chapter 2) 2 Can a Policy Maker Implement Mechanisms to Improve Recycling Decisions? (Chapter 3) 3 Consumer Returns in Online Retail My work in the area of consumer returns addresses some of the increasing challenges in online retail. Consumer product returns are a major issue for retailers and manufacturers. Returned merchandise in the U.S. was estimated at $369 billion out of sales of $3.7 trillion in 2018. Online retailers experience a higher return rate than brick-and-mortar stores; 25% of all goods bought online are estimated to be returned even 1 Forthcoming in Manufacturing and Service Operations Management. https://doi.org/10.1287/msom.2019.0836 2 Published in European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2019.05.046 3 Published in European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2018.11.010 ix though the return rate can vary substantially across different retail categories. Furthermore, more than half of all returns may not be resold at full price, which results in substantial financial losses for retailers and manufacturers. Returns are especially costly for manufacturers if retailers simply pass along the returned goods to the manufacturers. In Chapter 1 (joint with Professor Sampath Rajagopalan and Professor Amy R. Ward), we study whether a product manufacturer can play a proactive role in reducing consumer return rates without having to nego- tiate stricter return policies with retailers which may dampen sales. This is a challenging question to address for several reasons. First, there can be many potential reasons for consumer returns, such as retailer return policies, product, purchase, and consumer attributes. After controlling for these factors already known in the literature, it is not clear a priori whether any operational levers under a manufacturer’s control can still sig- nificantly reduce returns. Second, even if such operational levers, in particular, the production process affects return rates, it is difficult to separate out this effect, because most products are produced through machine- based production processes with minimal process variation. Third, it is hard to obtain detailed task-level operational data from an industry partner which provides a good empirical setting to test the theory, because many data sets are at the aggregate level. To address these challenges, we collected private corporate data sets from a leading U.S. manufacturer of automotive accessories that utilizes an ERP system to systematically track every operation performed on the order at various stages. Our data sets include when (date and time), who (employee ID), what (product and material type, retailer information, personalization and return if applicable; see Table 1.1 for an example) and where (consumer Zipcode) about each order produced. We study the drivers of return rates using a logistic regression model wherein the dependent variable is the probability of a return. We use unique approaches to control for endogeneity. We find that manufacturers can reduce product return rates substantially by allowing customers to personalize the product. In addition, our results suggest that achieving the right level of worker specialization and decreasing workload levels may help reduce return rates, but the effects are relatively x small and managers have to take into account the cost implications of their actions. These drivers may be more attractive than strict return policies because they will not dampen sales and may, in fact, increase sales in the long run because of the reputation gained from better quality and personalized product offerings. In Chapter 2 (also joint with Professor Sampath Rajagopalan and Professor Amy R. Ward), we inves- tigate a related but different question: predicting future return volume to address operational challenges in managing product returns. The primary contribution of this work is to provide a general data-driven prediction framework to help firms to keep track of returns by time period, product type, and retailer. To achieve this goal, we take three sequential steps in building prediction models. First, we develop an easy- to-implement baseline main effects model using four key factors: sales volume, time period, product type, and retailer. Second, we explore whether additional variables from production process can improve predic- tion performance. Third, we investigate whether adding second and third order interaction effects increases prediction accuracy. However, this approach generates a large number of predictor variables leading us into a high dimensional setting and warrants the need for a robust variable/model selection methodology. To ad- dress this issue, we use several high-dimensional machine learning methods (LASSO, LARS-OLS hybrid, SCAD, and Elastic Net) to derive a sparse model. In addition, we explore two notable tree-based machine learning methods, Random Forest and Gradient Boosting, to capture possible complex non-linear structure in the data. Out of all models considered, LASSO yields a predictive model achieving the best prediction accuracy for future return volume due to its ability to select informative interaction terms out of more than one thousand possible combinations. The advantage of LASSO is even more pronounced when the predic- tion model is updated on a rolling time horizon which is often the case for many forecasting models. The LASSO model also turns in consistent performance based on several robustness tests, which empirically validates and is consistent with the theory of LASSO’s consistent variable selection with high probability established under the irrepresentable conditions. xi Sustainable Operations In Chapter 3 (joint with Professor Greys Soˇ si´ c), we study how to improve recycling effectiveness of common materials (paper, plastics, metals, and glass), which contributes to the long-term sustainability of natural resources. The management of post-consumer products, however, poses serious challenges, partic- ularly when considering the large amount of municipal solid waste (MSW) generated by human activities. The MSW includes everyday items that we use and then dispose of, such as product packaging, bottles, or newspapers. On a global scale, the annual MSW generation in 2012 was estimated at 1.3 billion tons, which is expected to increase to 2.2 billion tons by 2025. The U.S. Environmental Protection Agency (EPA) report on MSW shows that the amount generated by Americans increased from 88.1 million tons in 1960 to 251.8 million tons in 2012, out of which EPA estimates that 132.5 million tons were disposed into landfills. The most represented MSW materials in the U.S. are paper (27%), plastics (12.8%), metals (9.1%), and glass (4.5%)—all highly recyclable materials that account for more than half of MSW. Recycling effectiveness and recycling decisions for these common materials are the focus of our paper. In this work, we aim to investigate some key questions about recycling across three dimensions: greenhouse gas emissions, operational costs, and aggregate costs (social costs of emissions plus operational costs.) First, we build supply chain models for cradle-to-grave and cradle-to-cradle supply chains to derive an analytical condition for recycling effectiveness, and use U.S. emissions and cost data to empirically validate that recycling is effective in reducing emissions for all the above-mentioned materials. Furthermore, our analysis shows that recycling is effective for all materials, with the exception of glass, with respect to both operational and aggregate costs. Second, we study optimal recycling decisions in terms of collection and yield rates in a socially optimal case, as well as in scenarios in which recycling decisions are made by a local government, a product manufacturer, and an independent recycling firm. Unlike some existing findings, we show that there are instances in which a product manufacturer or an independent firm might be the best choice for organizing recycling operations. Finally, we discuss and analyze incentives that a social planner xii should offer to recyclers to bring their efforts closer to the socially optimal choice. We obtain a novel result, which shows that a deposit/refund scheme implemented by a social planner with a refund to local governments might lead to a socially optimal collection rate. xiii Chapter 1 Impact of Task-Level Worker Specialization, Workload, and Product Personalization on Consumer Returns 1.1. Introduction Consumer product returns are a major issue for retailers and manufacturers. Returned merchandise in the U.S. was estimated at $369 billion out of sales of $3.7 trillion in 2018 (Appriss Retail 2018), an increase in both return volume and return rate from $261 billion out of $3.3 trillion in 2014 (The Economist 2014). E-commerce experiences a higher return rate than brick-and-mortar stores; 25% of all goods bought online are estimated to be returned (Adams 2017) even though the return rate can vary substantially across different retail categories (Appriss Retail 2018). Furthermore, more than half of all returns may not be resold at full price, which results in substantial financial losses for retailers and manufacturers (Cheng 2015). Returns may be especially costly for manufacturers if retailers simply pass along the returned goods to the manufacturers. Returns are also important because they are an important driver of customer sentiment, which impacts a firm’s reputation, especially in e-commerce (Barnhar 2019). While the costs of a high return rate have drawn attention to the management of returned goods in both the media and academic research (e.g., Howland 2018, Guide et al. 2006), the manufacturer’s role in reducing returns has received little attention beyond anecdotal accounts. On the retailer’s side, some firms are taking measures to reduce returns. For example, L.L. Bean is dropping the liberal return policy that was a key part of its value proposition for decades and Amazon has begun to ban certain shoppers from their site for excessive returns (Dennis 2018, Safdar and Stevens 2018). 1 Firms charge restocking fees and institute other policies that may help reduce returns. However, many firms are reluctant to institute strict return policies because while they may deter returns, they also may dampen sales (Anderson et al. 2009). The marketing literature has already identified many factors that influence returns, including product attributes (e.g., fit issues), purchase attributes (e.g., price, promotion), and retailer attributes (e.g., return policies, large store network) (see Petersen and Kumar 2009 and references therein). The literature, however, has not sufficiently studied factors that influence returns on the manufacturer’s side. On the manufacturer’s side, returns directly affect a firm’s bottom line because they are often not resal- able or must be sold at a lower price or a loss. Also, unlike the case with retailer and purchase attributes, manufacturers have greater control over several aspects of the production characteristics. Thus, improving the production process may lead to better quality, and in turn can help reduce returns, but does not apparently face the trade-off between sales and returns that a retailer faces when it implements a stricter return policy. In order to fill that gap in the literature, the primary objective of this paper is to empirically investigate the impact of production process–related factors on returns. Unlike prior studies focusing on retailers’ return policies and their impact on returns, we study how key operational levers available to manufacturers affect product returns, while controlling for different return policies and numerous product, purchase, and con- sumer attributes. In particular, we investigate the impact of two production variables on returns, viz. worker specialization (on identical or similar tasks) and production workload, both of which have been identified as important factors that influence productivity and quality in the Operations Management (OM) literature. The impact of these production variables is of interest to manufacturers of consumer products with labor- intensive production processes such as apparel and automobile accessories. We also study the impact of product personalization (e.g., embroidering the logo of a buyer’s alma mater in a car seat cover) on product returns because the psychology literature points out that personalization may increase a consumer’s attach- ment to a product (see Mugge et al. 2009 for an experimental study) and because a manufacturer can easily offer such personalization. In fact, personalization is expected to be the prime driver of marketing success 2 within five years (McKinsey 2019). To the best of our knowledge, no empirical study has explored the im- pact of these operational levers on returns. In addition, we include several control variables that have not been considered in prior studies on product returns. To explore the above issues, we collected data from a leading U.S. manufacturer of automotive acces- sories, which primarily sells seat covers, vehicle covers, and dash covers through various online retailers. The company sells products that are tailored to individual vehicle makes and models, and offers them in various fabric types and styles. Given the vast variety of offerings, the firm must manufacture products on a make-to-order basis and aims to ship them to consumers in 1 to 2 weeks. Production of the products re- quires several sewers, so the process design and level of worker specialization are critical issues for the firm. Moreover, due to the make-to-order production, management of workload is important from a production and lead time perspective. Finally, the firm has a very good Enterprise Resource Planning (ERP) system that tracks various aspects of every single item sold from order to delivery as well as possible return, including which sewers have worked on the product. For these reasons, this firm presents a good setting for our study. We study the drivers of return rates using a logistic regression model wherein the dependent variable is the probability of a return. We find that worker specialization is a significant factor that impacts the proba- bility of a return, even after controlling for numerous product, retailer, and purchase attributes. Interestingly, the impact of worker specialization is U-shaped; that is, the probability of a return first decreases over a range of specialization values, and then increases after specialization reaches a certain threshold. We also find that the probability of a return increases with workload, plausibly because higher workload may result in workers rushing and producing more defects. Finally, we find that product personalization in the form of logos reduces the consumer’s propensity to return a product. The effect of personalization on return rates is large and significant, while the effects of specialization and workload are small despite being significant. We demonstrate that the findings are robust by exploring alternative measures for worker specialization and 3 workload, changing some control variables, dropping a subset of the data, and analyzing potential endo- geneity issues. Managers should find our result on personalization interesting because it suggests that manufacturers can reduce product return rates substantially by allowing the customers to personalize the product. In addition, our results suggest that achieving the right level of worker specialization and decreasing workload levels may help reduce return rates, but the effects are relatively small and managers have to take into account the cost implications of their actions. These drivers may be more attractive than strict return policies because they will not dampen sales and may, in fact, increase sales in the long run because of the reputation gained from better quality and personalized product offerings. The remainder of the paper is organized as follows. We first discuss the related literature and highlight our contributions relative to this literature. Then, in section 2.3 we discuss the empirical setting and the data used in our study. In section 1.4, we develop the hypotheses, and discuss the relevant measures and the control variables used. In section 1.5 we discuss the estimation strategy, results, and robustness issues for estimating the return rate. We conclude with a discussion in section 1.6 and provide additional tables and figure in section 4.1. 1.2. Literature Review This study is related to three main streams of literature: (1) research in marketing and information systems on consumer returns, (2) research in OM on returns, (3) empirical studies in OM on the impact of specialization and workload. The literature in marketing on product returns focuses on the influence of consumer, retailer, and product attributes on returns but does not consider the impact of a manufacturer’s production process. Hess and Mayhew (1997) is among the earliest works to empirically study factors that impact returns. They develop 4 a hazard model for explaining and predicting the return rate and time to return using price and importance of fit as covariates and test them on data from a catalog company. They find price to be significant in explaining return rates. Anderson et al. (2006) utilize an economic model of consumer purchase and returns behavior and find support for the perceived value hypothesis, which predicts that consumer return rates increase with the price paid. Anderson et al. (2009) develop a structural model of a consumer’s decision to purchase and return a product, which enables a retailer to both measure the value to consumers of the return option and assess the costs and benefits of different return policies. In an experimental study, Wood (2001) finds that lenient policies do not necessarily increase returns due to the endowment effect. More recently, Janakiramana et.al. (2016) show that overall, return policy leniency increases purchases more than returns. Petersen and Kumar (2009) determine the factors in the firm-consumer exchange process that help explain product return behavior and the consequences of product returns on future consumer and firm behavior. Further, Petersen and Kumar (2015) show that a firm is able to increase both its short- and long-term profits when accounting for the consumer’s perceived risk related to product returns in addition to managing product return costs. Hong and Pavlou (2014) explore the impact of product fit uncertainty and quality uncertainty on product returns and customer satisfaction in online markets; data on returns, product fit and quality uncertainty for this empirical study were obtained from the consumers of major online sites using surveys. In contrast to the aforementioned research, our paper explicitly studies the impact of a manufacturer’s production process to explore how it can use its operational levers to influence the return rate, while control- ling for product, consumer, and retailer characteristics. For instance, unlike the quality uncertainty studied in Hong and Pavlou (2014), our focus is on the impact of operational levers on returns, where those operational levers can impact quality, and we use archival data rather than surveys. The OM literature on product returns is largely analytical in nature with the goal of using models to understand how different dimensions of retailer policies may impact returns—for example, restocking fees (Shulman et al. 2011) and return policies (Su 2009, Altug and Aydinliyim 2016). Lu and Chen (2012) study 5 analytically the impact of product quality and other key variables on a firm’s return policy, including re- stocking fees. They show interestingly that higher product quality need not imply a more generous return policy. Some recent works also conduct empirical studies on returns from the perspective of retailers and consumers. For example, Shang et al. (2017a) study both the return policy drivers from the retailer’s per- spective and the return policy value from the consumer’s perspective, and show that the value of a full refund policy to consumers may not be as large as one might expect. Rao et al. (2004) consider the impact on prod- uct returns of disclosure of inventory availability prior to purchasing products and the post-sale delivery reliability of purchased goods in online retail sales. Mollenkopf et al. (2007) study the impact of the returns management system (web interface, service quality, reverse logistics transactional flow, etc.) upon customer loyalty intentions using surveys of online customers. Griffis et al. (2012) study the relationship between a customer’s experience of product returns, and subsequent shopping behavior using actual purchase and returns history at an online retailer. There is a related stream of literature in OM that studies the value recov- ery from returned products by remanufacturing and issues related to return logistics (see Guide et al. 2006, Pinc ¸e et al. 2016 and references therein). In contrast to the aforementioned research, our study is empirical (not analytical) in nature, focuses on the manufacturer’s (not retailer’s or consumer’s) perspective, and is not concerned with remanufacturing or reverse logistics. Specialization and its impact on productivity have been of interest to managers and researchers for a long time, ever since Adam Smith and Frederick Taylor (Taylor 1911). More recent works have studied other potential benefits and costs of specialization. For example, in the OM literature, Staats and Gino (2012) investigate the effect of specialization in conjunction with variety on short- and long-term worker productivity in the completion of simple, repetitive tasks in a banking operation. To our knowledge, there have been very few studies that have explored the impact of specialization on quality, which could then influence returns. A somewhat related study is KC (2014) which finds that multitasking by physicians in a 6 hospital emergency department results in poorer quality as measured by higher patient readmission rates. Our focus is on the impact of specialization and process design, and not on the impact of multitasking by an individual worker. In our data, we can see, for a product, how many similar tasks each contributing worker has performed in the past, which can be different for different types of products and materials. This allows us to explicitly test for the significance of task-level worker specialization on product returns. There is some empirical work on the impact of product focus (or limited variety) on quality. In early work on the auto assembly operations, Fisher and Ittner (1999) find that greater product variety has a significant adverse impact on minor repair and major rework. More recently, Shah et al. (2017) study the impact of product variety, plant variety, and capacity utilization on product recalls in the auto industry. Neither study explores the impact of task-level worker specialization on product returns. Even if variety is unchanged, specialization levels can vary across workers and over time depending on how tasks are assigned. KC and Terwiesch (2011) examine three distinct levels of the organization (firm, operating unit, and process flow) and find that focus at each of these levels is associated with higher levels of quality. Workload, the second production process variable we study, has received a lot of attention in the OM literature especially in health-care settings. Some examples of recent empirical works include studies on the impact of physician workload on hospital reimbursement (Powell et al. 2012), impact of workload on the service time and patient outcomes in hospital operations (KC and Terwiesch 2009), and impact of work- load on sales and meal duration in a restaurant operation (Tan and Netessine 2014). Unlike these studies, we investigate the impact of workload, in conjunction with task-level worker specialization, and product personalization, on consumer returns. The relatively small effect size of workload in our study is similar to the finding in KC and Terwiesch (2009) that increased workload can result in early patient discharges which results in a small increase in the post-discharge mortality rate. 7 Another important lever that a manufacturer can use to impact return rates is product personalization, which has been shown to increase a consumer’s interest in and attachment to a product according to the consumer psychology literature. Mugge et al. (2009), in an experimental study, find that personalizing a product’s appearance increases the emotional bond with the product from a direct effect (as a result of the extended period of time spent with the product) and an indirect effect (via the personalized product’s self-expressive value). Howard and Kerin (2004) conducted field experiments and find that direct mail per- suasion with a hand-written note with the recipient’s name increased free sample requests when strong brand attributes were used. Our study appears to be the first one to investigate empirically the impact of product personalization on return rates. 1.3. Empirical Setting We first discuss the operational context and process for the study in section 2.3.1 and then describe the data in section 2.3.2. 1.3.1 Operational Context and Process Our data come from a manufacturer of make-to-order automotive accessories (referenced as Company A hereafter). We focus on three distinctly different product types manufactured in the U.S. and shipped to U.S. consumers—vehicle cover, seat cover, and dash cover. After receipt of an order, CompanyA manufactures and ships its products to consumers in around one to two weeks. Due to the nature of make-to-order products, the retailers serve as online sales channels and do not carry any inventory of finished goods. We visited their factory location in California and observed actual operations on multiple occasions between 2015 and 2018. We also met with the management to understand different product manufacturing processes, and how data is recorded in the ERP system. 8 Consumer Ordering Process: A consumer visits an online retailer, finds an automotive accessory that she likes, and submits an order. She needs to know basic information about the vehicle for which she orders the accessory, including make, model, year, and trim level. Once she has input information for her vehicle, she can choose the product she wants and specify fabric type, color, design, and whether to have a per- sonalized logo. Sometimes, a consumer may request multiple products in the same order. After an order is submitted to the retailer, the information is transferred to CompanyA, which manufactures and ships the product to the consumer directly. Manufacturing Process: Order labels are printed in response to customer order arrivals, and contain the detailed product(s) information. The production manager either immediately releases the order to the factory floor, or requests a delay, depending on current workload on the floor. The manufacturing process can be broadly categorized into three stages: pre-sewing, sewing, and post- sewing. The equipment and workers at the three stages are in distinct, demarcated areas of an open factory floor. We provide an overview of each stage next, but discuss process details related to the variables of interest in our study in greater depth in section 3. Afterwards, we discuss in detail work-in-process (WIP), workers, and product defects which could impact returns. The pre-sewing stage starts with printing the order label, which contains detailed instructions for each of the subsequent operations. An employee in charge of cutting fabric picks up the required fabric of certain type and color from raw material inventory based on the order label and then brings the fabric to one of the available computerized cutting machines. She then scans the order label to add the cutting instructions to the machine, which automatically cuts the fabric. Afterwards, she inspects the cut fabric pieces, puts them in a plastic bag with the order label attached, and brings the bag to a common station with bins of cut fabric bundles. From this common station, an employee called a runner picks up the cut fabric bundles and randomly routes them to the individual inbound bins of different sewers. 9 Next, during the sewing stage, the orders are processed by sewers who perform sewing operations such as joining, binding, and embroidery. The sewers are grouped into three different production areas, each dedicated to one of the three product types mentioned earlier. The number of sewers assigned to each area is based upon the demand rate and processing rate for the products. Sewers typically work on the same product type but can be moved to a different product type depending on changes in demand rate or sewer availability. The number of tasks in sewing and the nature of the task vary with the product type. For example, dash covers and vehicle covers may require sewing a few small and large pieces of fabrics respectively, whereas seat covers often require sewing dozens of small pieces. Another source of task variation comes from the materials used which are categorized into three levels of complexity of sewing—low, medium, high in materials codes. We provide the names and descriptions for each task and the product types and material codes on which they can be performed in Table 4.1 in section 4.1. Each sewer has an inbound bin and an outbound bin next to him that can hold a few units. The runner takes the bundles of cut fabric from the central station and places them in the inbound bin of the sewer and takes completed items from the outbound bin to another sewer if it requires additional sewing operations or to the packing stage. The runner assigns orders randomly to the sewers while ensuring that WIP at each sewer within a product pool is similar. Sewing is the most time-consuming and expensive part of the process (sewers are paid more than other workers) and is the bottleneck stage. The firm maintains a workforce level of sewers such that demand generally exceeds capacity so that sewers are always kept busy. In the post-sewing stage, finished goods are packed and moved to the packing/shipping station, then shipped to the consumer. The employees in packing inspect every product for common and easily identified defects which include checking if the sewing is loose, material is damaged, and whether the order label description matches the product. However, this inspection cannot identify issues such as the fit of a car accessory to the vehicle. 10 WIP: There is WIP before the sewing stage, and there is WIP at each of the sewers, as discussed above. The total WIP of cut fabrics by product type before and during sewing can be obtained from the ERP. The post-sewing WIP that accumulates in the packing stage can also be derived from the ERP, but this is small. The WIP at each sewer is not recorded, but it is visible to the sewer. Workers: The workers at the firm are paid on an hourly basis but a worker can also get a bonus based on their individual productivity which is tracked. So, there is some incentive to work faster. While this bonus may be an incentive to produce more output, a stronger incentive appears to be the impression workers make on management based on their productivity and quality. Anyone who performs poorly on a regular basis in terms of productivity and/or quality runs the risk of getting fired. Management strongly believes that every sewer should be skilled at every task and product type. As a result, even though sewers are grouped into specific production areas by product type, any individual sewer may work on a varied set of products and perform a varied set of tasks. To ensure this flexibility, new workers, after a probationary period, typically produce dash or vehicle covers initially, and are then moved (after gaining adequate sewing experience), to seat covers, which are considered the most complex product type in terms of skill required. Product Defects: Defects in the firm’s products can be classified into two broad categories: material defects and production process defects. Examples of material defects include rips, fading over time, color variation, and broken zippers. Material related defects often get identified in-house but there are instances in which this is not true and they are identified by the consumer soon after purchase (color variation) or many months after purchase (faded dash cover). Examples of production-related defects include incorrect assembly, improper sewing, missing straps, and missing holes for a headrest in a seat cover. These defects may occur because a sewer is rushing, fatigued, or inexperienced. Some of these defects cannot be identified during inspection—for instance, (i) a car cover has to be fit on a car to identify that something is wrong or 11 (ii) a missing hole in a seat cover for a headrest may not be identified because not all car seat covers need such holes. However, these defects are identified by a consumer soon after they attempt to use the product. The firm has not historically tracked the reason for returns and associated defects. Returns Handling: A product may be returned within the return period for refund, or beyond the return period for repair or replacement under warranty. All the returns are handled by CompanyA, not the retailers. However, the return policy is set by each retailer and their return policy may have a strong influence on returns. In our data, we are unable to distinguish between returns due to production quality from returns due to non-quality issues (e.g., impulse purchase related returns) because quality is a latent variable and we do not have data on the reason for a return. Return Policy of Retailers: For our analysis, we focus on the thirteen high-volume retailers that account for more than 90% of sales, and obtain their return policies on four common measures: return period, return authorization, restocking fees, and option to return to brick-and-mortar store. Details on the return policies of each of the thirteen retailers are provided in Table 4.2 in section 4.1. Each return policy is based on a contract between each retailer and CompanyA, and none of the policies changed during the study period based on our discussion with the management at CompanyA. 1.3.2 Order Data Description Company A utilizes the Microsoft ERP system to systematically track every operation performed on the order at the various stages that we discussed in the previous subsection, and Table 1.1 provides one example. 12 Table 1.1: A Sample Operational Data Set. OrderNo OrderDate SerialNo ScanDate Retailer ZIP Code y ProductID Material Task Logo EmpID ReturnDate 149038902 5-11-2015 L49325331 5-13-2015 xxx.com 90007 SCxxxx High (Leather) Printing Label USC001 xx01 N.A. 149038902 5-11-2015 L49325331 5-14-2015 xxx.com 90007 SCxxxx High (Leather) Cutting Fabric USC001 xx12 N.A. 149038902 5-11-2015 L49325331 5-15-2015 xxx.com 90007 SCxxxx High (Leather) Joining USC001 xx53 N.A. 149038902 5-11-2015 L49325331 5-15-2015 xxx.com 90007 SCxxxx High (Leather) Binding USC001 xx53 N.A. 149038902 5-11-2015 L49325331 5-18-2015 xxx.com 90007 SCxxxx High (Leather) Webbing Elastic USC001 xx32 N.A. 149038902 5-11-2015 L49325331 5-18-2015 xxx.com 90007 SCxxxx High (Leather) Logo-Embroidery USC001 xx26 N.A. 149038902 5-11-2015 L49325331 5-18-2015 xxx.com 90007 SCxxxx High (Leather) Packing USC001 xx34 N.A. y This column contains 5-digit ZIP Code (ZIP5) for the consumer’s shipping address. The example shows two pre-sewing tasks (printing label, cutting fabric), four sewing tasks (joining, binding, webbing elastic, logo-embroidery), and one post-sewing task (packing) performed on a product with the serial number L49325331 for order number 149038902. We can identify the product type by the first two characters in the ProductID (SC stands for seat cover). The OrderDate column shows that this product was ordered on 5/11/2015 (Monday). In the ScanDate column, we can see that the order label was printed two days later on 5/13/2015 (Wednesday). This implies that the production manager did not immediately release the order into production due to high workload on the floor. On 5-14-2015 (Thursday), an employee read the label to find out which fabrics to pick up from inventory and then cut the fabric in preparation for sewing according to the specification. Sewers are often assigned to perform only a single task on a given product. However, we observe that on 5/15/2015 (Friday), an employee with ID xx53 performed two consecutive sewing operations—joining and binding. On 5/18/2015 (Monday), a different sewer added webbing elastic, and another sewer added a logo through embroidery and finished this product. The order label contains instructions for whether a sewer should perform one task or two or three consecutive tasks, taking into account various order characteristics. Depending on the completion time, this product was shipped to a consumer on the same day or the next day. The “N.A.” value in the ReturnDate column shows that this order was not returned. As discussed, there is a 13 large variability among tasks based on the product type, task names, and materials codes. We provide further details on the tasks in the Table 4.1 in section section 4.1. Our study is restricted to orders placed between 2013 and 2015 for a total of 179,906 products. Out of these, 15,088 were returned by the end of 2015 and 644 more were returned in 2016. These show that the manufacturer in our study experienced an average return rate of 8.74%. The return rate fluctuated by retailer between 4.65% and 12.92%, and varied by product type (9.52% in dash cover, 8.09% in seat cover, 6.40% in vehicle cover). 1.4. Hypotheses and Measures In this section, we develop hypotheses related to the impact on return rates. The literature in marketing and operations has identified numerous factors that influence product return rates and we extend it to include manufacturing related factors that can impact returns. The marketing literature (e.g., Anderson et al. 2009, Petersen and Kumar 2015) adopts the notion that consumer returns are a result of a poor fit between the product and a consumer’s preferences and that fit is not fully observed by the consumer prior to purchase and receipt of the item. The information systems literature (e.g., Pavlou et al. 2007, Hong and Pavlou 2014) has identified product fit uncertainty and quality uncertainty as key drivers of product returns and customer satisfaction for experience goods. This notion is particularly valid in our context for several reasons. First, vehicle accessories are infrequently purchased products, similar to vehicles, so there is uncertainty about the fit and quality. Second, because the firm tries to customize the vehicle accessory to each specific vehicle, fit is especially important to a consumer in this context. Finally, because all the orders are placed online the consumer cannot physically assess the fit or the suitability of the product to their vehicle until after receipt 14 of the item. The manufacturer may be able to influence quality via operational levers but not product fit un- certainty, and so the ability of the manufacturer to influence return rates is unclear from the aforementioned literature, which motivates further study. In some of the OM literature, a similar approach theorizes that consumers return products because of valuation uncertainty, but that consumers can only determine a value, which depends on fit and quality, after receiving the product (e.g., Su 2009, Lu and Chen 2012). This approach adopts the framework that, having purchased a product, a return is more likely when the net value from return is greater than the net value from keeping the product. These net values are in turn impacted by numerous consumer and purchase char- acteristics (including the distribution channel and retailer through which the product is purchased) as well as specific factors that impact the return effort and cost. However, this literature does not explicitly consider the impact of product quality on the consumer’s propensity to return and production process characteristics that in turn influence quality. Our work explicitly considers the impact of production process characteris- tics on returns and also includes several new control variables that may impact return rates so as to reduce unobserved heterogeneity. Understanding the impact of these characteristics is important because the man- ufacturer has little direct control over consumer and purchase characteristics and return effort but does have control over the production processes that impact the quality. The primary dependent variable in our study is the probability of a return—we use this term interchange- ably with return rate—of a specific item purchased. 1.4.1 Factors Impacting Return Rates Figure 1.1 provides a framework that identifies the numerous factors that influence return rates such as consumer, product, and purchase characteristics as well as return effort. These factors may impact the value of keeping the product or returning it or both. The quality of the product influences returns but is a latent 15 variable and cannot be observed directly. Moreover, the impact of quality must be separated from other factors that impact returns. Returns Quality Year and Month Effects Consumer Characteristics Retailer Characteristics and Return Policies (latent variable) Personalization Product, Material, and Order Characteristics Worker Ability, Process Design Worker Specialization, Workload Figure 1.1: Factors Driving Consumer Product Returns. We are interested in variables related to the production process that can influence quality which in turn impacts return rates. This is because identifying which (if any) of these variables are significant potentially allows the manufacturer to design the production process in a way that lowers return rates. We simultane- ously explore the impact of product personalization on return rates. This is because if product personalization has a significant effect, the manufacturer can use this inexpensive lever to reduce return rates by allowing customers to personalize products, because adding personalized logos is not costly. We first discuss the primary variables of interest in section 1.4.2, then the control variables used in the study in section 1.4.3 which include several new measures that control for unobserved consumer hetero- geneity. 1.4.2 Causal Variables of Interest There are several variables in a production process that can impact output quality of a product, thus returns, as identified in Figure 1.1. These include worker specialization, workload levels as well as worker ability, 16 worker quality of work, process design, and quality of materials used. Our objective is to examine the poten- tial impact of two important factors, worker specialization and workload levels, on returns while controlling for other characteristics of the production process. Worker Specialization Specialization and allocation of tasks have a substantial impact on process performance in terms of typi- cal process measures such as process completion time, process quality, and labor productivity. If workers perform the same task or set of tasks repeatedly over time, worker specialization is higher. Such repetition (higher worker specialization) is likely to result in greater productivity due to learning curve benefits, time saved in switching between different tasks, etc. Learning curves and related benefits of specialization have been studied extensively in the context of productivity (Argote and Epple 1990, Narayanan et al. 2009, Staats and Gino 2012). However, to the best of our knowledge, the impact of specialization on output quality has been relatively unexplored. For example, Staats and Gino (2012) discuss in great detail the benefits and costs of specializa- tion and find evidence in the context of mortgage loan processing operation that worker specialization helps improve short-term worker productivity but workers doing a variety of tasks helps improve longer-term pro- ductivity. Still they do not address the issue of quality of output. Some have argued that similar benefits of specialization also extend to quality (Argote and Epple 1990, Compton et al. 1992, Jeang 2015) but such benefits have not been empirically validated. Note that excessive specialization and repetition of the same tasks over long periods of time may also lead to boredom and dissatisfaction resulting in lower productivity (Foley 2008) and quality (Ramdas et al. 2018). Hence, it appears that too much worker specialization can impair productivity and quality. Thus, by linking the literature on the impact of worker specialization on productivity and quality with consumer product returns, we formulate our first hypothesis as below: 17 Hypothesis 1. The effect of Worker Specialization on the return rate is U-shaped. The notion of share-based measures of specialization is well known in the economics, healthcare, and OM literature (Peri and Sparber 2009, Sahni et al. 2016, Narayanan et al. 2009, KC and Staats 2012). In the following, we develop two types of share-based measures for Worker Specialization which examines the effect of prior experience on the same and different tasks. Since multiple sewers are involved in the processing of an order, we need to measure specialization for the group of workers who processed an order. LetN i denote the set of sewers that worked on orderi. Therefore, the Worker Specialization associated with orderi should incorporate the specialization of all the workers inN i . Our primary measure is similar to Sahni et al. (2016) and is defined as the ratio of the total number of same tasks to the total number of tasks (same + different) during time windowt (just prior to the date of working on order i) performed by all the workers belonging to the set N i . In the computation of this measure, a task performed on orderi is considered to be same as a previously performed task by a worker if the type of task (one of thirteen types as in Table 4.1 in section 4.1 and the material code (one of three types) and the product type are identical. Otherwise, they are considered to be different. Mathematically, this can be expressed as P j2N i ns jt /( P j2N i ns jt + P j2N i nd jt ) wherens jt andnd jt are, respectively, the number of same and different tasks performed by workerj during time windowt (we consider several values fort). For example, suppose an order requires two workers andt = 4 weeks, and we know from the ERP system that worker 1 (2) performed 10 (30) same tasks and 10 (20) different tasks over the past 4 weeks. Then, the Worker Specialization value pertaining to this order is (10+30)/(10+30+10+20) = 4/7, which represents an average specialization across the set of workers who process orderi. Notice that this measure satisfies three properties: (1) The value of this measure is 0 when no worker has performed the same task(s) in the past. (2) It is equal to 100% when all the workers have performed only the same task(s) in the past and not worked on any other task. (3) It increases as the proportion of the same tasks to total tasks performed by the set of 18 workers for this order increases. Note that the sequence in which tasks were performed, whether same or different, by a worker is not relevant. This is because orders are assigned randomly to workers, as discussed earlier, and so the sequence in which workers perform tasks is random. Our alternative measure of Worker Specialization, which also satisfies the above three properties, is adapted from the Herfindahl-Hirschman Index (HHI) which has a long history in measuring market con- centration (Rhoades 1993). Similar measures based on HHI were used in Narayanan et al. (2009), KC and Staats (2012). In particular, we use the following measure: P j2N i ( ns jt ns jt +nd jt ) 2 =jN i j wherens jt andnd jt are as defined above andjN i j denotes the cardinality ofN i . This measure is similar to the primary measure described earlier except that we square the proportion of same tasks to all tasks for each worker before averaging across the set of workers who process orderi. Workload Workload levels, which are influenced by the production manager who releases orders to the factory floor, can have a substantial impact on productivity and quality. KC and Terwiesch (2009) cite literature that pro- vides evidence of productivity declining with increasing workload due to fatigue. They also provide evidence that mortality rates increase with increasing workload in cardio-thoracic surgery units. In our context, there is reason to believe that workload levels impact quality of output in sewing. The bins, in which the bundled pieces for various orders in process are placed, represent the work-in-process inventories and are visible to the sewers. Based on prior research, the visible queues are likely to impact the speed at which the sewers work and hence the quality of their work. Unlike the hospital setting in KC and Terwiesch (2009), the work- ers may be more careless in our setting because their actions do not have “life-and-death” consequences. Thus, we formulate the second hypothesis as follows: Hypothesis 2. Higher workload leads to higher return rates. 19 The primary measure we consider for Workload is the product type specific total WIP across all stages of production. We consider total WIP because WIP, independent of where it may accumulate, may influence the speed of work of the workers, which in turn impacts quality. For instance, WIP before sewing may impact quality of work of sewers while WIP before packing (after sewing) may impact quality of work in packing/inspection. One unit of WIP is one order. Suppose orderi is for product typep: Then, we compute the average work-in-process (WIP ip ) in the system for product typep during the period in which orderi is processed (during the production lead time of orderi). This is a good measure for Workload because, as discussed earlier, the WIP is visible to the workers and is likely to influence their speed and quality. We also consider the WIP at only the sewing stage, which includes WIP in the central bin and all the WIP at individual bins, as part of the robustness tests. We considered this measure because sewing is the most labor-intensive stage of production and sewers are more likely to be influenced by WIP than other workers. KC and Terwiesch (2009), in a different setting, divide the WIP by the number of resources (beds or transporters) available in the system. In our case, this would be equivalent to dividing by the number of sewers. However, the sewers in our setting may be assigned tasks for different product types based on not only Workload levels for each product type but also the task and product types for which they have the requisite skill. As such, it is not possible to measure the number of sewers by each product type and obtain a Workload measure based on average WIP divided by average number of sewers at the product type level. However, we can consider a Workload measure at the aggregate level that considers WIP divided by number of sewers across all product types, i.e. (WIP i =Sewers i ). We consider this alternative measure in the robustness check. 20 Personalization The words customization and personalization are often used interchangeably, however there is a subtle difference between these two terms in our setting. Through customization, a consumer may choose the fabric type, color, and other products for their specific vehicle accessory. On the other hand, personalization takes this idea a step further by offering the consumer an option to add a personalized logo (e.g., a special message of congratulations on one’s birthday, the mascot of one’s alma mater.) The literature has suggested a positive psychological effect of such personalization based on experimental work: a consumer is more likely to be emotionally attached to a personalized product (Mugge et al. 2009) and more likely to request free samples (Howard and Kerin 2004). We study whether such an effect leads to lower consumer returns empirically and formulate our third hypothesis as follows: Hypothesis 3. Product personalization leads to lower return rate. We measure Personalization of an order using a binary variable (an order requires a logo or not). 1.4.3 Control Variables The control variables included in our study can be classified into various categories using the framework in Figure 1.1, and we discuss each category as follows. Product, Material, and Order Characteristics. Product type is an important variable that can influence return rates both directly due to fit issues as well as indirectly through quality of output. In a study of an online retailer, Anderson et al. (2009) show variations in returns among different product categories. The extent of fit between a product and a consumer’s preference is likely to be better realized only after purchase for certain products, resulting in differences in return rates across products. Moreover, the importance of fit and uncertainty in fit varies across products (Hess and Mayhew 1997). In our context, there are three major 21 product types as discussed earlier. A slightly larger vehicle cover may be acceptable to a consumer, but a slightly loose seat cover may be regarded as unacceptable and returned. Seat covers cost much more than dash covers, so a consumer is more likely to go through the trouble of returning seat covers. In addition, the quality of output may differ across products due to differences in product type, process design, and process complexity, and this in turn may result in differences in return rates. We also categorize vehicles into twenty-five granular categories (e.g., sedan, coupe, sports utility vehicle) and control for vehicle type since the production process as well as the propensity to return may depend on this variable. Moreover, a consumer may customize a product by specifying the fabric type. The fabric type may impact the quality of output because the production process is more complex for some fabrics. Also, there are differences in wear and tear among different fabric types. So, within each product type, we control for fabric type using material codes. The company uses three codes—low, medium, and high to categorize materials, which takes into consideration the complexity of processing the fabrics. For example, the material code high includes leather, which is used to make premium seat covers and is more difficult to process due to its thickness and the nature of leather. While Anderson et al. (2009) do not find that return rates are affected significantly by whether a cus- tomer purchased one or multiple items in their order, they suggest that in other applications there may be a significant effect. In this study, about 18.7% of products are sold as part of an order with two or three items. Thus, we utilize the variable order size to control for this effect. Consumer Characteristics. Consumer characteristics are likely to impact return rates as discussed in Anderson et al. (2009) and Su (2009). We do not have data on the individual consumers but we do know their 5-digit zip codes. The absence of data on individual consumer variables is not a limitation in our context because most consumers purchase vehicle accessories infrequently and are likely to have purchased at most once during the study period. We control for several consumer attributes at the zip code level, 22 such as household income and household size, which have been used as control variables in Anderson et al. (2009). In addition, we consider several other control variables at the 5-digit zip code level such as population density (see details in Table 4.3 in section 4.1). All these variables by 5-digit zip code are obtained from the SimplyAnalytics database (http://simplyanalytics.com/), and together they capture a comprehensive set of demographic and socioeconomic attributes of consumers by 5-digit zip code. This has two advantages: First, it controls for various consumer attributes that may influence return rates and thus reduce unobserved heterogeneity. Second, including these control variables helps in eliminating, or at least substantially reducing, endogeneity in estimating the impact of personalization, which will be discussed later in detail in section 1.5.2. The comprehensive set of consumer attributes we include control for unobserved consumer characteristics that may be correlated with both the personalization measure and return rate. In addition to the consumer characteristics at the 5-digit zip code level, we also added the 3-digit zip code (first 3 digits) of an order as an additional fixed effect control. This measure controls for factors such as weather and presence/influence of a university, college, or sports team near the consumer’s location. These attributes are likely to be homogeneous within a 3-digit zip code boundary. Return rates may depend upon weather because of weather-related effects on the wear and tear of a product during its warranty period, which in turn impacts the return rate. The presence of a university, college, or sports team may influence the propensity to personalize an order. Other Production Process Characteristics. The key production process characteristics, Worker Spe- cialization, and Workload have been discussed earlier in section 1.4.2, and section 1.4.2 respectively. There are other factors that might influence output quality—sewer ability, and process design—which are dis- cussed next. Because these characteristics are likely to be correlated with the variables of interest and also influence return rates, we include them as control variables. Sewer Ability: According to company management, quality of output depends on the ability of sewers. 23 (a) Sewer Tenure: Sewing is a process that requires a lot of skill and it takes about two months for a sewer to achieve the skill level required to achieve an acceptable level of quality and productivity. The sewers are observed closely during their initial two-month probationary period and are asked to leave if they do not achieve acceptable performance. We do not include any orders processed by the sewers during the probationary period. As the sewer acquires more experience, he may get better over time. Therefore, we use employee tenure as a proxy for worker ability, which cannot be observed directly. Since multiple sewers are involved in the production of a product, we use the average tenure of all the sewers who produced a specific order. The average tenure is a good measure if the workers communicate among each other and more experienced workers help the less experienced ones. But the quality of work may depend upon the least experienced worker, especially if communication and cooperation are minimal. While we believe there is communication and cooperation among sewers at the focal firm, we do not know the extent of it, so we also tested an alternative measure as part of the robustness check: the minimum tenure of the sewers producing a specific order. While the order data used in the study is from 2013, we have information on their tenure with the firm from 2007. So, we used the employee’s start date prior to 2013 to calculate each sewer’s tenure with the company. The other processes such as cutting and packing do not require much skill or training. (b) Sewer Quality of Work: In addition to sewer ability measured by their tenure, we include another control variable to account for a sewer’s historical quality of work. In particular, supposeN i is the set of workers who work on orderi. We compute the average return rate of the workers in the setN i for all orders processed during time windowt (just prior to the date of working on orderi), for example,t = 28. To do this, for each employee inN i , we measure how many orders she processed in the time windowt and how many of those orders were returned, and derive her return rate by dividing the number of returns by the number of orders. Next, we obtain the average return rate of all the workers inN i . This variable captures the past quality of the work performed by the workers as measured by its impact on return rate. We primarily consider t = 28, but we also considered different values of t to account for the quality of work in the 24 past 2 weeks to 3 months as part of our robustness analysis. Additionally, the quality of an order may be determined by the worker with the worst quality performance or equivalently, the worker with the highest return rate among the workers producing an order. So, we also considered the maximum return rate of the set of workers producing an order as part of the robustness checks. Process Design: The process design for the sewing stage requires a specified number of steps for each product type and a sewer may complete one or more of the steps in the process for an order. So, the number of sewers who work on a specific order can vary. The number of sewers and number of sewing steps in processing an order can have an impact on the quality, especially given that the skill levels of the sewers is not homogeneous. Moreover, it also can influence the tasks performed by the sewer over time and therefore impact the variable Worker Specialization. Therefore, we control for this factor by including a variable called Process Design, which is measured as the number of sewers who worked on orderi divided by the number of sewing steps specified in the process design for orderi. The maximum value of Process Design is therefore 100 (unit: %), which represents a scenario wherein one sewer performs exactly one step in the process design. The value of Process Design is less than 100 when one sewer performs more than one step in the process. Typically, a sewer completes one step in the process but sometimes the sewer performs two consecutive steps (and occasionally three steps) as we showed in the example in Table 1.1. Suppose the process design called for four sewing steps and three sewers completed these four steps, then the Process Design value is 3 4 100 = 75. Retailer Characteristics. Based on previous research on the impact of return policies on sales and returns (Wood 2001, Janakiramana et.al. 2016 and references therein), the primary retailer attributes that we include are their return policies, which may vary along several dimensions. Below, we discuss the specific dimensions of a retailer’s return policies that are used as control variables. All the measures identified below are proxies for the return effort or cost incurred by the consumer. 25 Return Period: This measure represents the time window within which a product has to be returned for a refund or replacement for any reason. This window is not applicable for products that are returned because they are found to be defective by the consumer. In that case, the product can be returned at any time during its one-year warranty period but can only be replaced or repaired rather than refunded. In our study, nine retailers impose a 30-day return period, one allows 90 days, and three do not set a maximum return period. Restocking Fee: Some retailers charge a restocking fee, which is a percentage of the item purchase price, and this fee varies across retailers. A higher restocking fee represents a higher return cost to the consumer. The restocking cost percentage depends only on the retailer and does not vary with product type, material, or personalization. Return Authorization: Some retailers require a return authorization by calling their customer service or by using their online system before an item can be returned. We have a binary variable to capture whether return authorization is required or not. Another metric to measure the return policy is whether the retailer allows the consumer to return the product to their brick-and-mortar stores. We do not use this measure because it is highly correlated with the return period in our data set. Specifically, we find that retailers with a lenient return period (90 days and unlimited) are the only ones that allow in-store returns. In the main analysis, for return period we aggregate “30 days” and “90 days” into one category “limited”, and for return authorization we group “required via calling consumer service” and “required via online system” into one category “required”. In the robustness check, we use the uncompressed values for both variables. For further details, please refer to the summary of return policies of the thirteen online retailers in our study in Table 4.2 in section 4.1. While return policies are indeed important for explaining return rates, there may be other crucial factors associated with a retailer that influence returns. For example, unlike in experimental studies (e.g., Wood 26 2001), in our observational study, retailers with different return policies may attract different types of con- sumers who exhibit different return behaviors. Also, there may be other characteristics of a retailer (e.g., store locations, product lines carried, reputation, brand image) that may influence orders as well as return rates. Thus, we also consider retailer fixed effects as part of the robustness tests presented in section 1.5.4. Time Fixed Effects. Similar to Anderson et al. (2009) we include fixed effects for both year and month to capture seasonality in return rates as well as any idiosyncratic factors that may have influenced return rates in a given year. The monthly fixed effects capture factors such as consumers purchasing products more impulsively during holiday seasons or a product fading during the summer heat resulting in higher return rates. Time fixed effects also control for occasional free-shipping promotions. Based on our discussion with the manufacturer and retailers in our study, there were no price promotional sales (e.g., 50% off). 1.5. Return Rate Estimation and Results In this section, we first discuss the models to estimate the effects of the causal variables of interest and summary statistics in section 1.5.1, then discuss potential endogeneity issues in section 1.5.2, present the estimation results in section 1.5.3, and provide various robustness checks in section 1.5.4. 1.5.1 Estimation Strategy The dependent variable is the probability of a return, represented as Pr(Return i ) for orderi (when there are multiple orders within one order, we treat them separately). We estimate the following model (1.1) 27 that includes all three causal variables of interest—Worker Specialization, Workload, and Personalization— along with the control variables discussed earlier, represented by the vectorX. logit[Pr(Return i )] = 0 + 1 WorkerSpecialization i + 2 WorkerSpecialization 2 i + 3 Workload i + 4 Personalization i +X i 5 (1.1) To test Hypothesis 1 that the effect of Worker Specialization on return rates is U-shaped, we consider 1 and 2 in (1.1). Specifically, a negative value of 1 and a positive value of 2 suggest that as Worker Specialization increases untilmaxf 1 2 2 ;100g, the probability of a return decreases. Afterwards, as Worker Specialization continues to increase, the probability of a return starts to increase, which would support Hypothesis 1. This is because a quadratic function f(x) = ax 2 +bx +c given a > 0;b < 0 is convex and achieves its minimum at the positive critical point b 2a , and also because Worker Specialization does not exceed 100 (unit: %). To test Hypothesis 2, we use WIP as a measure of Workload as we discussed in section 1.4.2. A positive value of 3 supports hypothesis 2, that is, higher Workload leads to higher return rates. Personalization i is a dummy variable with 1 denoting the presence of a personalized logo. A negative value of 4 supports Hypothesis 3, suggesting that personalization of an order leads to a lower return rate. Summary Statistics We now provide summary statistics for the causal variables and some key control variables. To reduce the influence of outliers, for the continuous causal and control variables, we first winsorized the bottom and top 2% of the raw data prior to the subsequent analyses (see a discussion on winsorization in section 14 in Tukey 28 1962). The following summary statistics in Table 1.2 and correlation matrix in Table 1.3 of key production related variables are based on the winsorized data used for the analyses. Table 1.2: Summary Statistics of Production Related Variables Independent variable Mean Std Dev Min Max Worker Specialization (unit: %) Team y Average (past 4 weeks) 51.9 17.7 10.4 78.6 Team Average (past 3 months) 51.3 17.6 10.9 77.6 Workload (unit: 100 products) WIP (all stages) 6.1 4.1 1.3 17.4 WIP (sewing stage) 5.0 1.9 1.3 11.0 Worker Experience and Quality Team Average Tenure (unit: month) 62.9 17.2 25.2 95.3 Team Average Return Rate (unit: %, past 4 weeks) 6.5 1.9 2.7 11.3 Team Average Return Rate (unit: %, past 3 months) 6.5 1.6 3.1 9.6 Process Design (unit: %) 95.6 9.4 71.4 100.0 y We use the term team loosely to denote the set of sewers who worked on the product. There is no fixed team or assembly line as we explained in the manufacturing process in section 2.3.1. Table 1.3: Correlation Matrix of Production Related Variables 1 2 3 4 5 6 7 8 1. Worker Specialization (Team Average, past 4 weeks) 1.00 2. Worker Specialization (Team Average, past 3 months) 0.97 1.00 3. Workload (WIP, all stages) 0.03 0.04 1.00 4. Workload (WIP, sewing stages) 0.08 0.08 0.66 1.00 5. Team Average Tenure 0.03 0.02 0.37 0.15 1.00 6. Team Average Return Rate (past 4 weeks) 0.04 0.03 0.27 0.22 0.11 1.00 7. Team Average Return Rate (past 3 months) 0.04 0.04 0.29 0.26 0.13 0.83 1.00 8. Process Design z 0.41 0.41 0.26 0.05 0.30 0.22 0.26 1.00 Note: All correlations are significant at the 0.001 level. z See the discussion of variable inflation factor (VIF). We derived measures of Worker Specialization and Worker Return Rate for different time windows from t = 1 week to 6 months, and then derived the team average measures as we discussed in section 1.4.2 and section 1.4.3. Note that we use the term team loosely to denote the set of sewers who worked on the product. There is no fixed team or assembly line as we explained in the manufacturing process in section 2.3.1. 29 Not surprisingly, there was a high correlation between measures across differentt values, for example, the correlation between Worker Specialization (Team Average, past 4 weeks) and Worker Specialization (Team Average, past 3 months) is 0.97. To be concise, we provide summary statistics for the past 4 weeks and 3 months in Table 1.2, and uset = 4 weeks andt = 3 months in the main analyses, and uset = 1 week to6 months as robustness checks. The measure of Workload, the WIP specific to the product type at all stages during the production of an order, had a mean value 6.1 (unit: 100 products), whereas the corresponding sewing stage WIP had a mean value 5.0 which is about 82% of WIP from all stages. Notice the control variable Process Design has a 0.41 correlation with the causal variable Worker Specialization, but its small value of VIF = 1.50 does not indicate an issue with multicollinearity. To check for the robustness of the results, we run the analyses with and without controlling for this variable. The VIF values for the other variables shown in Table 1.3 fall in the range between 1.14 and 2.18 and so multicollinearity is not an issue. The proportion of products with Personalization is 2.8%. Details on the proportion of sales by product type, material code, vehicle type, order size, and return period are provided under “Summary statistics of categorical variables” in section 4.1. 1.5.2 Endogeneity Issues This study includes the main production related covariates that may potentially influence return rates. More- over, we have included numerous control variables that may impact return rates, as discussed earlier, to minimize potential sources of unobserved heterogeneity. We discuss potential econometric issues with the estimation of the model and steps taken to address them next. 30 Worker Specialization As discussed in section 2.3.1 and section 1.4.2, work is randomly assigned to workers (this is observed on the production floor and also confirmed in the data). This allows us to estimate the impact of Worker Spe- cialization on return rates with minimal bias, if any. Recall from our earlier discussion that while sewers are generally assigned to specific product types, the actual tasks they perform for that product type are randomly assigned to them. Moreover, even if sewers are reassigned to a different product type based on workload lev- els and their ability to perform the tasks, the actual tasks assigned to them are random. However, while the explicit assignment of work is random, we should consider potential omitted variable bias based on implicit factors. For instance, more capable employees may produce better quality and thus achieve lower return rates but their ability is not observable. Such employees may also produce more and hence get assigned more work. However, this does not necessarily induce bias in the estimation of Worker Specialization be- cause even if more work is assigned, the assignment of tasks is random. Return rates do not impact Worker Specialization either, also because of the random assignment of tasks, thus there is no reverse causality issue. Workload Generally speaking, production managers and floor supervisors in manufacturing firms may influence work- load levels as well as task assignments, but their influence may not be observable. However, the focal firm in our study operated one shift at the California facility during the period of this study and there was only one production manager and one floor supervisor. Hence, there is no potential bias in our estimation due to the management. Omitted variable bias: When workload is higher, more capable workers may get assigned more work and thus produce a greater proportion of output. They may also produce better quality which leads to lower return rates. Thus, without controlling for worker ability, the effect of Workload is confounded. Hence, we 31 have to control for the ability of workers to better identify the impact of Workload. To do this, we use Sewer Tenure and Sewer Quality of Work discussed in section 1.4.3 to eliminate potential estimation bias due to sewer ability. In particular, as part of the robustness tests, we control for the SewerTenure and Sewer Quality of Work of every sewer who works on an order and not just the average values of the team. Finally, we also minimize the potential for omitted variables bias due to process related factors by using the control variable Process Design discussed in section 1.4.3. Reverse causality: Another potential source of estimation bias may be due to reverse causality. Reverse causality can lead to the error term being correlated with the independent variables and can result in biased and inconsistent estimates of the parameters. Can return rates impact the variable Workload in our study? Specifically, suppose there are many returns in a particular period. Is it possible that this may impact and thus bias the estimation of the Workload on return rates? We think this is unlikely for the following reason. Return rates are only around 8% and only about 5 to 10% of the returned items are reworked or replaced. In fact, we find in the data that rework on average represents less than 0.2% of WIP. Instrumental variables: Even though estimation bias is not very likely as discussed above, we use two instrumental variables to address potential bias. First, we instrument workload using lagged values of WIP. Recalling that we use WIP as a measure of Workload, for any order i, we consider the WIP on the date two weeks prior to the production start date of order i as the lagged value of WIP or Lagged WIP. This is a relevant instrument because Lagged WIP is likely to be correlated with current period WIP for orderi because WIP levels change slowly. The level of WIP depends upon the release of orders into production and the production rate. The production rate cannot be changed easily for the reasons mentioned in section 2. This instrument also satisfies the exogeneity condition because the return rate of orderi will not be impacted by Lagged WIP, except through its effect on current WIP. The second instrumental variable we use is the volume of orders received but not released into production on the production start date of orderi. This Order 32 Volume is likely to be correlated with WIP, but should not directly impact the return rate of orderi except through its impact on WIP. Therefore, it satisfies the relevance and exclusion criteria. Personalization Because the decision to order a personalized logo is made by the consumer before making the return deci- sion, there is no reverse causality issues due to return rates on the Personalization variable. However, there might be endogeneity in the estimation of Personalization because consumers who select to personalize their products may have different characteristics (unknown to the researcher) than those who don’t and these may be correlated with the propensity to return a product. Hence, there is potential for selection bias, since we do not know if a personalized order came from consumers who are more likely to personalize or not. To address this endogeneity, we have controlled for a comprehensive set of socio- economic and demographic characteristics as discussed earlier in section 1.4.3. In addition, we explore two different approaches to address this selection bias as discussed next. Estimation of intent to personalize: We include a proxy variable to estimate and capture this effect. For each orderi, we compute the proportion of orders from the same ZIP3 that were personalized during the period from July 2012 until the week prior to the order date to derive a proxy variable, Intent To Personalize. This is a good proxy for the propensity to personalize by consumers as it uses the past history of personal- ization as a predictor of future intent to personalize (see Bucklin et al. 1998 for a similar approach to capture brand loyalty). The reason we consider ZIP3 rather than ZIP5 level to compute Intent To Personalize is that the order volume at ZIP5 level is much smaller with many ZIP Codes having zero or a few orders and so this measure can vary widely (from 0 to 100%) which yields an imprecise measure. For the same reason, we do not consider ZIP3 with less than 8 orders in the study period (bottom 10% at ZIP3 level). This leads to a small reduction in our data size from 179,906 to 172,284. 33 Instrumental variable: We use an instrumental variable for Personalization, Lagged Sewing Hours, as explained below. Products that are Personalized typically require more time for sewing, which includes all sewing tasks including embroidery. In our data, the mean time spent in sewing was 1.37 hours for non- personalized products and 1.53 hours for personlized products and the difference is statistically significant. Hence the time spent in sewing (we discuss how we measure this variable and discuss the associated chal- lenges in section 4.1), referred to as Sewing Hours henceforth, is a relevant instrument for Personalization. It is also reasonable to assume that Sewing Hours is unrelated to any omitted consumer characteristics that might impact returns. However, orders with longer Sewing Hours might lead to a higher quality and thus a lower return rate. For this reason, we consider Lagged Sewing Hours measured as the sewing time of the previous order which has the same product and material code and personalization option (binary). We use this new measure as an instrumental variable for each order. It is a relevant instrument because (1) it is correlated with the sewing time of the current order by construction, and (2) the sewing time of an order is correlated with Personalization. It meets the exclusion criterion because (1) the sewing time of the previous order should not directly impact the return rate of the current order, and (2) it is not likely to be correlated with any omitted consumer characteristics which may impact the decision to personalize. Promotion: Based on our discussion with the manufacturer and retailers in our study, there were no price promotional sales (e.g., 50% off) but the firm ran occasional free-shipping promotions which might have slightly influenced the orders received for certain products, and in turn influenced Worker Specialization and Workload as well as the return rates. We address this issue by controlling for time fixed effects (year and month), retailer fixed effect, and product fixed effects which together help control for the promotional effect. 34 1.5.3 Results The results from estimating equation (1.1) and variants to it, to test for robustness, are provided in Table 1.4 and we discuss them in detail next. Models 1 and 2 in Table 1.4 refer to the estimates of (1.1) with the only difference between them being that Model 1 uses the three dimensions of retailer return policies— Return Period, Return Authorization, and Restocking fees (described under Retailer Characteristics in sec- tion 3.3)—as control variables while Model 2 uses retailer fixed effects instead. We consider a model specification with retailer fixed effects because retailers may differ along several dimensions other than return policies and this is captured by retailer fixed effects. We find that the changes between Model 1 and Model 2 in the estimates of 1 , 2 , 3 , and 4 are within 0.6 times the standard error. Since the retailer fixed effects control for return policies as well as for other potential differences among retailers, we use retailer fixed effects in most of the remaining model specifications. We see that 1 < 0; 2 > 0 in both models 1 and 2, which together support Hypothesis 1 that the effect of Worker Specialization on return rates is U-shaped. When workers perform the same task repeatedly, it results in better quality but too much repetition results in quality degradation. The ratio 1 2 2 in both models 1 and 2 is around 57 (unit: %), suggesting that the probability of return reaches the minimum value when workers perform the same task around 57% of the time. We further find that the effect of Worker Special- ization is not significantly different when it ranges between 53 and 61. The marginal effect is significantly negative to the left of 53, and positive to the right of 61. For example, when we break down Worker Spe- cialization into ten segments each containing the same size of observations, the average marginal effect on the probability of a return is0:15% in the first segment (from 10.4 to 20.2), and 0.10% in the last segment (from 73.0 to 78.6). We provide the details of the average marginal effects in 10 segments in Table 4.4 and illustrate them in Figure 4.1 in section 4.1. 35 Table 1.4: Effect of Worker Specialization, Workload and Personalization on Return Rate y Model 1 Model 2 Model 2a z Model 2b z Model 2c z Hypothesis 1: Worker Specialization TeamAverage (past 4 weeks) 0.0218 *** 0.0240 *** 0.0287 *** 0.0241 *** (0.0036) (0.0036) (0.0034) (0.0036) TeamAverage 2 (past 4 weeks) 0.00019 *** 0.00021 *** 0.00026 *** 0.00020 *** (0.00004) (0.00004) (0.00003) (0.00004) TeamAverage (past 3 months) 0.0276 *** (0.0038) TeamAverage 2 (past 3 months) 0.00025 *** (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0219 *** 0.0207 *** 0.0193 *** 0.0250 *** (0.0035) (0.0036) (0.0036) (0.0035) WIP (sewing stage) 0.0271 *** (0.0064) Hypothesis 3: Personalization (yes vs. no) 0.2410 *** 0.2808 *** 0.2804 *** 0.2964 *** 0.2910 *** (0.0624) (0.0628) (0.0628) (0.0632) (0.0628) Controls Product and Order Characteristics Included Included Included Included Included Product and Material (fixed effect) Vehicle Type (fixed effect) Order Size (fixed effect) Process Design 0.0113 *** 0.0106 *** 0.0107 *** 0.0116 *** Not Included (0.0013) (0.0013) (0.0013) (0.0013) Worker Experience and Quality Team Average Tenure 0.0029 *** 0.0027 ** 0.0023 ** 0.0024 ** 0.0028 *** (0.0008) (0.0008) (0.0008) (0.0009) (0.0008) Team Average Return Rate (past 4 weeks) 5.6282 *** 5.6017 *** 5.5649 *** 5.5865 *** 6.0765 *** (0.7038) (0.7044) (0.7044) (0.7082) (0.7036) Retailer Characteristics Return Period 0.6908 *** (limited vs. unlimited) (0.0346) Return Authorization 0.1706 *** (required vs. not required) (0.0328) Restocking Fee% 0.0134 *** (0.0018) Retailer Fixed Effect Not Included Included Included Included Included Consumer SocioEconomic and Included Included Included Included Included Demographic Characterstics at ZIP5 3 Digit Zip Code (ZIP3) (fixed effect) Included Included Included Included Included Seasonality (year and month fixed effect) Included Included Included Included Included Likelihood Ratio ( 2 ) 4,923.2 *** 5,061.8 *** 5,070.6 *** 5,028.9 *** 4,991.6 *** AIC 103,712.6 103,592.1 103,583.3 102,500.9 103,660.2 N (data size) 179,906 179,906 179,906 179,906 179,906 y Logit coefficients are provided. Standard errors are shown in parentheses. p-value0:001; p-value0:01. To be concise, coefficients of control variables with more than 3 categories are omitted, but available from authors. z Models 2a, 2b, 2c are variants of Model 2 by changing the time window (from past 4 weeks to 3 months) when measuring Worker Specialization, changing WIP from including all stages to sewing stage only, and excluding Process Design from control variables, respectively. 36 We can see in models 1 and 2 that 3 > 0, supporting hypothesis 2. Moreover, 3 = 0:0207 in model 2 implies that as Workload increases by 1 (unit: 100 orders), the odds ratio of return increases bye 3 1 = 2:09%. On the other hand, if management reduces WIP by 1 by releasing fewer products into production, the odds ratio of return is reduced by 1e 3 = 2:05%. We can further compute the average marginal effect of Workload on the probability of a return to be 0.2% for each unit increase. We also find 4 < 0 from models 1 and 2 suggesting that product personalization leads to a substantial decrease in the odds ratio of return by 1e 4 = 21:42% in model 1 and 24:48% in model 2. We find that the average marginal effect of Personalization on the probability of a return is2:4%. So, personalized products are far less likely to be returned. The return policies of retailers have a substantial impact on return rates as expected and the impact is consistently significant. For example, in Model 1 the limited return period reduces the odds ratio of returns by 1e 0:6908 = 49:88%; when a consumer is required to obtain return authorization, the odds ratio of returns is reduced by1e 0:1706 = 15:68%; and 1% increase in restocking fees (e.g., 15% to 16%) leads to 1e 0:0134 = 1:33% reduction in the odds ratio of returns. In terms of average marginal effects on the probability of a return, limited return period, return authorization requirement, and restocking fees are 4:2%;1:2%;and0:1% respectively. A limited return period has a stronger effect in reducing returns than Personalization, the operational lever under the manufacturer’s control. However, we want to point out that many retailers are reluctant to institute strict return policies since they may dampen sales. In the following, we investigate alternative measures of the causal variables, Worker Specialization and Workload discussed in section 1.4.2, and section 1.4.2 respectively. Different time windows in Worker Specialization: Recall from section 1.4.2 that we defined Worker Specialization for orderi as the ratio of the total number of same tasks to the total number of tasks (same + different) during time windowt (prior to the date of working on orderi) performed by all the workers 37 that worked on orderi. In Model 2 in Table 1.4, the measure of Worker Specialization considers the prior 4 weeks in computing the percentage of tasks that are the same tasks out of all possible tasks performed by the set of workers processing an order. In Model 2a, we consider the prior 3 months (i.e.,t = 3 months instead of 4 weeks) in the definition of the measure. From the results of Model 2a, it is clear the effect of Worker Specialization on the return rate continues to be significant and U-shaped (Hypothesis 1) and the coefficient estimates are similar to those in Model 2. The effect of Workload continues to be significant and similar, although a bit weaker. The effect of Personalization also remained similar. In fact, we used differentt values between 1 week to 4 weeks and 1 month (30 days) to 6 months for the Worker Specialization measure. We find small changes in the coefficient of Worker Specialization as the time period is varied, but we do not find a statistically significant difference in different time periods (see Table 4.5 in section 4.1). Worker Specialization based on HHI: We also explored this alternative measure for Worker Special- ization for the time windows between the past 1 week and 6 months and continued to find support for Hypothesis 1. As expected, the magnitude of linear and quadratic effects of Worker Specialization are dif- ferent as compared to the primary measure but the signs and significance of coefficients remained the same (see Table 4.6 in section 4.1). We do not find a statistically significant difference in different time periods. The effect of Workload and Personalization remained similar. Alternative measures of Workload: We used an alternative measure of Workload wherein we consider only the WIP at the sewing stage. We find that the effect of Workload continues to be robust and an increase in Workload increases the probability of return as before—see results of Model 2b in Table 1.4. The coeffi- cient estimates are different primarily because the mean value of WIP at the sewing stage is only 5.0 versus 6.1 for total WIP (see Table 1.2). However, when we considered another measure,WIP i =Sewers i , we find that the increase in Workload leads to a higher probability of returns, but the coefficient is not significant. We suspect this change is due to the fact that the measure may not accurately capture capacity because (1) 38 as discussed earlier, sewers may be moved across products, (2) the volume that the same sewer can produce can vary substantially across products. As discussed in section 1.4.3, the variable Process Design controls for the number of sewers relative to number of sewing steps in processing an order which can have an impact on the quality. This variable was added to avoid the potential for omitted variable bias. The last column in Table 1.4, Model 2c, considers a variation of Model 2 which excludes the control variable Process Design. We find that the coefficient estimates of the variables of interest change only slightly. 1.5.4 Model Validations and Robustness In this subsection, we discuss additional robustness checks performed to validate the results on the return rate analysis shown in Models 1a–1b, 2d–2h in Table 1.5, wherein we only change the control variables. We expand the return policy measure in the following way. For the variable Return Period, we separate the limited category into 30 days and 90 days. For the variable Return Authorization, we break down the required value into “required via calling consumer service” and “required via online system.” We find the corresponding coefficients, reported as Model 1a in Table 1.5 below, are similar to ones in Model 1 in Table 1.4. To control for the historical quality of work of the workers producing an order, we used the average return rate of the set of workers producing an order in measuring Sewer Quality of Work. But the quality of an order may be determined by the worst worker or equivalently, the maximum return rate among the workers producing an order. So, we considered the maximum return rate, rather than the average, of the set of workers producing an order. To control for the experience of the workers producing an order, we used the average tenure of the team of workers that worked on it. But the quality of work of an order may depend upon the least experienced worker and hence the minimum tenure (among the set of workers producing an 39 order) rather than average tenure as discussed earlier. The results obtained by using the alternative measures forTenure and Sewer Quality of Work were similar for both Model 1 and 2 (within half standard errors) and are omitted due to space constraints. Table 1.5: Robustness Checks on Effect of Worker Specialization, Workload and Personalization on Return Rate y Model 1a Model 1b z Model 2d z Model 2e Model 2f q Model 2g Model 2h Hypothesis 1: Worker Specialization TeamAverage (past 4 weeks) 0.0219 *** 0.0209 *** 0.0229 *** 0.0233 *** 0.0235 *** 0.0235 *** 0.0209 *** (0.0036) (0.0037) (0.0037) (0.0036) (0.0039) (0.0036) (0.0037) TeamAverage 2 (past 4 weeks) 0.00019 *** 0.00019 *** 0.00021 *** 0.00021 *** 0.00021 *** 0.00021 *** 0.00019 *** (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0218 *** 0.0219 *** 0.0206 *** 0.0212 *** 0.0224 *** 0.0205 *** 0.0187 *** (0.0035) (0.0036) (0.0036) (0.0036) (0.0038) (0.0035) (0.0036) Hypothesis 3: Personalization (yes vs. no) 0.2554 *** 0.2904 *** 0.3270 *** 0.2622 *** 0.3418 *** 0.2912 *** 0.3212 *** (0.0628) (0.0640) (0.0642) (0.0636) (0.0666) (0.0624) (0.0632) Controls Team Average Return Rate (past 4 weeks) 5.5970 *** 5.1021 *** 5.5586 *** 5.3622 *** (0.7041) (0.7542) (0.6999) (0.7061) Team Average Return Rate (past 3 months) 7.0342 *** (1.0562) Team Average Tenure 0.0029 *** 0.0029 *** 0.0026 ** 0.0026 *** 0.0026 *** (0.0008) (0.0008) (0.0009) (0.0008) (0.0008) Each Worker’s Return Rate (past 4 weeks) Not Included Included Included Not Included Not Included Not Included Not Included Each Worker’s Tenure Not Included Included Included Not Included Not Included Not Included Not Included 3 Digit Zip Code (ZIP3) (fixed effect) Included Included Included Included Included Not Included Not Included Vehicle Model (fixed effect) Not Included Not Included Not Included Not Included Not Included Not Included Included All Other Controls Included Included Included Included Included Included Included Likelihood Ratio ( 2 ) 4,934.4 *** 4,933.2 *** 5,072.6 *** 5,043.5 *** 4,590.7 *** 3,797.7 *** 5,216.8 *** AIC 103,705.5 103,718.7 103,597.3 103,610.4 90,040.4 103,088.2 103,457.1 N 179,906 179,906 179,906 179,906 154,900 q 179,906 179,906 y Logit coefficients are provided. Standard errors are shown in parentheses. p-value0:001; p-value0:01. z Models 1b and 2d control for each worker’s return rate and tenure instead of team average return rate and tenure respectively. q Model 2f excludes orders in the last 6 months of the study, thus the smaller data size. In Model 1b and Model 2d shown in Table 1.5, we further controlled for sewer ability by using the historical quality of work and experience of each sewer producing an order, instead of using the team level measures discussed above. The effect of Personalization shows up a bit stronger (0:2904 in Model 1b vs0:2410 in Model 1,0:3270 in Model 2d vs.0:2808 in Model 2) and is within 0.8 standard errors, whereas the effect of Worker Specialization and Workload (WIP) are very similar. 40 We also explored the team average return rate over the previous 3 months for the control variable Team Average Return Rate, instead of the 4 weeks used in Model 2 in Table 1.4 and the results are in Model 2e in Table 1.5. It is apparent that the coefficient estimates of the variables of interest in Model 2e are similar to those in Model 2. We also explored if the time window used in the study may have influenced our findings. We considered a variation of Model 2 wherein we dropped the data from the last 6 months of the study and the results are reported as Model 2f in Table 1.5. We find that the effects of Worker Specialization, Workload and Personalization continue to be significant and similar. We also considered a model specification that excludes orders in the first 6 months of the study and a specification wherein we dropped 10% of the orders, randomly selected from the three years, and the results were robust (details available from the authors). To assess if the 3-digit ZIP Code plays an influential role in the model estimates, we dropped this control variable. Model 2g in Table 1.5 provides the results of this specification. We find that the coefficients of the variables of interest are about the same as in Model 2. This seems to suggest that consumer and their location characteristics that are captured by 3-digit ZIP Code do not represent potential omitted factors that influence the variables of interest. Additionally, we explored different ways of controlling for consumer characteristics by excluding the population density, using the median age instead of the age groups, using the total household expenditure rather than the expenditures in different categories, either using household expenditure or household income but not both, and found the results to remain robust. Finally, we included vehicle model as a control variable which contains 896 categories in model 2h in order to understand whether the variation among vehicle models may impact our results. We again find that the coefficients of the variables of interest are about the same as in Model 2. Notice that we do not include 3-digit ZIP Code in this model specification, because our data size is not large enough to accommodate both control variables each containing nearly 900 categories. 41 Overall, in all the above cases, we find that the coefficients for Worker Specialization, Workload and Personalization are similar across different model specifications and changes in the estimates are small. These results suggest that our results are robust to changes in the measures of the causal variables of interest, time period used to compute the measures, and changes in the control variables. 1.5.5 Endogeneity Analysis Results In this subsection, we provide the results of the analyses using instrumental variables and a proxy variable to address potential endogeneity issues discussed in section 1.5.2. With respect to the variableWIP , we first used Lagged WIP as an instrumental variable for Workload as previously discussed. The Wald weak IV test (Finlay and Magnusson 2009) on Lagged WIP rejected the null hypothesis atp-value = 0.0002 and so we conclude that Lagged WIP is a strong IV . Using this Lagged WIP, we further use the Wald test of exogeneity and failed to reject the exogeneity of causal variable WIP at p-value = 0.6698. The GMM-IVE (Baum et al. 2003) for WIP when instrumented by Lagged WIP is found to be 0.0209, which is within 0.05 standard error from the logit coefficient estimate of 0.0207 (see Model 2i in Table Table 4.7 in section 4.1 for details). The second instrument we explored forWIP is the Order Volume. The weak IV hypothesis is rejected atp-value = 0.0028 using the Wald weak IV test. Using Order Volume as an IV , we failed to reject the exogeneity of WIP at p-value = 0.3402 by the Wald test of exogeneity. The GMM-IVE for WIP when instrumented by Order Volume is found to be 0.0220 which is within 0.38 standard error from the logit coefficient estimate of 0.0207 (see Model 2j in Table Table 4.7 in section 4.1 for details). The change in the coefficient estimates of the other causal variables are small. Therefore, endogeneity vis-a-vis Workload does not appear to be an issue. Next, we consider endogeneity with respect to the variable Personalization. First, we discuss the results of including the proxy variable Intent To Personalize in Model 2. We find that it has a coefficient of0:7904 42 with standard error 0.3894 andp-value = 0.0424. It seems to suggest that consumers who are more likely to personalize are less likely to return a product at the ZIP3 level. We find that the coefficient estimate of Personalization when we include the proxy is within 0.46 standard error of the corresponding coefficient when we don’t include the proxy (see Model 2k in Table 4.7 in section 4.1 for details). Second, we considered using the IV , Lagged Sewing Hours as discussed earlier. The weak IV hypothesis is rejected atp-value = 0.0000 by the Wald weak IV test and indicates that Lagged Sewing Hours is a strong IV . Further, using Lagged Sewing Hours as an IV we conduct the Wald exogeneity test and find the p-value = 0.1231. The GMM-IVE for Personalization when instrumented by Lagged Sewing Hours is found to be0:2668 which is within 0.22 standard error from the logit coefficient estimate of0:2808 (see Model 2l in Table Table 4.7 in section 4.1 for details). The change in the coefficient estimates of the other causal variables are small. Therefore, endogeneity vis-a-vis Personalization does not appear to be an issue. 1.6. Discussion and Conclusion The results of our study suggest that Worker Specialization is a significant factor that impacts the quality of output, in turn impacting return rates. Moreover, the impact of Worker Specialization on return rate is U-shaped. Return rate decreases over a substantial range of Worker Specialization values but increases if Worker Specialization is too high. As Worker Specialization increases, a sewer is able to master a specific task which in turn reduces errors. However, we find that excessive Worker Specialization, and in particular, a scenario wherein a sewer performs the same task repeatedly over long periods of time, is not ideal. We find that this is the case whether the Worker Specialization is measured over a 4 week period or a 3 month period. In fact, we used different periods (1 week to 6 months) but did not find any statistically significant differences. Our results suggest that it is better for a sewer to periodically perform different tasks, whether these involve working on different products or different materials for the same product or even different set 43 of tasks (e.g. joining or binding or velcro) for the same product and material. Otherwise, boredom or fatigue may set in, resulting in errors. The average level of Worker Specialization at the firm in our study is about 52%, which is not far from the optimal level of specialization of 57%. Unlike prior studies which focus on the impact on productivity, we focus on the impact on consumer product returns. We find that higher Workload has a negative impact on return rates. Again, this is consistent with some of the OM literature (KC and Terwiesch 2009, Kim et al. 2017) on the impact of workload on quality, although these studies have primarily focused on health-care settings. In these settings, capacity constraints tend to be hard constraints due to finite bed capacity, while capacity is a soft constraint in our setting because the firm can schedule overtime or extra hours on a Saturday or delay the production of an item. However, these alternatives increase the cost of production or may result in canceled orders, and so there is still pressure on the workers to speed up when Workload increases, sacrificing quality. Moreover, the firm cannot increase the number of sewers at short notice. So, the managers face a difficult trade-off between a higher workload which could result in lower quality and a lower workload which may delay orders. The finding that has the most potential to translate into practice is the utilization of Personalization (say, in the form of personalized logos). While the literature has shown that it increases a consumer’s attachment to the product, our study appears to the first one to empirically validate that it has a very strong effect in reducing return rates. Adding logos is not costly, and so it provides the firm with an inexpensive lever to reduce return rates. Also, this does not impact sales negatively, unlike for instance strict manufacturer or retailer return policies, which may discourage returns but simultaneously discourage sales too. Moreover, products with logos have higher margins. In summary, Personalization provides multiple benefits. While the causal variables discussed above are the focus of this study, the effect of the control variables on return rates also provide some interesting insights, especially since our study is the first one to incorporate 44 some of these controls in a study of returns. We focus here only on those control variables whose coefficients are significant and stable and over which the firm has some control. From a production process perspective, it is interesting to see that Sewer Tenure is positively associated with quality. This suggests that worker ability, as proxied by tenure, may be important in reducing defects and return rates. This is recognized by Company A, which enjoys low turnover after the initial two-month period, during which they train the employees, and which ensures that they can achieve certain benchmarks in terms of productivity and quality. We also find that retailer policies have a substantial influence on return rates as one would expect; shorter or limited return periods, higher restocking fees, and requiring an authorization to return all imply lower return rates. Of course, this may be because consumers who are more likely to return products are less likely to purchase in the first place, deterred by the strict return policies. To that extent, such policies are a mixed blessing, because they also reduce sales as has been emphasized in the marketing literature (Hess and Mayhew 1997, Anderson et al. 2009). It is noteworthy that the production-related factors, Worker Specialization and Workload, have a signifi- cant, albeit small, impact on return rates through their effect on defects despite the fact that there are many possible drivers of returns as discussed in section 2. In fact, most of the prior literature has implicitly as- sumed that product and retailer attributes are the primary drivers responsible for product returns and do not even discuss production related factors. Our study also shows that manufacturers can offer increased Per- sonalization in the form of personalized logos or other product variants as this helps decrease return rates substantially. The impact of product returns is not really as significant for retailers as it is for manufacturers because retailers simply pass along the return to the manufacturer in many instances, as is true in our setting. So, the real cost of returns is borne by the manufacturer and these costs can be substantial. 45 Chapter 2 Predicting Product Return Volume Using Machine Learning Methods 2.1. Introduction In the retail industry consumer returns create a significant and costly issue for manufacturers and retailers. In 2015, consumers returned goods worth $261bn out of $3.3trn sold in the U.S. (The Economist 2014) and returned goods worth $642.6bn out of $14.53trn sold worldwide. Furthermore, more than half of all returns may not be resold for full price, which results in substantial financial losses (Cheng 2015). The rise in online sales (Business Insider 2017) has led to increasing return rates, sometimes exceeding 30% (Rudolph 2016). The issue is particularly problematic for online retailers that offer extensive product variety and customization options, making it more difficult to resell the returned items. Firms have an interest in developing a model for predicting return volume and understanding the under- lying factors associated with it for several reasons. These can be broadly grouped into two categories: (i) operational issues and (ii) financial issues. Returns can cause significant operational and logistics challenges because firms have to devote resources such as staff and space to process returns, identify if an item should be resold or disposed, etc. Moreover, if returned items have to be repaired, then this may negatively impact the workflow in the production process depending on the product type and workload levels. Financially, re- turn volume helps provide an estimate of the cost or loss due to returns. So, from a financial and operational perspective, understanding return volume is beneficial not just to the firm in our study, but also any firm facing a large return volume in the e-commerce era. Finally, anticipating return volume of a product type at a retailer in each period may be valuable in taking actions to reduce returns. For example, Jet.com offers a discount to customers who opt out of free returns (https://jet.com/help-center/faq). Rather than offering 46 such discounts for all product types, a manufacturer may be able to optimize its discounting strategy by targeting such discounts to specific product types offered at certain retailers that are likely to have higher returns. Such discounts may also be restricted to certain periods, for instance during the Christmas season when returns are higher. The primary objective of this paper is to build a good data-driven model to predict return volume in the future. Our study was done in collaboration with a leading manufacturer of automotive accessories in the U.S., referred to as CompanyA hereafter, whose real name is withheld due to confidentiality reasons. CompanyA primarily sells three types of products (seat cover, dash cover, car cover) through various online retailers. Customers can choose a car accessory matched to a specific car model year, color, fabric type and also customize the product with logos, specialized prints, etc. Customers place orders online via the retailer’s website and the firm makes each item to order and ships it in around a week. Customer return policies, whether strict or liberal, are dictated by the retailer. However, all returns are handled by Company A, not the retailers, who serve only as a sales channel. Due to the extensive variety offered, the odds are low that a product returned by one customer will be demanded by another one within, say, a few months. However, the firm checks each returned item to assess whether to put it back in stock (if it is not defective and is likely to be resold) or to dispose it. Many items are disposed or sold at a steep discount and cause a significant financial loss to the company, because extracting value from returned product is difficult in the focal firm of our study. This is unlike for other product categories such as appliances where a substantial part of the value may be recovered from a resale. Our predictive models are built using a large, detailed data set from CompanyA on every item that was sold and/or returned over 39 months. For each item, the firm provided us with data on order date, retailer, product type, production process details (including dates when each process step was completed and who worked on it), ship date, and return date. We also obtained aggregate information on production levels, workers, inspection policies, and return policies of retailers. 47 We first develop a baseline main effects model for predicting return volume using four factors deemed to be important based on our initial understanding of returns at Company A: sales volume, time, retailer and product type. Return volume is generally proportional to sales volume although the proportion (return rate) may vary by product type, retailer and over time. The retailer variable captures factors such as return policies, type of consumers who visit a retailer, which could influence return volume. For example, more impulsive purchases may generate higher return volume and such impulsive consumers may be more likely to visit certain retailers. Return volume may also vary by product type because certain product types may have greater fit issues (e.g., seat cover) or certain product types may be prone to defects in the manufacturing process. Finally, return volume may vary over time; for example, consumers may be more impulsive during holiday purchases. We then explore how additional variables such as manufacturing workload levels, process quality checks, production process complexity, and product personalization (e.g., logos) improve prediction performance — this leads to a full main effects model with a much larger set of independent variables. In addition to the main effects models discussed above, we also investigate whether adding second and third order interaction effects improves prediction. For instance, returns may be increasing over time at a particular retailer. Alternatively, the presence of personalized logos may impact returns for some products but not others or inspection may be valuable in reducing defects/returns for some products but not others. The incorporation of aforementioned interaction effects, however, results in a large number of predictor variables and warrants the need for a robust variable/model selection methodology. The traditional methods such as best subset selection, forward/backward selection (see Hocking 1976 for a review) are not applicable in our study, because we are in a high dimensional setting due to having more predictors than observations as will be clear later. To address this issue, we use four high-dimensional machine learning methods: Least Absolute Shrink- age and Selection Operator (LASSO, Tibshirani 1996), LARS-OLS hybrid (Efron et al. 2004), Smoothly Clipped Absolute Deviation (SCAD, Fan and Li 2001), and Elastic Net (Zou and Hastie 2005) that can yield 48 sparse models. In addition, we explore two notable tree-based machine learning methods, Random Forest (Breiman 2001) and Gradient Boosting (Friedman 2001) to capture possible complex non-linear structure in the data to improve prediction accuracy. Our contributions can be summarized as follows. We use various machine learning methods to build and test predictive models for return volume using a real data set that is comprehensive and includes retailer, product type, and process related variables. We show that in our setting retailer effects are stronger than product effects in predicting returns, and the baseline main effects model utilizing sales, time, product and retailer effects achieves a fair prediction performance. We consider higher order interaction effects (e.g., product type and retailer) and apply various convex and concave regularization methods for variable/model selection to derive a sparse predictive model that strongly improves prediction accuracy. In our study, we find that the optimal Elastic Net model coincides with the LASSO model, which achieves smaller prediction errors in the test data compared to all the alternative methods. It shows robust performance with similar prediction accuracy both in the training and test data. The remainder of the paper is organized as follows. In Section 2.2 we review the relevant literature. Section 2.3 discusses the empirical setting and the predictor variables derived from the data. In Section 2.4 we sequentially build main effects models. Section 2.5 explores higher-order interaction models with high-dimensional variable/model selection methods, and tree-based statistical machine learning methods. We provide results from robustness checks in Section 2.6, and discuss key take-aways from our study and future research direction in Section 2.7. 2.2. Literature Review Our study is related to several streams of literature, one of them being the marketing literature on consumer product returns. Hess and Mayhew (1997) are among the earliest to empirically study product returns, and 49 provide a model to predict the timing of returns for an apparel direct marketer. Janakiramana et.al. (2016) show that return policy leniency overall increases purchases more than returns. Anderson et al. (2009) iden- tify a considerable variation in the value of returns across customers and product categories at a mail-order catalog company. Petersen and Kumar (2009) determine the firm-customer exchange process factors that help explain product return behavior and the consequences of product returns on future customer and firm behavior. Urbanke et al. (2015) propose a returns prediction system for an online retailer to explore the im- pact of different levers on the likelihood of returns, for example, by artificially increasing delivery time to deter a consumer from purchase. The above-mentioned research is mostly concerned with factors impacting consumer’s decision to keep or return a product, and studies returns from the perspective of retailers. In con- trast, our paper develops data-driven predictive models for a manufacturer, which sells online an extensive range of product variants and is primarily concerned with the cost and logistics of handling returns, and is interested in predicting consumer returns due to various reasons (e.g. defect in product, consumer’s change of mind). Another relevant stream is the operations literature on returns, which is primarily focused on analytical studies of product returns, for example, returned component reuse (DeCroix et al. 2009), restocking fees (Shulman et al. 2011), return policies (Su 2009, Altug and Aydinliyim 2016, Shang et.al. 2017a, Ulku and Gurler 2017), remufacturing (Cerag et al. 2016, Calmon and Graves 2017), optimal retail assortment under consumer returns (Alptekinoglu and Grasas 2017), return strategy and pricing in a dual-channel supply chain (Li et.al. 2017). In contrast, our work is empirical in nature and focused on predicting returns. There are some works related to predicting returns for the purpose of remanufacturing. For example, Toktay (2003) reviews a few forecasting methods (e.g., using past sales and returns), and Tsiliyannis (2018) presents a stochastic method for real-time forecasting of product returns in remanufacturing. Our study focuses on data-driven prediction models for returns and is not concerned with remanufacturing, because the products in our study are made of fabrics that are not reused to make new products. 50 Some recent works in operations also conduct empirical studies on returns from the perspective of re- tailers and consumers. For example, Shang et.al.(2017b) analyze both the return policy drivers from the retailer’s perspective and the return policy value from the consumer’s perspective, and show that the value of a full refund policy to consumers may not be as large as one might expect. Akturk et.al. (2018) study omnichannel retailing in the context of a national jewelry retailer and suggest that introducing ship-to-store increased cross-channel customer returns of online purchases to physical stores. In contrast to these works, we study product returns from the perspective of a manufacturer. Our paper is also related to the literature on predictive analytics, which are applied to a variety of settings. In the operations research literature, however, there is still a relatively low volume of analytics- orientated studies (Mortenson et. al. 2015). Here are two examples: Oztekin et. al. (2018) develop a hybrid methodology to predict and explain the quality of life for patients undergoing a lung transplant, and Sevim et. al. (2014) develop an early warning system to predict currency crises using artificial neural networks, decision trees, and logistic regression. We utilize high-dimensional machine learning methods, which have become increasingly popular and widely used in areas such as genomics, neuroscience, social media analysis and high-frequency finance. They are not only utilized to obtain a good prediction accuracy, but also to address variable/model selection problems associated with various challenges such as noise accumulation, spurious correlation, scalability and stochastic errors. We refer readers to Fan et al. (2011), Varian (2014) for excellent reviews, and James et al. (2017), Hastie et al. (2009) for in-depth treatments of high-dimensional methods. One of the best known high-dimensional methods is LASSO or otherwise known asL 1 regularization, which has recently received some attention in the operations management literature for predictive models, and here are some recent examples. Ma et. al. (2016) apply LASSO to select key explanatory variables from a high dimensional data set for demand forecasting for SKU retail sales. Martinez et. al. (2018) use LASSO as one of the methods to develop a machine learning framework for customer purchase prediction in a non-contractual 51 setting. Bertsimas et al. (2016) use LASSO as one of the methods to predict the outcomes of clinical trials. In the context of a Red Cross fund-raising campaign, Ryzhov et al. (2016) employ LASSO to logistic regression models to identify key interactions between designs (e.g., the presence or absence of a free gift) and various donor segments. In contrast to the aforementioned literature, we study product returns, and extract features common to many product manufacturers from our data set. Furthermore, we consider higher- order interaction terms (e.g., product type and retailer) and initialize multiple machine learning methods (LASSO, SCAD, Elastic Net, Random Forest, Gradient Boosting) to derive and calibrate predictive models. 2.3. Empirical Setting In this section, we first introduce the operational context and process in our study in subsection 2.3.1. Sub- section 2.3.2 describes the data, and subsection 2.3.3 discusses how we derive predictor variables from the data. 2.3.1 Operational Context and Process CompanyA manufactures car accessories (seat covers, car covers and dash covers) at two factory locations – in California and Mexico. Consumers place orders at an online retailer for a specific vehicle (make, model, year, trim level) and a specific product type. A consumer can choose the fabric, color, design and whether to have a personalized logo. Sometimes, she may request multiple products in the same order. The order information is transferred to Company A which manufactures and ships the product to the consumer in about a week. Once CompanyA receives an order, it is released into production immediately unless there is substantial pending work. The entire manufacturing process can be broadly categorized into three stages. The pre- sewing stage comprises of printing the order label, which contains detailed instructions for each of the 52 subsequent operations, cutting of fabrics by computerized cutting machines, and placement of cut pieces in a plastic bag with the order label to be routed for sewing. During the sewing stage, sewers perform tasks such as joining, binding, embroidering and adding logos, which vary with the product types. In the last post- sewing stage, finished goods are inspected, packed and shipped to the consumer. There are some random inspections by the floor supervisor in the pre-sewing and post-sewing stages. Most products are exclusively made in the U.S. while some are produced jointly in both factories. Returns. A product may be returned within the return period for refund, or beyond the return period for repair or replacement under warranty. The return policy is set by each retailer and return policies determine aspects such as time within which a return has to be made for a refund, allowing returns to physical stores, etc. All the returns are handled by Company A, not the retailers. If a returned product is confirmed to be in a resalable condition, it is first kept in the warehouse depending on the available space, and then disposed if it is not sold within a certain time window. If a returned product is for repair or replacement, the manufacturer needs to allocate resources to meet the request. Therefore, the returns handling increases operational overhead in staffing and resources. 2.3.2 Data Description In our study, we focus on three main product types that comprise over 90% of sales volume for Company A: seat cover, car cover and dash cover. They are sold to consumers in the United States and most sales are through 13 retailers. There was a small fraction (0.17%) of the products that were returned and resold during our study period, but they were excluded during data cleaning because they comprised of a negligible fraction of the sales. This gives us a data set containing 331,390 products sold between July 2012 and September 2015, for a total of 39 months denoted as periodst = 1; ;39. In Figure 2.1, we show how 53 sales, returns (in units) and return rates change over 39 periods in the focal firm in our study. One can observe that both returns as well as return rates fluctuate over time. Though aggregate return volume in each period is of first-order interest, CompanyA is also interested in predicting return volume by each product type and each retailer for the following reasons. First, the revenue loss varies among different product types, for example, the revenue loss due to refund of seat cover is often higher than one for dash cover. Second, the ability to resell the returned product may also vary with the product type. Third, since different product types have different manufacturing processes, when products are returned for repair or replacement under warranty, the increased operational workload and costs may also be quite different. Fourth, the same seat cover may lead to a larger revenue loss due to return for refund through a retailer with a liberal return policy, but may result in less costly return for repair through a retailer with a 30-day return policy. Figure 2.1: Sales, returns and return rates over 39 months, between July 2012 and September 2015. Figure 2.2: Sales, returns and return rates by product type (left) and by retailer (right) over all periods. 54 There are many possible reasons why a particular product may be returned and understanding them is helpful when building a predictive model. Next, we provide a sample operational level data set obtained from CompanyA (see Table 2.1) to provide a context to discuss these reasons. Some values in the table are hidden or modified to preserve confidentiality. The data used in the study includes both retailer level and operational level data sets obtained from the company. The retailer level data contains the return policy and name of each retailer. ReleaseDate ScanDate OrderNo SerialNo Product Retailer Logo Operation EmpID Loc FName LName ReturnDate 5-11-2015 5-13-2015 149038568 L49325398 SCxxxx xxxx.com HON002 Printing labels xx01 US xxxx xxxx 7-10-2015 5-11-2015 5-14-2015 149038568 L49325398 SCxxxx xxxx.com HON002 Cutting fabrics xx12 US xxxx xxxx 7-10-2015 5-11-2015 5-15-2015 149038568 L49325398 SCxxxx xxxx.com HON002 Joining xx53 US xxxx xxxx 7-10-2015 5-11-2015 5-15-2015 149038568 L49325398 SCxxxx xxxx.com HON002 Binding xx53 US xxxx xxxx 7-10-2015 5-11-2015 5-16-2015 149038568 L49325398 SCxxxx xxxx.com HON002 Logo xx26 US xxxx xxxx 7-10-2015 5-11-2015 5-17-2015 149038568 L49325398 SCxxxx xxxx.com HON002 Random Inspection xx45 US xxxx xxxx 7-10-2015 5-11-2015 5-17-2015 149038568 L49325398 SCxxxx xxxx.com HON002 Packing xx34 US xxxx xxxx 7-10-2015 Table 2.1: A sample operational data set. This example shows 5 different operations performed on a product with serial number L49325398 in order number 149038568. We can identify the product type — seat cover — by the prefix of the product, and observe that this particular product was released into production on Wednesday, 5/11/2015 (which is the order date) yet due to backlog the label was not printed until two days later on Friday 5/13/2015. The next day, an employee read the label to find out which fabrics to pick up from inventory, and cut the fabric in preparation for sewing according to the specification. On Sunday 5/15/2015, an employee with ID xx53 performs two types of sewing operations — Joining and Binding. On Monday, 5/16/2015, a different sewer adds a logo and finishes this product. A floor supervisor (usually a sewer with more than 10 years of experi- ence) performs a random inspection on the product, does not notice any defects, and she passes the product to an employee who packs the product. Depending on the time of day, this product is shipped to a consumer on the same day or next day. The product is returned to the factory on 7/10/2015 as shown in the ReturnDate column. 55 Which factors may have contributed to this return? This product was ordered just before the summer. There may be a seasonality effect for returns if the product fades during the summer heat. Product type may influence returns; for example, seat covers usually cost much more than dash covers, so a customer is more likely to go through the trouble of returning seat covers. Seat covers might also have higher defects because of more difficult sewing operations. Retailer xxxx.com in Table 2.1 is found to have a 60 days return policy in the retailer level data set, and the product is returned between 30 days and 60 days, so the return may have been because the consumer changed his/her mind or due to a defect in the product. The production processes and resources used in manufacturing the product may cause defects and in turn result in returns. The example in Table 2.1 shows that two sewers performed three sewing tasks on this product, and we may ask if single tasking (three sewers, each doing a single task) leads to lower defects and thus lower returns. It is also possible that the consumer may have simply changed her mind, and historical returns may partly capture this factor. We could also check whether an order of multiple products lead to higher (or lower) returns. In the next subsection, we explore the specific predictor variables used in the study in more detail. The predicted variable in the study is Returns tij , that is, how many units of product type i will be returned out of sales through retailerj in periodt. As is clear from Table 2.1, every item that is returned can be tracked, and the details about retailer, product and production process characteristics for the item are available. While we collected data until October 2016, we analyze returns only for sales until Sep 2015 in our study so that almost all returns, which occur within one year, are captured. 2.3.3 Predictor variables Our focus in this subsection is to identify the variables that can help predict the volume of returns defined as Returns tij , where the subscriptst;i;j denote the period, product type and retailer respectively. As poten- tial predictors of returns, we consider production process and resources, multi-product order and historical 56 returns in addition to aforementioned factors — sales, time, product type, retailer. We list the predictor vari- ables reflecting these factors in Table 2.2 along with their definitions. In the following, we discuss each of these predictor variables and the justification for using them in the prediction models. Category Variable name Definition Response variable Returns tij Number of returns out of sales of product typei via retailerj in periodt. Sales effect Sales tij Number of sales of product typei via retailerj in periodt. Time effect Year t Sales year from 2012, 2013, 2014 to 2015, used to capture time trend. Month t Dummy variable for the month corresponding to period t, used to capture seasonality. Product effect Product i Dummy variable for product typei. Retailer effect Retailer j Dummy variable for retailerj ranked by volume. SewerCnt tij Average number of sewers per product amongSales tij . SewingTaskCnt tij Average number of sewing tasks per product amongSales tij . SewingDays tij Average number of days in sewing stage per product amongSales tij . BacklogDays tij Average number of backlog days before production per product amongSales tij . Production process ProductionDays tij Average number of days in entire production process per product amongSales tij . and resources Workload t Average number of finished products per employee in periodt. JointProduction% t Fraction of products jointly manufactured in periodt. CustomFabric% tij Fraction of products using customized fabrics amongSales tij . Logo% tij Fraction of products ordered with special logos amongSales tij . InspectionPreSewing% tij Random inspection rate before sewing amongSales tij . InspectionPostSewing% tij Random inspection rate after sewing amongSales tij . Multi-product effect MultiProduct% tij Fraction of orders with two or more products amongSales tij . Historical returns LaggedReturns tij Observed returns in period t from sales in periodst4;t5;t6. Table 2.2: Definition of response and predictor variables fort = 1; ;39;i = 1;2;3;j = 1; ;13: Sales. As sales volume goes up, return volume is likely to increase. So, we include sales as a predictor. Time. Similar to Anderson et al. (2009) we consider two types of time effects: trend effect and monthly fixed effect (e.g. consumers may purchase products more impulsively during holiday seasons resulting in higher returns.) The trend effect is captured by the predictor variableYear t 2f2012;2013;2014;2015g, which depends on the periodt; for example,t = 1; ;6 implies 2012,t = 7; ;18 implies 2013, and so on, recalling that the dataset begins in July 2012. The monthly fixed effect is captured by the dummy variable Month t 2fJanuary; ;November;Decemberg, which depends on the month the period t corresponds to; for instance,Month 1 indicates July,Month 2 equals August, and so on. We provided the returns pattern over the 39 periods in Figure 2.1. As an alternative to using year and month variables, we 57 de-trended and de-seasonalized the data before estimating the models but we found little difference (see section 4.2.1 for details). Product. The three product types in our study — seat cover, dash cover and vehicle cover — have distinct characteristics, and may have product specific fixed effects that influence returns. For example, a slightly larger vehicle cover may be considered fine by consumers, but a slightly loose seat cover may be regarded as defective and returned. We provided the returns for each product type in Figure 2.2, and found that the return rate of car cover was much lower than that for the other two products. In a study of an online retailer, Anderson et al. (2009) show variations in returns among different product categories. Therefore, we could expect that product effects are important in predicting return volume. Retailer. Based on previous research on the impact of return policies on sales and returns (e.g., Janaki- ramana et.al. 2016 and references therein) and given different returns policies of retailers in our study, we would expect return volume to vary with retailers. In addition, there may be other important factors associ- ated with a retailer that influence returns. Retailers with different return policies may attract different types of customers who exhibit different return behaviors. The number of brick-and-mortar stores of a retailer may have an impact on returns because more locations may make it easier to return a product: a warehouse club in our study operates hundreds of stores, whereas an auto specialty store has thousands of locations where a consumer may return a product. Therefore we expect that the retailer’s return policy and other characteristics may play an important role in returns, which are both captured by retailer indicator variables, as we showed earlier in Figure 2.2. In our analysis, we also explored incorporating variables to reflect different dimensions of return policies such as return period, in-store return acceptance, in addition to the fixed retailer effect but we did not find the additional variables helpful in increasing the prediction accuracy. Production processes and resources. Unlike prior studies of returns which considered only product and consumer purchase related factors, we consider various factors related to the production process that 58 may contribute to returns due to defects. We measure most of the variables in this category as an average over each period, product and retailer combination. We track the average number of sewers and sewing tasks bySewerCnt tij andSewingTaskCnt tij for each product, to understand if more sewers or fewer sewing tasks per sewer (e.g. grouping some sewing operations into one task) lead to lower defects, and therefore are useful in predicting returns. We useSewingDays tij as a proxy to the actual sewing time, and we may expect this predictor to be negatively correlated with returns, that is, if sewers spend more time in sewing a product, the quality of the product may increase and the likelihood of returns may decrease.BacklogDays tij and ProductionDays tij reflect different aspects of the manufacturing process and may be useful in predicting returns. We are interested in whether the monthly workload of the factory and the fraction of items jointly produced in Mexico and US impact returns, and measure these effects byWorkload t ,JointProduction% t for each period. We investigate the effect of special customization on returns byCustomFabric% tij for the usage of in-house custom fabric, andLogo% tij for personalizing products with custom-logos, and the effect of random quality inspections by floor supervisor on returns before and after the sewing stage by InspectionPreSewing% tij andInspectionPostSewing% tij . Multi-product effect. Anderson et al. (2009) do not find a significant effect of multiple product pur- chase on returns in their study, but suggest that this may not always be true and in other applications, return rates may depend on whether a consumer purchased single or multiple products in an order. In our study, about 9% of products are sold as part of an order with two or more customized products. We utilize MultiProduct% tij to capture and investigate this effect. Historical returns. We are interested in capturing new trends in returns that may not be captured by the aforementioned predictor variables. For example, recent returns data may include a change in consumer’s purchase and return behaviors, such as increased usage of smartphones to make purchases (Martin 2016) which may be more impulsive and lead to higher returns than average online orders. In addition, using lagged values to predict current period’s value is not uncommon (for example, see Wilms 2017). We use 59 a predictor variable called LaggedReturns tij to capture this effect, using historical returns data. To do this, we consider three criteria: 1) we want the returns status of historical data to be accurate, 2) we want to capture recent returns trend, 3) we want to reduce noise in low-volume returns. To satisfy these requirements, we defineLaggedReturns tij :=Returns t6;ij +Returns t5;ij +Returns t4;ij to predictReturns tij . Next we discuss each of these points. In the following Figure 2.3, we observe that about 90% of returns occur within the first 4 months, thus the returns status largely becomes finalized within four months after sales of an item. For this reason, when we consider historical returns data, we want to go back at least 4 months, in other words, we want to useReturns tn;ij forn 4 for the prediction ofReturns tij to satisfy our first criterion. Returns data from more than half a year ago may not reflect recent returns trend, and for this reason we propose to use Returns tn;i;j forn 6 to meet our second criterion. To reduce noise coming from low-volume returns, we aggregate historical returns over three months to satisfy our third criterion, instead of picking one of the variablesReturns t4;ij ;Returns t5;ij ;Returns t6;ij . Please see section 4.2.2 on details on how we construct the variable LaggedReturns for the test periods. 0.000 0.005 0.010 0.015 0.020 0 100 200 300 Days to return density Figure 2.3: A histogram of days to return for products returned within a year. We provide summary statistics of predictor variables in Table 2.3. 60 Variable Min Mean Median Max SD Returns 0.00 21.05 6.00 509.00 49.53 Sales 1.00 243.70 99.00 2744.00 406.10 SewerCnt 1.00 3.28 3.27 6.75 1.14 SewingTaskCnt 1.00 3.61 3.86 8.75 1.33 SewingDays 1.00 1.99 1.80 8.00 0.77 BacklogDays 0.00 0.48 0.17 6.00 0.83 ProductionDays 2.00 7.07 6.97 15.00 3.23 Workload 410.00 1033.40 1117.40 1832.80 428.41 JointProduction% 0.00% 19.05% 0.42% 100.00% 29.50% CustomFabric% 0.00% 5.41% 0.00% 73.84% 12.33% Logo% 0.00% 2.74% 0.00% 72.73% 6.84% InspectionPreSewing% 0.00% 0.07% 0.00% 26.07% 1.00% InspectionPostSewing% 0.00% 11.97% 0.00% 116.67% 24.96% MultiProduct% 0.00% 7.22% 2.97% 99.69% 16.82% LaggedReturns 0.00 58.37 16.00 1490.00 148.17 Table 2.3: Summary statistics of response and predictor variables. Data sizeN total = 1;360 represents the number of data points in our model because we model the return volume per product type, per retailer, per time period. One can notice a large variation among returns (and sales) ranging from 0 to 509 (and 1 to 2,744) depending on the period, product type and retailer. It requires an average of 3 to 4 sewers to finish a product and some sewers perform more than one task; the average time spent in the sewing stage is less than 2 days. Each employee, on average, finishes 1,033.40 products per period, as seen in Workload. When a product fails a post-sewing random inspection, it is sent back for rework and may be inspected again by the supervisor, which leads to a maximum possible 200% post-sewing inspection rate and explains the highest inspection rate of 116.67% for some period, product type and retailer. TheLaggedReturns are aggregated over three months and its summary statistics show a similar pattern as the ones forReturns, suggesting that historical returns may be an important predictor variable. Recall from Section 2.3.2 that our data contains 331,390 products sold between July 2012 and September 2015, thus 331,390 represents the total number of transactions (items purchased). As we discussed at the beginning of this subsection, we are modelingReturns tij — the volume of returns per product type, per store, per time period. Thus, the index “tij” represents one data point, therefore we have a much smaller set of data points,N total = 1;360. Since t = 39 periods, i = 3 product types, and j = 13 retailers, one might 61 assume thatN total = 39313 = 1;521. The reasonN total = 1;360 < 1;521 is due to missing data points, that is, no sales and hence no returns for certain “tij” values (see Figure 4.2 in section 4.2.5 for details). 2.4. Main Effects Models In this section, we explore various models to predict return volume using some or all of the variables listed in Table 2.2. We would ideally like a parsimonious model that has good predictive power and can be easily implemented in practice. Then, a natural question is — can we use only sales, time, product type and retailer information to build a model with reasonable prediction performance? We consider this model to be the baseline main effects model in our study, because these variables can be readily derived from a company’s ERP system and an operations manager can easily implement this predictive model using a spreadsheet, without the effort required to incorporate the remaining predictor variables. In subection 2.4.1, we sequentially add the predictor variables discussed above, and then present in subsection 2.4.2 the results of model fit (training set) and prediction (test set) for all the models. 2.4.1 Model Specification In the following simple model (2.1), we first use the predictor, Sales, to predict how many units out of such sales will be returned. Returns tij = 0 + 1 Sales tij + tij (2.1) 62 In the next model (2.2) we explore whether trend and seasonality effects help increase the prediction of return volume. Returns tij = 0 + 1 Sales tij + 2 Year t + t 3 Month t + tij (2.2) We now want to check the effects of product types and retailers on the prediction of return volume, but we don’t know which effect is more important in predicting returns. Thus, we first investigate the product effect in model (2.3) and retailer effect in model (2.4) individually, and then both effects in the baseline main effects model (2.5) simultaneously. Returns tij = 0 + 1 Sales tij + 2 Year t + t 3 Month t + i 4 Product i + tij (2.3) Returns tij = 0 + 1 Sales tij + 2 Year t + t 3 Month t + j 5 Retailer j + tij (2.4) Returns tij = 0 + 1 Sales tij + 2 Year t + t 3 Month t + i 4 Product i + j 5 Retailer j + tij (2.5) To simplify the exposition, we adopt column vector notation (shown in bold). For example,U consists of the remaining 13 variables shown in Table 2.2, and we add it to obtain the full main effects model (2.6) below. Returns tij = 0 + 1 Sales tij + 2 Year t + t 3 Month t + i 4 Product i + j 5 Retailer j + T 6 U + tij (2.6) For all the models (2.1) to (2.6) above, we considered a family of power transformations (Box-Cox 1964) for our response variableReturns tij to maximize normality before fitting models to the data; however, we did not find a need for a transformation. 63 2.4.2 Results from Main Effects Models To evaluate our models, we assign the first 33 periods (7/2012 to 3/2015) to be our training set, and the last 6 periods (4/2015 to 9/2015) to be our test set. We discuss alternative ways of splitting the data into training and test sets in our robustness checks in Section 2.6. For models (2.1) to (2.6) we present in the following Table 2.4 the model fit in training set, and the prediction performance in test set. Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Number of predictors 1 13 15 25 27 40 Data size 1140 1140 1140 1140 1140 1140 R 2 0.864 0.867 0.869 0.908 0.912 0.921 Training set AdjustedR 2 0.863 0.865 0.867 0.906 0.910 0.918 AIC 9864.255 9860.589 9843.836 9459.401 9410.657 9315.068 MSE 333.524 325.527 319.655 224.186 214.050 192.395 Data size 220 220 220 220 220 220 Test set R 2 0.836 0.838 0.844 0.888 0.895 0.923 MSE 402.506 396.787 381.472 275.189 257.709 189.386 Table 2.4: Prediction performance of 6 main effects models trained on 33 periods and tested on 6 periods. In our study, we measure the model fit and prediction performance by MSE (equivalently, Prediction Error) and R 2 . For the purpose of model comparison and selection for main effects models, we focus on adjustedR 2 and Akaike Information Criterion (AIC). Alternative measures may include Mallow’sC p , Bayesian Information Criterion (BIC), Risk Inflation Criterion (RIC), and predictedR 2 . In the OLS setting, C p and AIC are proportional to each other, therefore only one is needed. BIC and RIC generally place a heavier penalty on models with more variables compared to AIC (see Foster and George 1994.) Predicted R 2 method is identical to leave-one-out cross-validation (CV , Stone 1974), and is asymptotically the same method as AIC for model selection (Stone 1977). We observe that the simplest model (2.1) yieldsR 2 = 0:864 for training set, andR 2 = 0:836 in test set for predicting returns over the future 6 months. This shows that the predictor variable sales by itself explains a large portion of variability in return volume, and that sales is a good predictor of return volume as expected. In the subsequent models (2.2) to (2.5), when we sequentially add time, product type, retailer, 64 product type and retailer effects to model (2.1), we see that in both training and test sets,R 2 increases and MSE decreases indicating that we achieve not only an increasingly better model fit in the training set, but also a higher prediction accuracy in the test set. We also find that knowing the retailer is more important than knowing the product type when predicting returns, by comparing models (2.3) and (2.4). Our largest model (2.6) — with 13 additional predictors inU compared to model (2.5) — obtains the lowestAIC = 9315:068, the highest AdjustedR 2 = 0:918; and if we adopt conventional model selection methods, we may consider model (2.6) to be the best main effects model for training set. This model also has the best prediction performance in test set. Model (2.6) may have one potential drawback for use in practice, because the required overhead from data collection and analysis for many of the variables inU is substantial. By comparison, our second best model (2.5) may be preferred by CompanyA, because it only requires sales, time, product type and retailer information, thus it is much easier to implement by operations managers. For these reasons, we consider models (2.5) and (2.6) as the two best main effects models; and to address the aforementioned trade-off between models (2.5) and (2.6), we first provide in Table 2.5 on the next page the coefficient, standard deviation and significance levels for all the main effects models. We notice that two predictor variables — MultiProduct% andLaggedReturns — show up as significant at 0.001 level in model (2.6). A natural question that arises is whether one should choose one or both of these significant predictors from model (2.6) to add to model (2.5) to achieve prediction performance close to model (2.6) yet without the added overhead for implementation. This question then further invites another question — what is the best model out of all possible models based on the 40 variables in model (2.6)? Finding the best subset of predictor variables can be onerous due to the potential model space size 2 p 1. The best subset selection method also suffers from a lack of stability (Breiman 1996). 65 Predictor variables Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Sales 0.119 (0.001) *** 0.119 (0.001) *** 0.121 (0.001) *** 0.111 (0.001) *** 0.113 (0.001) *** 0.099 (0.002) *** Year -2.168 (0.703) ** -2.248 (0.698) ** -2.323 (0.596) *** -2.449 (0.584) *** -2.146 (1.406) January 7.509 (2.640) ** 7.629 (2.619) ** 6.795 (2.207) ** 7.091 (2.160) ** 5.503 (2.401) * February 5.656 (2.597) * 5.734 (2.576) * 5.064 (2.169) * 5.224 (2.122) * 4.484 (2.401) March 2.480 (2.603) 2.533 (2.582) 2.462 (2.172) 2.589 (2.125) 3.205 (2.267) April 0.290 (2.820) 0.278 (2.797) 0.329 (2.353) 0.320 (2.301) 1.807 (2.371) May 4.459 (2.820) 4.436 (2.797) 4.568 (2.353) 4.540 (2.301) * 6.475 (2.374) ** June 1.432 (2.833) 1.431 (2.810) 1.739 (2.364) 1.757 (2.312) 4.322 (2.417) July -1.130 (2.544) -1.191 (2.523) -0.566 (2.123) -0.631 (2.077) 2.388 (2.132) August 2.051 (2.555) 2.135 (2.535) 2.217 (2.132) 2.387 (2.086) 3.777 (2.308) September 0.716 (2.530) 0.667 (2.509) 0.847 (2.111) 0.800 (2.064) 1.792 (2.517) October -1.315 (2.530) -1.296 (2.509) -1.332 (2.111) -1.282 (2.064) -0.404 (2.437) November -2.971 (2.530) -2.977 (2.509) -2.802 (2.111) -2.786 (2.065) -2.065 (2.497) Product 1 (dash cover) -6.137 (1.373) *** -8.287 (1.142) *** -9.894 (1.900) *** Product 2 (seat cover) -2.608 (1.374) -4.688 (1.147) *** -6.956 (3.590) Retailer 1 29.670 (2.810) *** 29.760 (2.748) *** 18.930 (2.893) *** Retailer 2 -10.770 (2.216) *** -11.460 (2.170) *** -9.767 (2.558) *** Retailer 3 -17.520 (2.228) *** -18.300 (2.183) *** -15.050 (2.152) *** Retailer 4 -16.300 (2.193) *** -16.810 (2.147) *** -15.840 (2.072) *** Retailer 5 5.938 (2.212) ** 5.499 (2.165) * 6.958 (2.313) ** Retailer 6 -4.459 (2.208) * -4.566 (2.159) * -3.672 (2.113) Retailer 7 -6.106 (2.175) ** -6.380 (2.128) ** -5.026 (2.085) * Retailer 8 -4.334 (2.172) * -4.530 (2.125) * -3.662 (2.065) Retailer 9 -4.281 (2.171) * -4.447 (2.124) * -4.465 (2.033) * Retailer 10 0.202 (2.425) 1.304 (2.380) 0.425 (2.288) Retailer 11 -0.662 (2.271) 0.007 (2.223) 0.276 (2.136) Retailer 12 -1.001 (2.771) -1.073 (2.710) 0.163 (2.814) Workload 0.000 (0.003) SewerCnt -1.591 (2.301) SewingTaskCnt 1.097 (2.384) SewingDays -1.431 (0.853) BacklogDays 0.545 (0.714) ProductionDays 0.097 (0.253) CustomFabric% -8.025 (4.538) Logo% -6.793 (8.682) InspectionPreSewing% 35.990 (40.230) InspectionPostSewing% -1.052 (7.213) JointProduction% 1.721 (4.338) MultiProduct% -10.980 (3.107) *** LaggedReturns 0.052 (0.005) *** Table 2.5: OLS results for main effects models in the training set. Standard errors are shown in parentheses. ***, **, and * denote statistical significance at the 0.001, 0.01 and 0.05 confidence levels respectively. The model selection issue becomes even more challenging if we want to explore the effect of interaction terms to improve model performance, in which case we have a larger number of predictors in the model, and thus an even larger number of potential models. Even though the model performance is our primary con- cern, we are also interested in selecting a stable and sparse model for predicting returns and to implement 66 it in practice.In the next Section 2.5, we discuss multiple machine learning methods to address the afore- mentioned challenges in model selection and to achieve our goal of obtaining a parsimonious and stable model. 2.5. Incorporating Interaction Effects The main objective of this section is to explore higher order interaction terms to see if adding such terms to the main effects model helps improve prediction performance. To do this, we first specify a model with a large number of interaction terms in subsection 2.5.1, which creates a challenge in fitting the traditional OLS model to the data. To overcome this challenge, we introduce LASSO in subsection 2.5.2 as a method to select predictor variables, and present the prediction performance of two models selected by LASSO. Then, in subsection 2.5.3, we provide an interpretation of the “more sparse” LASSO model and its prediction performance for some high volume retailer product pairs. Finally, in subsection 2.5.4 we employ alternative methods and show a comparison of prediction performance among such methods. 2.5.1 Model Specification We restrict our attention to the following three categories of higher order interaction terms that may help improve prediction performance of the full main effects in model (2.6). As in model (2.6), we use vec- tor notationsMonth = (January; ;December) T ,Product = (Product 1 ; ;Product 3 ) T and Retailer = (Retailer 1 ; ;Retailer 13 ) T . I. Quadratic effect: We are interested in the effect of Sales 2 tij because we have shown that sales is a strong predictor of return volume in all the main effects models, and our residual analysis indicated a possible quadratic effect of sales on returns. 67 II. 2-way interaction effects: The 2-way interactions of predictor variables may help predict returns more accurately. For example, we can ask: Does the effect of sales volume on return volume vary depend- ing on the retailer? The interaction termSalesRetailer addresses this question. For another example, historical returns are shown to be significant and have positive correlation with returns (see Table 2.5). How- ever, the effect of historical returns could increase or decrease over time and this would get discovered by including the interaction termLaggedReturnsYear. 2-way interactions 3-way interactions 3-way interactions SalesYear SalesProductYear ProductYearLaggedReturns SalesMonth SalesProduct Month ProductYearMultiProduct% SalesProduct SalesProduct Retailer Product MonthLaggedReturns SalesRetailer SalesProductLaggedReturns Product MonthMultiProduct% SalesLaggedReturns SalesProductMultiProduct% ProductLaggedReturnsMultiProduct% SalesMultiProduct% SalesRetailerYear RetailerYearLaggedReturns ProductYear SalesRetailer Month RetailerYearMultiProduct% Product Month SalesRetailerLaggedReturns Retailer MonthLaggedReturns Product Retailer SalesRetailerMultiProduct% Retailer MonthMultiProduct% ProductLaggedReturns SalesLaggedReturnsYear RetailerLaggedReturnsMultiProduct% ProductMultiProduct% SalesLaggedReturnsMonth LaggedReturnsMultiProduct%Year RetailerYear SalesLaggedReturnsMultiProduct% LaggedReturnsMultiProduct%Month Retailer Month SalesMultiProduct%Year RetailerLaggedReturns SalesMultiProduct%Month RetailerMultiProduct% Product RetailerYear LaggedReturnsYear Product Retailer Month LaggedReturnsMonth Product RetailerLaggedReturns LaggedReturnsMultiProduct% Product RetailerMultiProduct% MultiProduct%Year MultiProduct%Month Table 2.6: 2-way and 3-way interaction terms The question that arises is, which interaction terms should we consider? We begin with our original set of predictorsSales,Year,Month,Product;Retailer used in model (2.5), and additionally con- sider the two predictors found to be significant at the 0.001 level in model (2.6) — MultiProduct%, LaggedReturns; then, we utilize all the 2-way interactions among these predictor variables to create a new set of predictor variables shown in Table 2.6. BecauseMonth,Product andRetailer are each a vector of 12, 3 and 13 dummy variables, we can see, for example,Product Retailer (here denotes 68 Cartesian product) creates 39 interaction terms. VectorV includes all the 2-way interaction terms in Table 2.6, and one can easily verify there are 337 predictor variables inV . III. 3-way interaction effects. We use 3-way interactions to achieve higher accuracy in returns predic- tion, and also to address questions such as: Is return rate of any particular retailer predicted to increase over time? Because return rate equals returns divided by sales, the interaction termSalesRetailerYear addresses this question. We consider potentially meaningful 3-way interactions among the above-mentioned key predictors — Sales, Year, Month, Product;Retailer;MultiProduct%;LaggedReturns. Vector W includes all such 3-way interaction terms shown in Table 2.6, and one can verify that there are 1,336 predictor variables inW . Finally, we specify a new model in equation (2.7) below, which includes all the interactions discussed above. Returns tij = 0 + 1 Sales tij + 2 Year t + t 3 Month t + i 4 Product i + j 5 Retailer j + T 6 U + 7 Sales 2 tij + T 8 V + T 9 W + tij (2.7) This model has a total ofp = 1;717 predictors, which comprise of 43 main effects, 1 quadratic term, 337 2-way interactions, and 1,336 3-way interactions. Recall that in the main effects model (2.6) we manually dropped 3 binary dummy variablesDecember,Product 3 ,Retailer 13 to remove redundancy, however we no longer do this for model (2.7) and will instead let LASSO select predictor variables for us. For these reasons, we have 43 main effects now, increased from 40 in model (2.6). Recall that we have a training set data sizeN = 1;140 and thus we havep > N, and we are effectively in a high-dimensional setting. For this reason, some type of penalty is needed to reduce the number of variables used in the model, and most importantly to perform a proper model selection and address problems such as spurious correlation, noise accumulation, and non-uniqueness of the linear model solution. To do these, in subsections 2.5.2 and 2.5.3 69 we employ LASSO, which enjoys an appealing theoretical property — the oracle inequalities (Bickel et al. 2009), meaning that under some conditions LASSO can recover the true model with high likelihood, given that the true model is sparse. Since most of the predictor variables in (2.7) are interaction terms, and not all of them are likely to play an important role in predicting returns, we expect sparse predictive models to fit our data well. To simplify the exposition, henceforth we useX l = (x l1 ; ;x lp ) T to denote all the predictor variables, andy l to denote the response variable in (2.7) forl = 1; ;N. 2.5.2 LASSO Analyses In this subsection, we focus on LASSO which solves the following convex optimization problem (2.8) to obtain the LASSO estimate ^ Lasso for data(X l ;y l ),l = 1; ;N. ^ Lasso = argmin ( 0 ;)2RR p 2 4 1 2N N X l=1 y l 0 p X m=1 x lm m ! 2 + p X m=1 j m j 3 5 : (2.8) Here is a tuning parameter, which assigns an appropriate level of penalty, and continuously shrinks co- efficients, and can force some to go to exactly zero to obtain a sparse model (see section 3 in Hastie et al. 2009). Therefore, it is vital to obtain good values of for successful model selection, and in our study we utilize the k-fold cross-validation (CV) method. Generally,k = 5 or10 works well in practice and for our study, we use the option k = 10 which is widely used in recent statistics literature. The reason we use CV instead of other measures such as AIC for model selection is to estimate the prediction error in the test set and compare different models (see section 5 in James et al. 2017) Notice that without theL 1 penalty term P p m=1 j m j, the LASSO problem (2.8) reduces to a standard OLS problem. With the the L 1 penalty term, the problem (2.8) is still a convex optimization problem, and this optimization problem can be solved efficiently using cyclical coordinate descent algorithms. It is important that all the predictors be standarized to have mean 0 and standard deviation 1, so that the different 70 scales of variables do not impact the optimization problem. To implement LASSO with 10-fold CV , we utilized R-package glmnet from Friedman et al. (2010). Figure 2.4: Selecting based on 10-fold CV . Model 7a Model 7b Number of predictors provided 1,717 1,717 Data size 1,140 1,140 Tuning parameter type min 1se Training set Tuning parameter value 1.809 4.378 Number of predictors selected 19 9 R 2 0.958 0.934 MSE 103.754 161.908 Data size 220 220 Test set R 2 0.928 0.930 MSE 177.815 171.824 Table 2.7: Prediction performance of 2 LASSO models. We show a plot of cross-validation fit with respect to different values of in Figure 2.4, where the two dotted vertical lines correspond to model fit for two tuning parameters: min (left) and 1se (right). Here min denotes the tuning parameter value that achieves the minimum mean CV error, whereas 1se represents a larger tuning parameter which leads to the smallest model such that mean cross-validated error is within one standard error of the minimum. In our study, we have min = 1:809 and 1se = 4:378 and, using these penalty values LASSO gives reduced models 7a and 7b in Table 2.7, which have only 19 and 9 predictors selected respectively out of a total of 1,717 predictors in equation (2.7). We find that the LASSO models 7a and 7b outperform the two best main effects models (2.5), (2.6) with respect to MSE andR 2 in both training and test sets; and the “more sparse” model 7b exhibits a more robust performance with a smaller gap in MSE between training and test sets (161.908 vs. 171.824), when compared to the “less sparse” model 7a (103.754 vs. 177.815.) Hence, we focus on the “more sparse” model 7b referenced as the LASSO model hereafter. 71 Period 34 35 36 37 38 39 Over the entire 6 test periods Model 5 206.460 331.218 243.908 163.228 308.388 297.050 257.709 MSE Model 6 126.230 242.053 202.965 93.578 224.846 251.791 189.386 LASSO 56.030 156.162 86.369 131.564 276.216 313.843 171.824 Model 5 0.833 0.748 0.945 0.941 0.896 0.833 0.895 R 2 Model 6 0.903 0.816 0.954 0.966 0.924 0.859 0.923 LASSO 0.960 0.881 0.980 0.952 0.907 0.824 0.930 Table 2.8: Prediction performance of three models (trained on periods 1 to 33) for each of the 6 future periods. In Table 2.8, we show the prediction performance of model (2.5), model (2.6), and the LASSO model (all trained on periods 1 to 33) in each test period from 34 to 39, and also over the entire 6 test periods. One can observe that if we apply these predictive models to the entire 6 test periods (34 to 39), then the LASSO model reduces the MSE of the baseline main effects model (2.5) by 257:709171:824 257:709 = 33:3%, and the MSE of the full main effects model (2.6) by 189:386171:824 189:386 = 9:3%. However, if we apply such predictive models only in the first test period 34, then LASSO model has a more pronounced advantage in prediction performance by reducing the MSE of model (2.5) by 206:46056:030 206:460 = 72:8%, and the MSE of model (2.6) by 126:23056:030 126:230 = 55:6%. To understand the robustness of the above finding, we conducted further analyses by using the data from periods 1 to p 1 to build the model, and then tested the model in period p for each prediction period p2f35;36;37;38;39g. The results are provided in Table 2.9. The LASSO model reduces the MSE of model (2.5) by 144:358126:085 144:358 = 12:7% to 206:4656:03 206:46 = 72:9% (average 43.0%) and reduces the MSE of model (2.6) by 126:424126:085 126:424 = 0:3% to 126:23056:03 126:230 = 55:6% (average 29.7%). Period 34 35 36 37 38 39 Model 5 206.46 319.520 252.153 144.358 282.045 256.877 MSE Model 6 126.23 204.381 209.460 126.424 217.225 246.960 LASSO 56.030 103.170 100.651 126.085 192.630 223.589 Model 5 0.833 0.756 0.943 0.948 0.905 0.856 R 2 Model 6 0.903 0.844 0.953 0.954 0.927 0.861 LASSO 0.960 0.921 0.977 0.954 0.935 0.874 Table 2.9: Prediction performance for each of the 6 future periods with models updated every period. 72 Because forecasting models are often implemented on a rolling horizon basis, it may be advisable to update the LASSO model every month and use it for the first test period for a more accurate prediction. Updating the LASSO model is easier than one might expect. The afrontmentioend R-package glmnet that implements LASSO is well-documented. All we need to change are the variable names and the data set names. It took 10 seconds to train and test the LASSO model in our desktop computer (Windows 10, Intel Core i7-8770 CPU, 8Gb RAM 2666MHz, 1Tb 970 Samsung Evo SSD). So, we believe model updating is not going to be onerous from a cost or time perspective. 2.5.3 Selected Predictors and Their Performance We first provide the 9 predictor variables and their coefficients in the LASSO model in Table 2.10. These can be interpreted as the strongest effects identified by LASSO to predict returns, and have been shown to achieve robust prediction performance both in the training and test data. It is noteworthy that the LASSO model chosen is very easy to implement in practice to predict future returns, as one only needs to compute Sales,LaggedReturns — which can be easily done in a spreadsheet — and use them along withYear and two retailer dummy variablesRetailer 1 ;Retailer 5 . Predictor category Predictors selected Coefficients main effects Sales 3.13E-02 LaggedReturns 3.12E-02 quadratic effect Sales 2 2.80E-05 SalesYear 1.31E-06 SalesRetailer 1 9.34E-03 2-way interactions SalesRetailer 5 7.61E-03 SalesLaggedReturns 6.89E-08 LaggedReturnsYear 2.67E-06 3-way interactions SalesYearRetailer 1 8.46E-07 Table 2.10: Predictors and coefficients selected by LASSO w.r.t. 1se 73 We first note that the coefficients of all 9 predictor variables are positive, and also that only two main effectsSales,LaggedReturns are selected by LASSO, which is quite different from main effects models (see Table 2.5.) Also notice that the LASSO coefficient ofSales is 0.0313, reduced from 0.099 in model (2.6) shown in Table 2.5. A key reason is that the effect ofSales is broken down and absorbed into quadratic termSales 2 , as well as 2-way and 3-way interaction terms which includeSales. As the coefficients ofSales andSales 2 are both positive, the LASSO model shows that the predicted returns are convex and increasing in sales. This suggests that the likelihood of returns increases for each incremental unit sold. One possible explanation is that production process capacity limitations are pushed as sales increase (for example, sewers are pressured to work faster) leading to more errors and thus returns. We then observe the 2-way interaction terms selected by the LASSO model.SalesYear suggests that as time goes by, sales has a greater effect on returns, that is, we can expect higher return rates year over year. This may be because as competition increases, retailers become more lax in accepting returns to please customers and keep them from going to competitors (e.g., see Montaldo 2019). Recall that onlyRetailer 1 (auto specialty store with a strong bargaining power) andRetailer 5 (warehouse club) carry liberal return policies, and the two interaction termsSalesRetailer 1 andSalesRetailer 5 show that for the same sales, these two retailers contribute more to returns than other retailers.SalesLaggedReturns indicates that when historical returns are higher, sales generates higher returns, i.e. higher return rate. Also we see fromLaggedReturnsYear that the impact of historical returns increases over time. We now pay attention to the only 3-way interaction terms selected by the LASSO model:SalesYear Retailer 1 . This shows that return rate of retailer 1, which carries a liberal return policy, has increased over the years more than for others. In a way, sales through this retailer are becoming “more problematic”. We end this subsection by comparing the prediction performance for the LASSO model vs. models (2.5), (2.6). We do this for the retailer and product pairs that have higher observed returns, because that is 74 where all three models show the best prediction performance. Figure 2.5 shows how well the three models predict returns for the future 6 periods for top 6 retailer-product pairs which account for 68.3% of total return volume. When compared to models (2.5), (2.6), we find that the LASSO model predicts returns closer to the observed returns when they are high enough. It is also interesting to observe that forRetailer 6 ;Product 1 the LASSO model predicts returns substantially better than models (2.5), (2.6) for the first test period, as is consistent with our discussion in the last paragraph of subsection 2.5.2. For low volume returns, the three models overall do not provide nearly as good a prediction performance. This is expected because such low volume returns have higher coefficient of variation. For completeness, we provide prediction results for all retailer product pairs for future 6 months in Figure 4.2 in section 4.2. 0 100 200 300 400 1 2 3 4 5 6 Returns (t, 2, 1) Horizontal axis denotes test period t = 1 to 6. Vertical axis is return volume in period t, product i, retailer j. Observed Model 5 Model 6 LASSO 0 100 200 300 400 1 2 3 4 5 6 Returns (t, 1, 2) 0 50 100 150 200 1 2 3 4 5 6 Returns (t, 1, 3) 0 50 100 150 200 1 2 3 4 5 6 Returns (t, 1, 5) 0 25 50 75 100 125 1 2 3 4 5 6 Returns (t, 1, 6) 0 25 50 75 100 1 2 3 4 5 6 Returns (t, 1, 7) Figure 2.5: Observed vs. predicted returns for some retailer product pairs (see colors online.) 75 2.5.4 Alternative Methods to LASSO Our goal in this subsection is to fit three alternative high-dimensional statistical models, and two tree-based statistical machine learning methods to our data and compare their prediction performance against LASSO. The results are provided in Table 2.11. LASSO LARS-OLS hybrid SCAD Elastic Net y Random Forest Gradient Boosting Data size 1,140 1,140 1,140 1,140 1,140 1,140 Training set R 2 0.934 0.961 0.947 0.934 0.990 0.996 MSE 161.908 94.888 129.674 161.908 25.036 10.606 Data size 220 220 220 220 220 220 Test set R 2 0.930 0.912 0.874 0.930 0.878 0.882 MSE 171.824 216.610 308.920 171.824 298.208 290.564 Table 2.11: Prediction performance of alternative methods against LASSO. Note y : Optimal Elastic Net is reduced to LASSO (see details on the next page.) High-dimensional machine learning methods In this subsection, we discuss three alternative high-dimensional statistical models. In our setting, they all select 9 predictors which we discuss in detail below. The first model we consider is called LARS-OLS hybrid (Efron et al. 2004) or OLS post-LASSO (Bel- loni and Chernozhukov 2013). This model involves two stages: in the first stage, it utilizes LASSO to select predictor variables only; in the second stage, it uses OLS to estimate the coefficients of the selected predictor variables — also known as debiasing. By construction, this method uses exactly the same 9 predictor variables as LASSO (see Table 2.10). The rationale for this approach is to reduce bias in the coefficients estimated by LASSO, because LASSO tends to shrink the nonzero coefficients towards zero compared to OLS. Similar to Efron et al. (2004), in our study we find that the LARS- OLS hybrid method achieves a smaller MSE in the training data set, compared to the LASSO model; however, it results in a large MSE in the test set. 76 Recall that LASSO is a convex regularization method with L 1 penalty. Next, we consider a con- cave regularization method — Smoothly Clipped Absolute Deviation (SCAD), which yields nearly unbiased estimators (Fan and Li 2001). Both LASSO and SCAD solve the following penalized least- squares problems to achieve sparse solutions: min ( 0 ;)2RR p 1 2N jjy 0 1Xjj 2 2 +jjp ()jj 1 (2.9) where we use compact notations for data (X;y), whereX 2 R Np is a design matrix,y2 R N is a response vector, andp () = p (jj) = (p (j 1 j);p (j 2 j); ;p (j p j)) T is a penalty for a vector of regression coefficients. Here, the penalty functionp (t) is defined ont2 [0;1) indexed by possibly more than one tuning parameter in. It can be observed that LASSO is a special case of (2.9) with one tuning parameter 0 and a penalty function p (t) := p (t) = t. On the other hand, SCAD utilizes two tuning parameters 0; > 2 and a penalty function defined as 0 ; (t) = n I(t)+ ( t) + ( 1) I(t>) o , which leads to p (t) :=p ; (t) = t (t) 2 2( 1) I(t>) I(t )+ 1 2 2 ( +1)I(t> ): Notice that p ; (t) is concave in t, and as ! 1, the penalty functions of SCAD and LASSO coincide for t > 0. To solve (2.9) for SCAD, one may search for the optimal values for ; over two-dimensional space, however it is shown that 3:7 is shown to be a robust choice (see section 2.1 in Fan and Li 2001). In our study, we considered 2 [3:5;4:0] in R-packagencvreg (Breheny and Huang 2011) with 10-fold CV , and find that the choice of has little impact on MSE in the training and test sets, and we choose = 3:9 which leads to 9 predictor variables, which is not surprising (see 77 a simulated example comparing SCAD against LASSO in Table 3 in Fan et.al. 2009). Like LARS- OLS hybrid, SCAD outperforms LASSO in the training data; however, LASSO still achieves smaller MSE in the test set in our study. A notable generalization of LASSO is the Elastic Net (Zou and Hastie 2005) which makes a com- promise between theL 1 (LASSO) andL 2 (Ridge) penalties, and solves the following optimization problem: min ( 0 ;)2RR p 1 2N jjy 0 1Xjj 2 2 + jjjj 1 + (1) 2 jjjj 2 2 (2.10) Notice that (2.10) involves two tuning parameters2 [0;1] and 0, and it is reduced to LASSO when = 1, and to Ridge regression when = 0. In some simulation studies (e.g., Table 1, Table 2 in Zou and Hastie 2005), Elastic Net is shown to outperform both LASSO and Ridge. To implement Elastic Net for our study, for a range of values between 0 and 1, we utilize the R-package glmnet with 10-fold CV to derive predictive models with respect to 1se as we do for LASSO. We find that = 1 leads to a model with the minimum MSE in the training set, therefore conclude that the optimal Elastic Net is reduced to LASSO, thus also selects 9 predictors. Tree-based machine learning methods We next consider two statistical machine learning methods based on trees, namely Random Forest (Breiman 2001) and Gradient Boosting (Friedman 2001), which may further improve prediction performance when complex, nonlinear structures are present in the data. Both of these methods are rooted in the ensemble idea, that is, producing multiple trees which are then combined to create a single model to improve the predic- tion accuracy. Unlike the aforementioned high-dimensional statistical methods that yield sparse predictive 78 models, the ensemble models based on Random Forest and Gradient Boosting can be difficult to interpret despite potential improvement in prediction accuracy. Random Forest. To produce multiple trees, this method employs bootstrap (Efron 1979) to createB training samples, and then grows a random-forest tree from each bootstrapped sample until a certain minimum node size (e.g., 5) is reached. Often the prediction performance improves sharply in the beginning as the number of trees increases, but the performance stabilizes when we have enough trees. We begin our analysis by using 500 trees denoted by B = 500 as recommended in Hastie et al. (2009). Growing the tree is done as follows: in each and every step of split in the tree, randomly choosem predictors out of allp predictors as split candidates, and then use only the best one out of these m predictors. A key idea behind the Random Forest method is the random sampling of split candidates, which results in a fresh sample of m predictors chosen at each split. Thus, the choice of m impacts the prediction performance and m becomes a tuning paramater and this parameter is optimized by cross-validation. We follow Bertsimas et al. (2016) and consider m values among fb 1:5 2 p 3 c;b 1:5 1 p 3 c = 859;b p 3 c; ;b 1:5 15 p 3 c = 1g. We use the minimum node size 5 which ensures no split when growing the tree if the node size is less than 5 (see an example in Breiman 2001). To avoid a potential overfitting issue, we conducted further numerical experiments with larger values of minimum node size from 5 to 50 similar to Figure 15.8 in Hastie et al. (2009) but did not see an improvement in prediction performance in the training set (see Table 4.11 in section 4.2.3). We also experimented with B from 500 to 2,500 but the prediction performance in the training set did not improve and remained quite similar (see Table 4.12 in section 4.2.3). We did not consider tuning another potential parameter, tree depth, because it is controlled by the minimum node size — the larger the minimum node size, the shallower the trees. 79 We implemented Random Forest in the R-package randomForest (Liaw and Wiener 2002) and found the optimal m = 859 by 10-fold CV . This method fits the training data set well, in particular, it achieves a very high R 2 = 0:990. In the test set, however, it obtains lower prediction accuracy as compared to LASSO. Gradient Boosting. This alternative tree-based machine learning method, in contrast to Random For- est, grows trees in a sequential way to reduce bias as described next. We first build up to B trees each withd+1 terminal nodes to the training data set, then repeatedly update each tree by adding a shrunken version of the new tree by a factor,2 (0;1). Note that the new tree is fit on the current residuals, not on the response variables. At each iteration, a fraction of the training data is sampled without replacement which is further used to grow the next tree. Because this is done in an adaptive way, the new tree depends on the previous tree. Finally, we combine all the trees to obtain an ensemble model as we did for Random Forest. As discussed above, we consider four key parameters to fit a Gradient Boosting model: d;;;B (see more details in section 10.12 in Hastie et al. 2009) and implemented Gradient Boosting in the R-package gbm (Ridgeway 2007). The parameterd is often called depth of the tree; is referred to as shrinkage parameter or learning rate; is the subsampling rate; the optimal number of iterationsB is determined by cross validation, which is also denoted as early stopping in some literature (e.g., see Zhang and Yu 2005, Yao et.al. 2007). We used = 1 because our set of predictor variables already includes higher-order interaction terms. We begin model fitting by exploring a range of small shrinkage parameters 2 [0:0005;0:1] as suggested by Hastie et al. (2009) with default subsampling rate, = 0:5 which tends to work well though perhaps is not optimal. For each we allow the algorithm to grow up to 5000 trees and for this value we derive the corresponding optimalB by 10-fold CV . For example, for = 0:1 we 80 find that the best cross-validation iteration is obtained in 1234 iterations, therefore the corresponding B = 1234. We find that in our data set < 0:01 leads to a poorer model fit in the training data sets. Therefore, we focus on values between 0.01 and 0.1 and further calibrate the model by tuning both parameters;. We provide details on the model calibration in Table 4.13 and Table 4.14 in section 4.2.4. The best calibrated model with respect to the training data set is obtained by = 0:1; = 0:4;B = 1140 which achieves MSE = 10.606 and R 2 = 0:996; however, in the test set it obtains MSE = 290.564 andR 2 = 0:882. This gradient boosting model performs slightly better than Random Forest in our study but does not outperform LASSO in the test set. To summarize, we find that the models with unbiased estimators (LARS-OLS hybrid, SCAD) fit the training set better than LASSO, but yield lower prediction accuracy in the test set, which suggests bias- variance trade-off as discussed above. The reduction of Elastic Net to LASSO indicates that the true un- derlying model is much more likely a sparse model as we expected at the end of Section 2.5.1. It is not surprising that the two tree-based methods (Random Forest, Gradient Boosting) fit the training set very well, however, their prediction performance in the test set suggests likely overfitting issues of these complex models despite the optimal choice of tuning parameters. In our setting, the LASSO model shows up as the best because it obtains the smallest MSE in the test set among all the models considered, and also because its MSE in the training and test sets are very close, which suggests that the LASSO model is a robust choice. 2.6. Robustness checks In our main analysis, we focused on training our predictive models on 33 periodsf1; ;33g and then testing the prediction performance for the 6 future periodsf34; ;39g. In this section, we evaluate the robustness of three predictive models: models (2.5), (2.6) and the LASSO model on different test sets. In 81 our study, we focus on empirically investigating whether the LASSO model consistently selects the same 9 predictors as in the main analysis shown in Table 2.10, and also check the sensitivity of prediction perfor- mance on such test sets. In subsection 2.6.1, we construct different test sets that contain 6 randomly chosen periods, for example,f3;13;25;34;35;37g. Next, in subsection 2.6.2, we check the robustness of the length of test period using alternative test sets with 5 and 7 future periods. For both of these scenarios, we compare the results with our finding in the main analysis. 2.6.1 Test on 6 random periods In this subsection, we construct a test set by randomly choosing 6 periods over the set of periodsf1; ;39g, and assign the remaining 33 periods to the training set. We repeat this process 4 times to create 4 such test sets to check if different random test sets lead to substantially different results. We obtain test peri- odsf3;13;25;34;35;37g for case 1,f10;15;19;27;28;34g for case 2,f4;8;15;25;29;38g for case 3, f2;5;17;27;30;33g for case 4. For each of the 4 cases, we build three predictive models using model (2.5), (2.6) and the LASSO model on the corresponding training sets, then test their prediction performance in each test set. The results are given in Table 2.12 for models (2.5) and (2.6), and Table 2.13 for the LASSO model. Main analysis Case 1 Case 2 Case 3 Case 4 model 5 model 6 model 5 model 6 model 5 model 6 model 5 model 6 model 5 model 6 Training set Data size 1,140 1,140 1,145 1,145 1,146 1,146 1,152 1,152 1,154 1,154 R 2 0.912 0.921 0.910 0.919 0.911 0.922 0.914 0.924 0.913 0.924 MSE 214.050 192.395 224.295 202.027 226.203 196.866 212.314 186.034 219.111 190.382 Data size 220 220 183 183 256 256 256 256 256 256 Test set R 2 0.895 0.923 0.917 0.941 0.912 0.922 0.897 0.912 0.901 0.912 MSE 257.709 189.386 188.735 134.561 175.970 156.695 248.364 213.197 209.560 187.039 Table 2.12: Comparison of 4 cases of random test periods against the main analysis for models 5 and 6. First, we find that the LASSO model selects the same 9 predictors in cases 1 to 4 as the ones found in the main analysis. This is consistent with the theory of LASSO’s consistent variable selection with high 82 probability that was established under the irrepresentable conditions (Zhao and Yu 2006, Meinshausen and Buhlmann 2006). Second, we observe that the prediction performance in the 4 cases shows some fluctuation for different test periods. Third, we find that the LASSO model outperforms both main effects models in the training and test sets in all 4 cases as in the main analysis. The advantage of the LASSO model over model (2.6) is not as substantial, when compared to model (2.5). For instance, the LASSO model reduces the test MSE in model (2.5) by 33.3% in the main analysis, and between 17.8% and 32.0% among 4 cases. By comparison, the LASSO model reduces the test MSE in model (2.6) by 9.3% in the main analysis, and between 4.2% and 18.2% among the 4 cases. Main analysis Case 1 Case 2 Case 3 Case 4 Data size 1,140 1,145 1,146 1,152 1,154 Training set 1se 4.378 5.273 4.619 5.245 4.824 R 2 0.934 0.924 0.932 0.925 0.928 MSE 161.908 189.366 172.608 183.696 180.537 Data size 220 215 214 208 206 Test set R 2 0.930 0.944 0.936 0.916 0.924 MSE 171.824 128.335 128.143 204.272 160.598 Table 2.13: Comparison of 4 cases of random test periods against the main analysis for the LASSO model. 2.6.2 Test on 5 and 7 future periods Our goal in this subsection is to understand if the choice of training set periods impacts the predictive mod- els and their performance. To do this, we consider two alternative analyses: train all three predictive mod- els on periodsf1; ;34g and test their performance on periodsf35; ;39g; then also train on periods f1; ;32g and test on periodsf33; ;39g. We show the results in Table 2.14. Similar to the main analysis, we find that the LASSO model continues to select the same set of 9 pre- dictors in the two new test sets containing 5 and 7 future periods. This indicates that the “sparse model” selection by LASSO is consistent and robust with respect to the different test periods we considered. 83 Main analysis Test on 5 periods Test on 7 periods model 5 model 6 LASSO model 5 model 6 LASSO model 5 model 6 LASSO Data size 1,140 1,140 1,140 1,177 1,177 1,177 1,104 1,104 1,104 Training set 1se NA NA 4.378 NA NA 5.484 NA NA 5.321 R 2 0.912 0.921 0.934 0.911 0.921 0.922 0.914 0.922 0.926 MSE 214.050 192.395 161.908 213.599 190.106 188.451 214.041 192.990 182.958 Data size 220 220 220 183 183 183 256 256 256 Test set R 2 0.895 0.923 0.930 0.903 0.926 0.918 0.886 0.914 0.927 MSE 257.709 189.386 171.824 259.609 197.879 218.545 259.903 197.624 166.056 Table 2.14: Comparison of 5 and 7 test periods against the main analysis (6 periods) for three models. Now we compare prediction performance using the measure MSE. In the main analysis, the choice of LASSO over models (2.5) and (2.6) achieved a reduction in the test MSE by 33.3% and 9.3% respectively. When we train our models on 34 periods and test on 5 periods, the LASSO model reduces the test MSE of model (2.5) by 15.8%. However, it increases the test MSE of model (2.6) by 10.4%. This indicates that LASSO does not outperform model (2.6) when the MSE was computed over the 5 test periods. Nonetheless, if we only consider the prediction performance in the first test period (trained on periods 1 to 34, tested on period 35 only) we can see from Table 2.8 in section 2.5.2 that LASSO still beats model (2.6) and reduces the MSE by 204:381103:170 204:381 = 49:5%. In summary, even though the full main effects model (2.6) is competitive in prediction performance compared to the LASSO model based on MSE computed over the entire set of test periods, we find that the LASSO model consistently outperforms both main effects models in the first few periods. This suggests that the LASSO model is the better choice when the predictive model is implemented on a rolling horizon basis. 2.7. Discussion In this paper, we developed data-driven models to predict future return volume and applied them to a firm that sells car accessories with large product variety. We explored various factors that could help predict re- turn volume — sales, time, product features, retailer, production process and resources, multi-product order 84 and historical returns, which are not exclusive to the particular firm in our study. We evaluated various main effects models and an interaction effect model with convex and concave regularization, to build prediction models that have good prediction accuracy and are easy to implement in practice and also provide a pre- liminary understanding of important factors associated with return volume. We also considered tree-based machine learning methods to improve on the prediction accuracy. We found that LASSO was effective in selecting a small number of interaction terms, which are useful in prediction, out of a large number of pos- sible candidates. LASSO identified a parsimonious model that achieved the highest accuracy in predicting future return volume. Sales show up as an important predictor across all models. In the LASSO model, we find that the pre- dicted return volume is convex and increasing in sales, suggesting that the likelihood of returns increases for each incremental unit sold. One possible explanation is that production process capacity limitations are pushed as sales increase (for example, sewers are pressured to work faster) leading to more errors and thus returns. The LASSO model also suggests that as time goes by, sales has a greater effect on returns, that is, we can expect higher return rates year over year. Historical returns and retailer fixed effects are found to be useful in predicting returns in all models. Historical returns capture recent trends in returns that are due to both defects and non-defects. This variable may capture the effect of trends in manufacturing defects and/or consumers’ impulse purchasing behaviors in recent months. Retailers may have different return policies which may influence returns due to non- defects, but not returns due to defects. The LASSO model selects only two retailers (auto specialty store and warehouse club) with liberal return policies in predicting returns, and only when these two retailers interact with other effects. The two-way interactions between retailers and sales indicate that both these retailers are predicted to yield higher returns rates than others. In addition, the three-way interaction term shows that the auto specialty 85 store, but not the warehouse club, is predicted to have increasing return rates over time. This should be of concern to Company A because this retailer accounted for 24.0% of total sales, and had the highest return rate at 13.6% between July 2012 and September 2015. Since returned products at Company A cannot be resold in most cases, they will have to carefully weigh the cost of such a high return volume from this retailer in determining the terms of trade with this retailer. They should also explore the reasons for the high returns with the retailer. It was expected ex ante that product type would be useful in predicting returns. The rationale was that the three products — dash cover, seat cover and car cover — have distinct features, designs, purchase/usage characteristics and they go through different manufacturing processes that may have varying defect rates. In fact, the results from the main effects models (see Table 2.5) show that dash cover products lead to significantly lower return volume than vehicle cover products. The LASSO model, however, did not select product type in predicting return volume. Similarly, the LASSO model did not select any of the production process and resources related variables, which were ex ante expected to be related to defects and useful in predicting returns. This suggests that the returns due to defects in the firm in our study may not be substantial, which is consistent with the finding in a study (Lawton 2008) that only about 5% of returns are due to true defects. We noticed in our analysis that products with logos or other types of customization appeared to have lower returns. However, we do not find them to be useful in prediction in any of the models, likely because sales of such highly customized products are very small at Company A. However, the lower return rate suggests that perhaps Company A could consider promoting such products to consumers. The inability to distinguish returns due to defect from other returns is one of the limitations of our study. Unfortunately, CompanyA does not systematically track the reasons for returns. If we are able to accurately identify returns due to defects, then we could ask interesting questions related to defects: whether defects 86 differ substantially among different products, whether production process and resources are important in predicting defects, etc. An important issue for future research is the potential costs and benefits of retailer return policies. For example, do we want retailers to strictly enforce return policy or should we allow retailers to be liberal in their return policy and in enforcing it? With stricter return policies and enforcement, there may be fewer returns, however, this may discourage consumers from making purchases. The trade-off between sales and returns is not immediately clear. A field experiment, which modifies return policies of select retailers and tracks subsequent changes in returns, may be able to address this question. When we can accurately extract defects among returns, we may be able to address some system design questions, by analyzing effects of production process and resources on defects. For example, should we increase random inspections by supervisors, if we find that such random inspections reduce defects? Another example is – do workers who speed up produce greater defects resulting in higher returns? 87 Chapter 3 Recycling Common Materials: Effectiveness, Optimal Decisions, and Coordination Mechanisms 3.1. Introduction The management of post-consumer products poses serious challenges, particularly when considering the large amount of municipal solid waste (MSW) generated by human activities. The MSW includes everyday items that we use and then dispose of, such as product packaging, bottles, or newspapers (see more at https://archive.epa.gov/epawaste/nonhaz/municipal/web/html/). On a global scale, the annual MSW generation in 2012 was estimated at 1.3 billion tons (short ton unless otherwise specified; 1 short ton = 2,000 lbs 0.907 metric ton), which is expected to increase to 2.2 billion tons by 2025 (Hoornweg and Bhada-Tata 2012). The U.S. Environmental Protection Agency (EPA) report on MSW—EPA (2016)—shows that the amount generated by Americans increased from 88.1 million tons in 1960 to 251.8 million tons in 2012, out of which EPA estimates that 132.5 million tons were disposed into landfills. The most represented MSW materials in the U.S. are paper (27%), plastics (12.8%), metals (9.1%), and glass (4.5%) (hereafter “common materials”)—all highly recyclable materials that account for more than half of MSW. Recycling effectiveness and recycling decisions for these common materials are the focus of our paper. While most people intuitively agree on the environmental benefits of recycling, there are currently op- posing views about overall desirability of recycling. One stream of opinions focuses on the environmental impact and argues that the waste reduction is the ultimate goal, and wants to push recycling rate to 100%, 88 which aligns with zero waste philosophy 1 . The others, however, are more concerned with the economic impact of recycling and propose that more waste should be sent to landfill or incinerators. For instance, al- though Tierney (2015) opines that recycling is costly (compared to landfill) and ineffectual, he acknowledges the potential benefits of greenhouse gas (GHG) emissions reduction. Nash (2016) reports that a decrease in the cost of primary materials makes secondary materials no longer cost competitive, resulting in 4 billion containers disposed in landfills over two years in California. We consider the entire product life cycle to determine the effectiveness of recycling. Specifically, we study three aspects of recycling: GHG emissions, operational costs, and aggregate costs, which include the social costs (the estimated economic societal dam- ages due to increased GHG emissions) and the operational costs. We focus on simple consumer products made of common materials (e.g., bottles or cans) prevalent in MSW. Three rates are generally used to measure recycling: collection rate (the fraction of products collected for recycling, also called recycling rate, see NAPCOR and APR 2015 for PET recycling), yield rate (the fraction recycled into secondary materials, see Venditti 2014 for paper recycling), and recovery rate (product of collection rate and yield rate, also called utilization rate). We find that such products exhibit collection rates between 30% and 70%, and yield rates between 60% and 100% (see more details presented in Table 4.21.) However, these numbers still do not provide a good indication of whether recycling is beneficial, which motivates us to first derive analytical conditions under which recycling is effective with respect to emissions, operational costs, and aggregate costs. We show the importance of the yield rate in determining the effectiveness of recycling (see, e.g., Pauck et al. 2014 for paper recycling.) Using EPA estimates for emissions data, the social cost factor of emissions, and collecting and calculating all relevant operational costs, we demonstrate that in our setting, recycling of common materials is both environmentally beneficial 1 http://zwia.org/standards/zw-definition/, http://www1.nyc.gov/assets/dsny/zerowaste/residents.shtml 89 and cost effective in the U.S., with the exception of glass, for which we achieve an environmental benefit but at a loss. 2 Following the abovementioned analysis, we ask a natural and fundamental question: Who should be in charge of recycling decisions? Our paper considers the collection and yield rates as recycling decisions, with the assumption that the decision maker may outsource actual recycling operations to a third party. Our benchmark case assumes that a social planner makes recycling decisions, and is interested in the entire life cycle of products, which includes primary resources extraction, manufacturing, transportation, consumption, landfill and recycling 3 . We then consider three centralized recycling scenarios in which recycling decisions are determined by one entity: a local government (hereafter, the government), a product manufacturer (here- after, the firm), and an independent recycling firm (hereafter, the recycler.) 1. When recycling decisions are made by the the government, its responsibility includes recycling and landfill and the related costs. Ideally, the local government and the social planner should have the same objective, but in reality the former is more concerned with its direct responsibility (Walls et al. 2003). We discuss this in detail in Section 3.5.2. 2. When recycling decisions are made by a firm (e.g., Stonyfield recycles plastic containers in collabo- ration with Whole Foods Market, https://www.preserveproducts.com/recycle/programs/gimme-5-pr ogram-171), the firm’s primary interests include the cost of primary and secondary materials as well as the cost of product manufacturing. We discuss this in detail in Section 3.5.3. 3. When a recycler makes recycling decisions, its primary concern is the price competition between the secondary materials that the recycler generates and the primary materials. Declines in primary 2 While our empirical results are restricted to the U.S., our analytical models can be applied to different regions and yield potentially different results, depending on the local emission and cost structures. For more information in EU setting, see, e.g., European Environment Agency 2017 report, EU Circular Economy Action Plan. 3 The federal government can play this role (if we consider the scope of the U.S.) or the California state government (if we restrict our attention to the State of California). 90 materials’ costs (e.g., PET) may put the recycler’s business in jeopardy (Johnson 2016). We discuss this in detail in Section 3.5.4. We characterize and compare the optimal recycling decisions under the abovementioned scenarios, in which one entity determines both the collection and yield rates. We then consider decentralized recycling decisions: namely, what if decisions on collection and yield rates are made by two different entities? For such decentralized recycling, we consider cases in which either the social planner or the government determines the collection rate, because the collection of post-consumer products is usually organized at the municipal level, while the recycling entity chooses the yield rate. We derive novel results and provide simple incentive mechanisms that could be offered to recycling entities to bring their efforts closer to socially optimal choices. The remainder of the paper is organized as follows. We complete the introduction by reviewing the relevant literature. In Section 3.3, we describe our supply chain models and derive analytical conditions for recycling effectiveness. In Section 3.4, we use U.S. emissions and cost data to investigate the implications for the common materials. In Section 3.5, we formulate centralized recycling decision problems and compare optimal decisions of different entities. We explore decentralized recycling and incentives to induce socially optimal recycling in Section 3.6. In Section 3.7, we present a case study of a proposed legislation on PET recycling, as well as some extensions in Section 3.8. We conclude our paper with managerial insights in Section 3.9. In the online supplemental materials, we present proofs in section 4.3.1 and a detailed derivation of emissions and costs in sections 4.3.2 and 4.3.3 respectively. 91 3.2. Literature Review Our research is related to six streams of literature: (1) recycling post-consumer products, (2) multi- objective models in sustainability, (3) environmental analysis of recycling, (4) cost analysis of recy- cling/remanufacturing, (5) social cost of emissions, and (6) waste management. In what follows, we review the relevant literature in each stream, and highlight our contributions. Many important research questions exist on the topic of recycling post-consumer products. For products such as electronics and appliances, the literature on Extended Producer Responsibility generally focuses on take-back legislation (e.g., Massarutto 2014, Zhou et. al. 2016), as well as the remanufacturing of end-of- use products—e.g., disposable cameras or photocopiers (Geyer et al. 2007). Unlike these papers, our study focuses on simple products made of common materials that are prevalent in MSW. For common materi- als recycling, many studies have examined problems such as dual stream vs. single stream collection and separation of recyclables (Fitzgerald et al. 2012), curbside recycling (Aadland and Caplan 2006), curbside vs. non-curbside recycling (Abbott et. al. 2017), collection planning (Teixeira et. al. 2004), vehicle routing for collection (Bruecker et. al. 2018), multi-period collection (Elbek and Wohlk 2016), sorting recyclable materials (Toso and Alem 2014), flexibility of recycling (Coratoa and Montinari 2014), and technological, design, marketing innovations aspects of recycling (D’Amato et. al. 2013, Zoboli et. al. 2014). In contrast to the abovementioned papers, we focus on two aspects of recycling decisions: collection of post-consumer products and recycling such products into secondary materials. The first part of our work belongs to a stream of sustainability research that uses multi-objective mod- els. Niakan et.al. (2013) focus on inventory and transportation costs and carbon emissions. Accorsi et.al. (2015) build a mixed-integer linear programming model to determine the optimal geographic location of the network with an application to the furniture industry in Italy. Govindan et.al. (2016) develop a fuzzy multi-objective optimization model with an application to a medical syringe and needle producer in Iran. By 92 comparison, our paper focuses on an environmental and economic analysis (considering both societal and operational costs) of various common materials’ recycling. We analyze conditions that lead to a reduction in long-term average emissions and costs, and demonstrate the importance of yield rate. We collect U.S. data for emissions and costs to confirm our abovementioned intuition on the environmental benefits of common materials’ recycling and show, through our analysis, that recycling is also cost-effective for all materials except glass. The research on recycling of common materials has often focused on environmental impact (without considering operational cost) of a single recycling cycle. For example, Craighill and Powell (1996) provide a life cycle assessment and economic evaluation of the environmental impact of a few common materials, and compare a single waste disposal cycle with a single recycling cycle. Unlike their paper, our model considers multiple recycling cycles, incorporates operational costs of the underlying systems, and provides conditions under which recycling is preferred cost-wise to not recycling. Several studies have considered the impact of recycling specific materials of interests. Schmidt et al. (2000) analyze the use of PET and glass bottles for packaging of carbonated soft drinks in Germany and consider the broader environmental impacts, such as water and wood consumption, in addition to emissions. However, their work does not include the underlying costs and realized collection rates. Perugini et al. (2005) quantify environmental performances of recycling of plastic containers in Italy and compare them with landfilling, incineration, and feedstock recycling. Their model focuses on a single post-consumer use cycle, does not consider operational costs, and finds that recycling is always environmentally preferable. Kuczenski and Geyer (2011) provide a comprehensive analysis of the resource requirements and environmental impact of PET bottles in California in 2009. They conclude that material recovery makes a small contribution to the environmental impact, as the majority of such impacts come from pre-consumer stages, and potential improvement could come from improved utilization of secondary materials. Although this conclusion is in line with our results, this study focused on a single cycle and did not consider operational costs. Our empirical analysis provides minimum 93 yield rates under which recycling is beneficial as well as estimates of primary materials costs under which recycling ceases to be profitable. Several papers in operations literature have studied recycling and/or remanufacturing in supply chains and focused on costs and profits, but have not considered the environmental impact. Savaskan et al. (2004) analyze the choice of the party responsible for collection in closed-loop supply chains with remanufactur- ing. They assume a fixed unit remanufacturing cost and define collection cost as a convex function of the collection rate (independent of the scale of operations.) Their paper concludes that the party closest to the customer (i.e., the retailer) is the best choice for collection from the manufacturer’s perspective. Atasu et al. (2013) expand on the model from Savaskan et al. (2004) by adding to the collection cost a component that captures economies/diseconomies of scale, hence, the collection cost could be convex or concave. They conclude that a manufacturer’s collection is preferable with diseconomies of scale. Both papers assume a price-setting retailer facing a price-sensitive demand. We consider recycling (instead of remanufacturing) of common materials with a price-independent demand and allow for different parties to be responsible for selecting collection and yield rates; in addition, we allow the unit recycling costs depend on yield rate (i.e., are not constant) and show that the recycler might be the best choice for the recycling entity under some set- tings. We believe that our assumption of price-independent demand is reasonable in a setting which focuses on post-consumer products, such as plastic and glass bottles, or aluminum and steel cans, that are found in MSW. Most of these products are packaging materials/containers for beverages (e.g., soda, water, wine) and canned foods (e.g., processed fruits, vegetables, fish), thus it is reasonable to assume that a manufacturer (e.g., Nestl´ e, Pepsi) will determine the quantity they need based on demand for their final product (drink or food), and not on the price of the container. We further validated this assumption with the management of one of the largest PET recycling firms in the U.S., who confirmed that their customers (mainly manufactur- ers of consumer beverages) are not sensitive to the price of recycled plastic resins. We want to note that our manuscript is different from the studies that analyze durable goods (e.g., electronics, cars), which are more 94 likely to be price-dependent (for a more detailed discussion and the scope of common materials, see EPA background 2015.) GHG emissions have an impact on agricultural productivity, human health, property damages from in- creased flood risks, and the ecosystem due to climate change. Knowlton et al. (2011) estimate that climate change-related events have caused health costs in excess of USD $14 billion. Despite such high social costs of emissions, there is limited work related to its impact on operational decisions. Aflaki and Netessine (2017) consider both system and emissions costs in renewable energy and show that charging a higher price for emissions could have a negative impact by discouraging investment. In our setting, an increase in the so- cial cost of emissions could cause an increase or decrease in recycling efforts depending on the relationship between emissions and cost structures. The second part of our paper is related to a stream of literature that analyzes waste management and its service providers. Our paper considers scenarios in which recycling decisions are made by a local govern- ment, a firm, or a recycler, and analyzes the optimal collection and yield rates for each case. Walls et al. (2003) provide an empirical look at waste management and recycling markets for 1,000 U.S. communities. Their data shows that government provisions dominate in central cities of metropolitan areas (e.g., in 70% of central city communities, government employees handle waste and recyclable collection). This supports our use of a government recycling model in addition to firm’s and recycler’s model. This paper concludes that political influence and regulations have little impact on a government’s choice of service provider, and that costs of providing service and transaction costs play a significant role in deciding whether to choose a public or private option. This is in line with our use of cost minimization as the government’s objective. Walls (2003) studies contracts between governments and waste management service providers and explores incentives for improving waste diversion. The paper discusses contracts for seven U.S. communities that mainly use private contractors and achieve high-waste diversion rates, finding that very diverse options can 95 be used (i.e., incentives for achieving a desired collection rate, ownership of revenues from sale of materi- als, and so forth.) In most cases, no direct incentives were used for achieving a desired collection rate. Our model suggests that such an incentive would be desirable, which could be indirectly implemented through a deposit/refund scheme. Palmer et al. (1996) develop a model of waste disposal and calculate the waste reduction in response to deposit/refunds, advance disposal fees, and recycling subsidies. They apply their model to common materials to evaluate the intervention level required to reduce waste by 10%, and con- clude that a deposit/refund policy dominates over the other options. Their model assumes a price-dependent demand, and as such, a deposit that acts as a tax, which increases the price and impacts the demand. We assume that demand is constant and not influenced by a deposit and show that under this assumption, the government might reduce the collection rate if it implements a deposit/refund fee with a firm or recycler, but that a social planner can implement a deposit/refund scheme to increase the collection rate chosen by the government. 3.3. The Model Suppose that a simple product made of a single material is either recycled into the same product (e.g., bottle) or diverted to a different product (e.g., non-bottle.) The life-cycle of a product starts with virgin (primary) input; by recycling a post-consumer product instead of sending it to a landfill, some additional quantity of secondary material is generated. We now introduce some notations. Definition 1. Let n2 N 0 be the number of recycling cycles (non-negative integer). We will use '(n) to denote a general impact function of the number of recycling cycles. Depending on the context, it can denote the amount of GHG emissions ('() = e()), the operational cost ('() = s()), or the aggregate cost— social cost of emissions plus operational cost('() =()). 96 u(n) denotes the total quantity of the product obtained by sending one product made from primary materials throughn recycling cycles. '(n) denotes the total value of' resulting from sending one product made from primary materials throughn recycling cycles. ' e (n) denotes the effective value of' from making one product, that combines manufacturing from primary and secondary materials. Formally,' e (n) := '(n) u(n) : m Primary Material Manufacturing & Transportation Product Manufacturing & Transportation Consumer’s Usage Transportation & Landfill v u l (a) Non-recycling case m Primary Material Manufacturing & Transportation Product Manufacturing & Transportation Consumer’s Usage Transportation & Landfill Recycling Operations Transportation To Product Manufacturing Facility Consumer’s Transportation For Recycling Outside Options v u l t c r t m o 1c c cy c(1)(1y) c(1y) (b) Recycling case Figure 3.1: A simplified product life cycle. Figure 3.1a depicts a cradle-to-grave life cycle in which a product is not recycled and goes directly to a landfill. We analyze the emissions and costs that occur through the life cycle of a product manufactured from primary materials and the notations for' from each process for a single product unit are defined in Table 3.1. Subscripts denote different processes in the life cycle:v denotes processes related to manipulation of primary materials,m denotes processes related to manufacturing and transportation of the product,u denotes processes related to the end consumer usage, andl denotes processes related to the landfill. We note here that for common materials under consideration we have' u = 0 (no cost or emissions.) 97 Asn = 0 without recycling, we haveu(0) = 1; '(0) =' v +' m +' u +' l ; ' e (0) = '(0) u(0) ='(0): Product Recycling (n> 0) Suppose that a product can be recycled, as depicted in Figure 3.1b. We usec2 [0;1] to denote the collection rate; thus, 1c portion is going to the landfill, corresponding to path u ! l. When c = 0, this case collapses to the cradle-to-grave model shown in Figure 3.1a. As an example, NAPCOR and APR (2015) shows a 31.2% collection rate for PET recycling in the U.S. in 2013. Supply Chain Member nodei ' at nodei Primary materials manufacturing and transportation v ' v Product manufacturing and transportation m ' m Consumer’s usage u ' u Transportation to landfill and landfill l ' l Consumer’s transportation for recycling t c ' tc Recycling operations r ' r Transportation to product manufacturing facility t m ' tm Outside option o ' o Table 3.1: Notation for' (per unit of product) The collected fraction, c, for recycling has three possible recycling outcomes: closed-loop recycling back to the same product (branchr! t m ! m) in the amount ofcy, wherey2 [0;1] captures the yield rate; open-loop recycling into outside options denoted byc(1y) for some2 [0;1] (branchr! o, see Section 3.8.1 for a PET example in California); and disposal of the remaining portionc(1)(1y) (branchr!l). Emissions and costs of the three abovementioned processes are captured in' r , which may depend on collection ratec, yield ratey, and the outside option; therefore, we assume' r = ' r; (c;y) 4 . The recycling decisions on collection and yield rates have implications on the costs (and emissions): for example, if a recycling firm provides more recycling stations or advertises to increase its collection rate, its 4 The reason we use as a subscript rather than a decision variable is that we assume that the outside option is exogenous to the recycling decision maker. For example, Freytas-Tamura (2018) reports China announced that it would no longer accept plastics and paper products for recycling, which is an outside option to the U.S. and is exogenous to the U.S. recycling decisions. 98 unit operational cost may go up. Similarly, if a firm wants to increase its yield rate, it may need to invest in new technology for recycling, which may increase its unit cost. Specifically, we make the following assumption: Assumption 3.3.1. We can decompose' r =' r; (c;y), the impact function of converting 1-unit of collected post-consumer material into secondary materials, into three processes as follows: ' c (c;y) =' c (c): the impact function of collecting c-unit out of every 1-unit of post-consumer material available. We assume this function is only dependent onc, increasing and strictly convex on[0;1]. ' p (c;y) =' p (y): the impact function of processing 1-unit of collected post-consumer material intoy-unit of secondary materials. We assume this function is only dependent ony, increasing and strictly convex on[0;1]. ' d; (c;y) =' d; (y): the disposal cost/diversion benefit of the remaining (1y)-unit of material (out of 1-unit of collected material). For some 2 [0;1], we assume that a fraction (1) goes to the landfill, while fraction goes to open-loop recycling:' d; (y) = (' l 0(1)' o )(1y), where ' l 0 ' l > 0 is disposal cost, and' o 0 is the benefit generated from selling the post-consumer product as input for outside products. Based on the above assumption on ' r; (c;y), it costs 1 c ' c (c) to collect 1 c c = 1 unit of post-consumer material for the downstream manufacturing process with recycled input. As a result, we have ' r =' r; (c;y) = 1 c ' c (c)+' p (y)+' d; (y) = 1 c ' c (c)+' p (y)+(' l 0(1)' o )(1y): To simplify the exposition, we use ' r in place of ' r; (c;y) and ' d (y) in place of ' d; (y) when the meaning is clear from the context. We now discuss other members of the supply chain from Table 3.1. We use subscripto to denote the outside option andt to denote the transportation processes. We assume that 99 ' v ;' m ;' u and' l are independent ofc;y (in models with and without recycling) 5 . Consumer transportation cost for recycling,' tc , in general depends on the collection rate,c: that is, when more places accept post- consumer products for recycling, the consumer’s transportation distance decreases. However, as our data indicates that boths tc ande tc represent a very small fraction of total operational costs and emissions (see Tables 3.2 and 3.3), these changes have little impact and are not considered here. We next describe how we derive the long-term average emissions or costs. Starting with a product made from primary materials, after n recycling cycles, the total quantity of the same product generated through this process is given byu(n) = 1+cy++c n y n = P n i=0 c i y i : The total impact function value (emissions/costs) generated during this process can be broken down as follows: From the cradle-to-gate cycle and from consumer usage (nodesv;m;u):' v +' m +' u : From product disposal (nodel):' l [(1c)++(1c)c n y n ] = (1c)' l P n i=0 c i y i : From recycling (nodest c ;r):(' tc +' r )(c++cc n1 y n1 ) =c(' tc +' r ) P n1 i=0 c i y i : From material process in the product manufacturing and from consumer usage (nodes t m ;m;u): (' tm +' m +' u )(cy++c n y n ) =cy(' tm +' m +' u ) P n1 i=0 c i y i : Assuming that we can recycle products infinitely, 6 whency6= 1, the total quantity of product, the total value of', and the effective unit value of' are: u(1) = lim n!1 u(n) = 1 1cy . 5 One may argue that the firm may invest in design to make products easier to recycle, which could increase the yield, therefore 'm may depend ony. Although this may be true for complex products manufactured from multiple materials, for single-material products considered here (e.g., bottles and cans) we assume that manufacturing does not impact the yield. 6 Technically, paper may not be recycled indefinitely, because in every recycling cycle the fibers become shorter (https://archive. epa.gov/wastes/conserve/materials/paper/web/html/faqs.html) and are mixed with new fibers during manufacturing. In the case of office paper, at the current yield rate of 60.29% (see Table 3.2), a marginal 2.9% of recycled fibers are retained after seven recycling cycles (https://archive.epa.gov/wastes/conserve/materials/paper/web/html/faqs.html). 100 '(1) = lim n!1 '(n) = ' v +' m +' u +(1c)' l +[(1c)cy' l +c(' tc +' r )+cy(' tm + ' m +' u )] 1 1cy . ' e (1) = '(1) u(1) = (1cy)' v +' m +' u +(1c)' l +c(' tc +' r )+cy' tm . One can verify' e (1) also holds forcy = 1. We now introduce our first result; the proof is straight- forward. Proposition 1. (Minimum yield rate for recycling effectiveness) When' vnet :=' v ' tm > 0 7 , recycling improves the value of' (i.e.,' e (1)<'(0)) if and only if y>x ' := ' r +' tc ' l ' vnet : (3.1) For simplicity, for our numerical analysis in Section 3.4 we assume closed-loop recycling, that is, = 0. As the use of outside options in general reduces costs (i.e., yields a lower value of' r ), values ofx ' obtained when = 0 represent the maximum lower bound for which recycling is effective. In our analytical results (starting from Section 3.5), we assume a general open-loop framework and allow to vary between 0 and 1. 3.4. Recycling Effectiveness In Subsections 3.4.1, 3.4.2, and 3.4.3, we discuss some practical implications of Proposition 1 from three perspectives—emissions, operational costs, and aggregate costs, respectively, for common materials shown in Table 3.2. To utilize the EPA emissions data (EPA Plastics 2015, EPA Paper 2015, EPA Metals 2015, EPA Glass 2015), we follow the same definition of materials used by the EPA. Because glass material does not 7 We verify that this condition holds for all of the common materials in our consideration in Tables 3.2 and 3.3. 101 have a stable intermediate state before becoming manufactured into a product (DOE 2002), we use “glass container” to represent both glass material and glass product. 3.4.1 Emissions In this subsection, we assume ' = e. We illustrate Proposition 1 by using EPA emissions estimates to derive the minimum yield rates that assure recycling reduces emissions for a few common materials. This is presented in Table 3.2, in which the emissions unit is MTCO 2 E (Metric TonCO 2 Equivalent) per ton. Observe that, because paper becomes degraded in landfills by anaerobic bacteria and producesCH 4 , office paper produces much higher GHG emissions than other materials during landfill operations, as compared to other materials. As a result, office paper recycling at any yield rate is environmentally beneficial. We note that recycling yields additional benefits not considered in our analysis. For instance, Kuczenski and Geyer (2011) and Craighill and Powell (1996) evaluate the impact of recycling on acidification and eutrophication potential. This implies that recycling is, in fact, environmentally beneficial even at lower yield rates than those presented in Table 3.2. Product Material e v e r e tc e tm e l x e Actual yield rate,y PET container PET resin 2.21 0.62 0.018 0.085 0.04 28.29% 69.68% HDPE container HDPE resin 1.54 0.38 0.018 0.075 0.04 24.44% 81.80% Office paper Paper pulp 0.53 0.53 0.000 0.000 1.75 0 % 60.29% Aluminum cans Aluminum ingot 7.46 0.27 0.018 0.008 0.04 3.35% 100.00% Steel cans Tinplate 2.74 0.76 0.018 0.148 0.04 28.48% 98.00% Glass container Glass container 0.46 0.14 0.018 0.010 0.04 25.12% 85.00% Table 3.2: Minimum Yield Rates With Respect to Emissions. 3.4.2 Operational costs We now consider the case' =s and analyze the operational cost of recycling,s r (c;y). The first component, collection cost s c (c), can include the recycling entity’s cost of providing recycling stations, transporting 102 materials to a recycling facility, advertising, enforcement, or a monitoring cost. Following some examples from literature (Savaskan et al. 2004, Geyer et al. 2007, Atasu et al. 2013), we assume that the cost can be represented by an increasing, strictly convex function. 8 This seems reasonable, as increasing the collection rate after reaching a certain threshold (say, from 70% to 80%) might require a significant cost increase, and it might be practically impossible to achieve a 100% collection rate. Similar logic applies to the second component, processing costs p (y): in this case, achieving a yield rate close to 100% might be very costly or even impossible. The assumption for the last component, disposal cost/diversion benefits d (y), implies that the unit landfill cost does not exceed the cost of handling the non-recycled portion of material, and that material not used in closed-loop recycling can be used in the manufacturing of outside products. Note that it might be desirable for the recycling entity to use a lower value ofy (or even to sety = 0) when the outside option is profitable. In Table 3.3, we present the values of lower bounds for some common materials, in which unit is USD per short ton (see section 4.3.3 for details). While emission data were mostly obtained from EPA reports, no such aggregate source exists for costs, thus our numbers come from a variety of sources. For all common materials except glass, the actual yield rate exceeds the minimum yield rates, therefore, recycling is effective in reducing the operational cost. With glass, the unit operational cost of the primary material is very close to the corresponding cost of the recycled material, and this increases the lower bound. This phenomenon is confirmed in practice, in which some municipalities opt out from recycling glass (e.g., Spartanburg, SC; 8 Affine functions may also be reasonable, but in our setting lead to less interesting and less realistic corner solutions for optimal collection decisions. We also explored a family of more general functionsf(x), which achieves the minimum value of first derivative at some point,x2 [0;1] (x = 0;1 each corresponds to convex, concave functions respectively); however, the main results and conclusions of our paper do not change. 103 Brigham, UT; Gwinnett, GA 9 ; and so forth.), while others collect glass, to prevent it from ending up as litter, and then send it to landfill (e.g., Denver, CO; Chattanooga, TN; Atlanta, GA 10 ; and so forth). Product Material s v s r s tc s tm s l x s Actual yield rate,y PET container PET resin $1,733.49 $794.32 $5.43 $154.19 $90 44.94% 69.68% HDPE container HDPE resin $1,421.05 $818.00 $5.43 $136.05 $90 57.08% 81.80% Office paper Paper pulp $784.92 $506.47 $0.00 $0.00 $90 53.06% 60.29% Aluminum cans Aluminum ingot $1,519.51 $655.16 $5.43 $16.11 $90 37.95% 100.00% Steel cans Tinplate $1,098.28 $641.90 $5.43 $298.01 $90 69.64% 98.00% Glass container Glass container $1140.67 $1148.04 $5.43 $17.33 $90 90.67% 85.00% Table 3.3: Minimum Yield Rates With Respect to Operational Costs Note that the abovementioned conclusion may change if the cost of primary materials decreases. The price of PET and HDPE fluctuates with oil prices, and an additional decrease in the primary materials cost can reverse the relationship, that is, recycling may cease to be cost-effective. It is easy to verify that when the cost of the primary PET material drops to $1,172.82 (a decrease of 32%), to $1,032.46 (a decrease of 27%) for HDPE, and to $690.73 (a drop of 12%) for office paper, recycling of respective materials ceases to be profitable with the current yield rate. This is in line with several media reports (Daniels 2016, Nash 2016). 3.4.3 Aggregate costs—operational and emissions costs We use to denote the unit social cost caused by emissions (i.e., social cost factor), and use an estimate = $109 per MTCO 2 E (U.S. Government 2013) to account for societal damages due to increased emissions. We denote the aggregate cost by' i = i := s i +e i , wheres i denotes the operational cost at processi, 9 http://americanrecycler.com/8568759/index.php/news/glass/1572-market-for-recycled-glass-remains-strong-despite-challeng es, http://brighamcity.utah.gov/curbside-recycling.htm, http://www.gwinnettcb.org/glass-recycling-facts/ 10 http://www.westword.com/news/most-colorado-glass-doesnt-get-recycled-but-thats-starting-to-change-6833033, http://www.timesfreepress.com/news/local/story/2015/aug/14/glass-not-getting-recycled-chattanoogas-new-s/319805/, http: //www.myajc.com/news/local-govt--politics/metro-atlanta-recyclers-reject-glass-ship-landfills/Nd82esxPLUTvCb6963WyWJ 104 ande i denotes the emission-induced social cost from the same operation. Table 3.4 presents the minimum yield rates for this model 11 . Product Material v r tc tm l x Actual yield rate,y PET container PET resin $1,974.38 $862.30 $7.35 $163.46 $94.36 42.81% 69.68% HDPE container HDPE resin $1,588.91 $859.46 $7.35 $144.23 $94.36 53.47% 81.80% Office paper Paper pulp $842.69 $564.30 $0.00 $0.00 $280.75 33.65% 60.29% Aluminum cans Aluminum ingot $2,332.22 $684.81 $7.35 $17.20 $94.36 25.82% 100.00% Steel cans Tinplate $1,396.94 $724.79 $7.35 $314.14 $94.36 58.90% 98.00% Glass container Glass container $1,190.70 $1,165.37 $7.35 $18.42 $94.36 88.15% 85.00% Table 3.4: Minimum Yield Rates With Respect to Aggregate Costs When > 0, we can show minfx e (c;y);x s (c;y)g < x (c;y) < maxfx e (c;y);x s (c;y)g by Lemma 1 (see section 4.3.1.) Notex s (c;y) = x (c;y) when = 0, showing that the minimum yield rate for the aggregate cost model increases in whenx e (c;y) > x s (c;y) and decreases whenx e (c;y) < x s (c;y). In other words, whenx e (c;y) is low, the emission effect dominates the cost effect (i.e., recycling is beneficial for the environment even at a low yield), and a higher reduces the minimum yield rate for the aggregate cost model—which holds for all considered materials. If the cost effect dominates the emission effect, then an increase in makes recycling desirable at a higher yield rate. 3.5. Centralized Recycling Decisions In this section, we study optimal recycling decisions made by one entity: the social planner in subsection 3.5.1, the government in subsection 3.5.2, the firm in subsection 3.5.3, and the recycler problem in subsection 3.5.4. We then compare their optimal choices in subsection 3.5.5. 11 Our model can be modified to incorporate the case in which the social cost of emissions increases by a same factor, say>1, every recycling cycle, as long ascy<1: as the cost of, say, emissions from landfill in the first round is(1c)e l , in the second round (1c)e l cy, and so on, the total social cost of emissions from landfill can be written as (1c)e l P 1 i=0 i c i y i . Consequently, the total effective aggregate cost from landfill can be written as (1c) s l + 1cy 1cy e l —the only modification required is to replace by 1cy 1cy . 105 General Emissions Operational Aggregate Supply chain member Function Cost Cost ' v e v s v v Primary material manufacturing and transportation ' m e m s m m Product manufacturing and transportation ' u e u s u u Consumer’s usage ' l e l s l l Transportation to landfill and landfill ' tc e tc s tc tc Consumer’s transportation for recycling ' tm e tm s tm tm Transportation to product manufacturing facility ' vnet =' v ' tm e vnet =e v e tm s vnet =s v s tm vnet = v tm See definitions of' v and' tm above ' r; (c;y) e r; (c;y) s r; (c;y) r; (c;y) Recycling operations ' c (c) e c (c) s c (c) c (c) Collectingc-unit out of every 1-unit of post-consumer material ' p (y) e p (y) s p (y) p (y) Processing each unit of collected material intoy-unit of secondary materials ' d; (y) e d; (y) s d; (y) d; (y) Disposal/diverting of remaining(1y)-unit ' l 0 e l 0 s l 0 l 0 Disposal of 1-unit of material ' o e o s o o Diversion of 1-unit of material to outside option Table 3.5: Emissions, Operational Cost, and Aggregate Cost (per unit of product) Notation Definition e e (1) Long-run effective unit GHG emissions to society with recycling s e (1) Long-run effective unit operational cost to society with recycling (c;y) Long-run effective unit aggregate cost to society with recycling G=F=R (c;y) Long-run effective unit aggregate cost when recycling is done by government/firm/recycler x e=s= (c;y) Minimum yield rate for reduction of emissions/operational cost/aggregate cost Optimal collection rate Optimal yield rate Recycling by Optimum criteria c y social planner (first-best) Minimizing aggregate cost c G=F=R y G=F=R government/firm/recycler Minimizing aggregate cost Table 3.6: A summary of definitions for centralized recycling. We provide a summary of notation used to derive the effective cost to the society and carried over from previous sections in Table 3.5, where c and y denote collection rate and yield rate, respectively, and a summary of definitions on the long-run effective emissions and costs for different entities in Table 3.6. 106 3.5.1 Social planner’s problem We assume that the social planner is concerned with overall societal costs, which are incurred at every stage. Effective cost to the society can be calculated as (c;y) :=s e (1)+e e (1) = 1cy;1;1;1c;c;c;cy h s v ;s m ;s u ;s l ;s tc ;s r; (c;y);s tm | + e v ;e m ;e u ;e l ;e tc ;e r; (c;y);e tm | i = 1cy;1;1;1c;c;c;cy v ; m ; u ; l ; tc ; r; (c;y); tm | = 1 (c)+c 2 (y)+ 3 (3.2) where 1 (c) := c (c)+c[ tc l ]; 2 (y) := p (y)+ d; (y)y vnet = p (y)+( l 0(1) o + vnet )(1y) vnet ; and 3 := v + m + u + l , which is independent ofc andy. Based on (3.2), the first-best decision for the social planner’s problem is obtained by solving min (c;y) = 1 (c)+c 2 (y)+ 3 subject to 0c 1; 0y 1: (3.3) Under a simplifying assumption on the minimum cost of consumer’s transportation for recycling, tc := c for some> 0, we have the following result. Proposition 2. (Optimal collection and yield rates in the social planner’s problem) There exist optimal collection and yield rates, c and y , that minimize the social planner’s cost in problem (3.3), and each solution is unique. The optimal yield rate is non-decreasing with respect to l 0(1) o + vnet , and the optimal collection rate is non-decreasing with respect to l 2 (y ). The details on how to derive the optimal collection rate, c , and yield rate, y , can be found in the proof of Proposition 2, given in section 4.3.1. In Figure 3.2 below, we provide an illustration of the above results. Implications of Proposition 2 are rather intuitive. If the benefit from recycling the original product 107 into outside products increases (larger o ), the social planner favors open-loop recycling; on the other hand, if the cost of primary materials increases, the social planner wants to increase the yield in the closed-loop recycling. Similarly, if disposal to landfill becomes less costly, or if the cost benefit of recycled materials decreases, the social planner has less incentive to collect material for recycling. 1 0 p 1 (0) l 0(1) o + v net 0 0 p 1 (1) y (a) Optimal yield rate,y 1 0 c 1 (0) l 2 (y ) 0 0 c 1 (1) c (b) Optimal collection rate,c Figure 3.2: An illustration of optimal collection and yield rates in the social planner’s problem. We first analyze costs in two local optimization models—the government’s problem and the firm’s prob- lem. In both cases, although we assume that the entity responsible for recycling determines the collection and the yield rate, it can outsource the actual process to a third party. We then consider a scenario in which a recycler is in charge of recycling. As we assume that the recycling entities can outsource the actual process to a third party, we use the same costs in all cases and compare the recycling efforts in all scenarios. Our models in this section are consistent with Savaskan et al. (2004) and Atasu et al. (2013). Both papers compare three models, with the manufacturer, the retailer, or the recycler responsible for recycling, respectively (they do not consider the government). Unlike our research, both of these papers assume price- dependent demand and analyze the model with remanufacturing. However, similar to our assumptions in this section, they assume that the recycling entity determines “the fraction of current generation products remanufactured from returned units,” which corresponds to recycling ratecy in our model, and use the same cost functions across different models. In addition, while their models only consider operational cost, we also study the environmental impact. 108 3.5.2 Government’s recycling problem In this section we assume that the local government is in charge of recycling decisions. In theory, the gov- ernment should have the same objective as the social planner (that is, to minimize the societal cost), but in practice the government is often concerned with minimizing its own cost (organizing the landfill and recy- cling operations—nodesl andr in Figure 3.1b). This view is backed by Walls et al. (2003), who conclude that local governments are primarily motivated by cost. Thus, the effective cost of government, when it is responsible for recycling, can be found as G (c;y) := 1c;c l ; r; (c;y) | = G;1 (c)+c G;2 (y); (3.4) where G;1 (c) := c (c)+(1c) l and G;2 (y) := p (y)+( l 0(1) o )(1y): Based on expression (3.4), to minimize the cost, the government solves min G (c;y) = G;1 (c)+c G;2 (y) subject to 0c 1; 0y 1; (3.5) which leads to the following result. Proposition 3. (Optimal collection and yield rates in the government’s problem) There exist optimal col- lection and yield rates,c G andy G , that minimize the government’s cost in problem (3.5), and each solu- tion is unique. The optimal yield rate is non-decreasing with respect to the disposal cost/diversion benefit, l 0(1) o , and the optimal collection rate is non-decreasing with respect to the cost difference between landfill and recycling, l G;2 (y G ). Our conclusions in this case are similar to those in the social planner’s problem: if the benefit from diverting material into an outside product increases (larger o ), the government prefers to use open-loop recycling. 109 If landfill costs decrease, or if the cost of recycling increases, the government has less incentive to collect material. One significant difference (compared to the social planner’s choices) is that the government’s decisions are not impacted by primary material cost. 3.5.3 Firm’s recycling problem We now assume that the firm is in charge of recycling decisions and that the relevant costs occur in nodesv, m,r andt m in Figure 3.1b. The effective cost can then be found as F (c;y) := 1cy;1;c;cy v ; m ; r; (c;y); tm | = F;1 (c)+c F;2 (y)+ F;3 (3.6) where F;1 (c) := c (c); F;2 (y) := p (y) + ( l 0(1) o + vnet )(1y) vnet ; and F;3 := v + m ; which is independent ofc andy. It follows from (3.6) that, to minimize its cost, the firm solves min F (c;y) = F;1 (c)+c F;2 (y)+ F;3 subject to 0c 1; 0y 1; (3.7) which leads to the following result. Proposition 4. (Optimal collection and yield rates in the firm’s problem) There exist optimal collection and yield rates,c F andy F , that minimize the firm’s cost for problem (3.7), and each solution is unique. The optimal yield rate is non-decreasing with respect to l 0(1) o + vnet and the optimal collection rate is non-increasing with respect to F;2 (y F ). The main difference between this result and Proposition 3 are parameters that impact the rate change. Similar to the social planner, the firm is concerned with the primary material costs and the outside option, which influence the firm’s choice of yield rate. However, as the firm is not responsible for product disposal, its decisions about collection rate are not impacted by landfill cost changes. 110 3.5.4 Recycler’s problem We now assume that an independent party is in charge of recycling decisions. Driven purely by its benefit, this recycler shuts down operations if its operates at a loss. Suppose the firm is willing to pay a certain fraction, , of the primary material cost to obtain the secondary material and have it transported to the manufacturing facility. If the firm is willing to pay a premium for the secondary material, we have > 1; otherwise 1. 12 Recall that the unit cost of secondary material is 1 y r (c;y), and its unit cost of transportation to the firm is tm . Therefore, the recycler operates when 1 y r (c;y) + tm v . Unlike previous problems that considered multiple recycling cycles, we define the recycler’s problem as a single period setting in the sense that at the beginning of each period, we have 1 unit of post-consumer product available, out of which c-unit is collected, and cy-unit of secondary material is generated. The firm then combines cy-unit of secondary material with (1cy)-unit of primary material to manufacture 1 unit of product, which goes to the consumer and, after usage and disposal/recycling, the second period begins. This contrasts with the previous scenarios in which the social planner and the firm were both concerned with a possible reduction in the primary material consumption due to the use of secondary material over multiple recycling cycles, or when the social planner and the government were concerned about the amount of material diverted from the landfill over multiple recycling cycles. In this scenario, the recycler is only concerned with the amount of secondary material it can obtain in any given recycling cycle, hence it is enough to consider a single period. The recycler, when it is responsible for recycling, wants to maximize its benefit,cy v tm 1 y r (c;y) =cy v cy tm c r (c;y): Note that max cy v tm 1 y r (c;y) = c (c)c p (y)+ l 0 + v tm (1y)( v tm ) subject to 0c 1; 0y 1; 12 With the exception of office paper, discussed later, > 1 is rarely observed in practice. Our discussion with a PET recycling firm in California did reveal, however, that some companies pay a premium for recycled PET. 111 hence the recycler solves min R (c;y) := c (c)+c p (y)+ l 0(1) o + v tm (1y)( v tm ) subject to 0c 1; 0y 1: (3.8) Proposition 5. (Optimal collection and yield rates in recycler’s problem) There exist optimal collection and yield rates,c R andy R , that maximize the recycler’s benefit in (3.8), and each solution is unique. The optimal solutions are non-decreasing with respect to l 0(1) o + v tm . The implication for the recycler is thus very similar to the firm’s recycling decisions discussed in Propo- sition 4. 3.5.5 Comparison of Optimal Recycling Decisions We now compare the optimal recycling efforts of all the abovementioned centralized decisions. Proposition 6. (Optimal rates comparison) Let := p(y R )p(y )(y R y )( l 0(1)o+v net ) v > 0. Then, we have the following results: 8 > > < > > : > 1++ l v 2 1;1++ l v i 1 9 > > = > > ; () 8 > < > : y R >y y F >y G ; c R > maxfc ;c F ;c G g; y R >y y F >y G ; c c R > maxfc F ;c G g; y y F y R >y G ; c >c F c R : This result shows that the optimal yield rates chosen by the firm and by the social planner coincide and exceed the level chosen by the government; that is, y y F > y G . This is good news, as we need no additional mechanisms to induce an optimal yield level under the firm’s problem. The relationship between optimal collection levels chosen by the firm, the government, and the social planner depends on landfill and primary materials costs. Most notably, we can show that when vnet G;2 (y ) G;2 (y G ) y , thenc F < c 112 c G ; that is, when the cost of primary material is low, the government, which cares only about landfill and recycling costs, chooses a collection rate higher than the socially optimal one in order to curb its landfill cost. When the firm is willing to pay a premium for secondary materials, the recycler always chooses the highest yield rate; if the premium is high enough, the recycler also chooses the highest collection rate. In most settings (with the exception of office paper), the secondary materials are sold at a lower price then the primary materials (see Table 3.4), and the recycler attains lower recycle and yield rates than the firm. When a “green” firm pays too much for secondary materials to the recycler, the social planner may resort to taxing the secondary material to induce the recycler to lower its price, which may curb the optimal rates to their first-best level. This would effectively penalize the recycler for making excessive recycling efforts and discourage the firm from paying a premium for secondary materials. We now compare our results to those from Savaskan et al. (2004). 13 Let us denote the retailer by the subscript ret. Savaskan et al. (2004) assume a convex collection cost and constant remanufacturing cost, and conclude thatc y >c ret y ret >c M y M >c R y R . In our model, the processing cost is not constant, and this relationship does not always hold. More precisely, when the cost of secondary material is high enough (high ), we can havec R y R >c y >c M y M . As previously mentioned, our analysis assumes that the unit cost functions remain unchanged regardless of the entity responsible for recycling, as each recycling entity can outsource the actual recycling process to a third party. Now, if we assume that some of the recycling entities have more options than others and are able to achieve lower cost due to, say, economies of scale, the abovementioned results could change. For instance, if we assume that the firm cannot achieve the same economies of scale as the social planner, the firm would face a steeper processing cost and consequently select a lower yield rate to reduce this cost. In 13 Atasu et al. (2013) allow for economies/diseconomies of scale in collection costs (represented by concave and convex compo- nent of the collection cost, respectively), and show that with economies of scale, the optimal recovery rate (product of collection rate and yield rate) is always 0 or 1. As we do not consider concave costs, we limit our comparison to Savaskan et al. (2004), although the total collection cost may be convex even with economies of scale. 113 such a case, we can havey F < y . This type of analysis is beyond the scope of this paper and therefore omitted. 3.6. Decentralized Recycling Decisions and Coordination Mechanisms In this section, we assume that independent parties choose the collection rate and the yield rate. This sce- nario differs from Savaskan et al. (2004) and Atasu et al. (2013) and is closer to what can be observed in practice (compared with the centralized optimization problems discussed in the previous section). However, as will be seen in our analysis, we use results from centralized optimization models to obtain insights about decentralized cases. We assume that one entity (the social planer or local government) determines the desired minimum collection rate, and after observing this value, the entity responsible for recycling chooses its yield rate. In practice, it is more likely that the local government will determine the collection rate by making decisions about curbside recycling containers, drop-off recycling zones, recycling centers, and so forth, but we con- sider both options for completeness. We use backward induction and start with the second decision, the optimal yield rate. Recall that we assume that recycling cost is separable inc andy. As such, the optimal yield rates correspond to those obtained in centralized optimization models—y G ,y F , andy R —if the local government, the firm, and the recycler are responsible for recycling, respectively. The entity responsible for determining the collection rate anticipates this value when it makes its decision. First, suppose that the social planner determines c. As we have previously shown, the firm always chooses the same yield rate as the social planner, and we obtain the following: Theorem 1. (Social planner selects the collection rate) Suppose that the social planner chooses the collec- tion rate. Then, selecting the firm as the entity responsible for recycling leads to socially optimal decisions without implementation of additional coordinating mechanisms. 114 Thus, the social planner prefers to have firms responsible for recycling. This preference may not always be possible, so we discuss the social planner’s options under other scenarios in the forthcoming subsections. Next, suppose that the government chooses the collection rate. As we have shown in Proposition 6, government always selects the lowest yield rate (when compared with the firm or the recycler). As a result, if the firm or the recycler selects the yield rate (that is, wheny =y F ory =y R ), then G;2 (y) G;2 (y G ). In response to this increase, the government would select the collection rate lower than c G when it does not select the yield rate (that is, ify > y G ). Recall that our discussion of Proposition 6 concluded that the government chooses collection rate which exceeds the first-best when the cost of primary materials is low. Thus, allowing the firm or the recycler to select the yield rate in such a case reduces the collection rate chosen by the government and results in an improved systemwide performance. However, whenc G <c , choosing y >y G would move the collection rate chosen by the government even further away from the first-best, so it is better to let the government select the yield rate as well under this scenario. This is summarized in our second theorem below. Theorem 2. (Government selects the collection rate) Suppose that the government chooses the collection rate. Then, when vnet < G;2 (y ) G;2 (y G ) y ; systemwide performance can be improved if recycling is dele- gated to the firm or to the recycler; otherwise, society benefits if the government also takes over recycling responsibilities. Theorem 2 and the data collected (see Table 3.4) suggest that when the government determines the collection rate, paper and glass might be ideal for recycling by the firm or by the recycler. For reader’s convenience, we provide a summary of notations used in this section in Table 3.7. 115 Notation Definition I G;y =I R;y Incentive to government/recycler for improving the yield rate y G;I =y R;I Government’s/recycler’s yield rate in response to incentive I G;c Incentive to government for improving the collection rate c G;I Government’s collection rate in response to incentive c G;d Government’s collection rate in response to deposit d Deposit/refund collected by the government D Deposit/refund collected by the social planner Table 3.7: A summary of notations for decentralized recycling. 3.6.1 Monetary incentives—taxes and rebates We next analyze how to improve performance of the decentralized systems to ideally achieve the first-best rates. We consider both cases—in which the collection rate is determined by the social planner and by the government—and discuss incentive schemes that can induce the firm, the recycler, and the government to make socially optimal decisions. We first focus on the optimal yield rate. Theorem 3. (Incentives for socially optimal yield rate) Suppose that the social planner determines the collection rate. If the government conducts the recycling, the social planner should offer an incentive equal toI G;y = y G;I vnet ; wherey G;I is the government’s choice of yield rate under incentiveI G;y . If the firm conducts the recycling, the social planner does not need to offer any incentives. If the recycler conducts the recycling, the social planner should offer an incentive equal toI R;y = y R;I (1 ) v , wherey R;I is the recycler’s choice of yield rate under incentiveI R;y . Under the mechanisms previously described, the social planner can induce the recycling entity to select the first-best yield rate. The decision on which entity to choose depends on the size of the required payout. Clearly, the easiest option is to have the firm responsible for recycling, as this does not require any incentives. 116 If, however, this option is not supported with the current practice and existing infrastructure, the choice between the recycler and the government depends on the relationship between the value of the recycled material and the cost of transportation for manufacturing. That is, when the value of the recycled material is high enough ( v > s tm ), it is cheaper to incentivize the recycler; otherwise, the government is the better choice. Note thatI R;y can actually amount to a tax whenever secondary materials are costly and the recycler’s yield exceeds the socially optimal one ( > 1). Thus, our calculations indicate it is usually easier to incentivize the recycler to achieve optimal yield rate. Next, we assume that the government determines the collection rate. As we have shown in Proposition 6, if the local government chooses both the collection and the yield rates, the optimal yield rate chosen by the government is always lower than the socially optimal one, and the optimal collection rate chosen by the government is usually lower than the socially optimal one. One exception is the case in which primary materials are very inexpensive and the government chooses a higher collection rate to reduce the amount of material sent to the landfill. As a result, when primary materials are cheap, the social planner might need to introduce taxes in order to reduce the government’s collection rate. However, if the socially optimal yield rate is chosen,y >y G , the government would in response reduce its collection rate, and the need for taxes never occurs. Thus, if the recycling entity is incentivized to choose the socially optimal yield rate, the social planner always need to incentivize the government 14 if the planner wants the government to implement the socially optimal collection rate. Theorem 4. (Incentives for socially optimal collection rate) Suppose that the government determines the collection rate. If the recycling entity is incentivized to implement the socially optimal yield rate, a social 14 Although theoretically the social planner might need two mechanisms, taxes and incentives, to induce socially optimal collec- tion rate by the government, the first case will never occur if the socially optimal yield rate is chosen. 117 planner who wants to achieve the socially optimal collection rate needs to offer to the government an in- centive equal toI G;c =c G;I y vnet ; wherec G;I is the government’s choice of collection rate in response to incentiveI G;c . As previously discussed, if the social planner wants to implement socially optimal collection and yield rates, the best option is to determine the collection rate itself, and let the firm be responsible for recycling. However, if this arrangement cannot be implemented, our result shows that the government would select an optimal collection rate when provided with an incentive proportional to the recovery rate, which is the product of the yield rate and the collection rate. We note that, in practice, finding socially optimal yield and collection rates is a non-trivial problem, and that different entities can have different emissions and underlying costs (our model assumes that emissions and costs are equal for all parties). However, we hope that our model will encourage a social planner to incentivize the recycling entities to improve their choices. Our discussion with a PET recycling firm in California revealed that the California Recycle Market Development Fund (http://www.calrecycle.ca.gov/ RMDZ/) provides an incentive for each pound of material recycled and sold to a California manufacturer, and indicated that even small incentives can make a big difference when primary material costs decrease. 3.6.2 Deposit/refund Palmer et al. (1996) use a model of waste generation and recycling with price-dependent demand to analyze the impact of three policy interventions: deposit/refund, advance disposal fee, and recycling subsidy. They conclude that deposit/refund is the least costly mechanism for reducing MSW disposal. Unlike their model, our model assumes that demand is not price-dependent, which enables us to obtain some novel results. Although Palmer et al. (1996) see the impact of a tax/refund through a change in demand due to higher 118 price, we show that this mechanism can improve the system performance even when the demand is not price-dependent. In California, the state government implements a recycling policy for beverage containers. All manufac- turers or importers are required to pay the recycling fee, say depositd, to the state, which they later collect from their customers who then charge their customers, and so on. The customer who consumes the beverage can dispose of the container or return it for recycling and recuperate the deposit (indirectly) from the gov- ernment. If we consider the government’s problem described in (3.5), we can observe that the government obtainsd for every unit of primary product sold, and then has to returncd after the first cycle;ccyd after the second recycling cycle,cc 2 y 2 d after the third recycling cycle, and so on. Consequently, the first part of the government’s cost function changes to c (c)+(1c)( l d). Let us denote the government’s optimal collection rate in the model in which the government implements the deposit/refund model byc Gd . We then have the following result. Proposition 7. (Optimal collection rate in government’s problem with deposit/refund) If the government chooses the collection rate and implements a deposit/refund policy, it will reduce the collection rate,c Gd < c G . The optimal collection rate is non-increasing with respect to deposit. The abovementioned result is not surprising: deposits reduce the government’s cost, but when more material is collected, the government needs to issue more refunds, which then increases costs. Consequently, we have the following corollary. Corollary 1. (Incentives for a socially optimal collection rate when the government implements the de- posit/refund model) Suppose that the government determines the collection rate and uses the deposit/refund model. If the recycling entity is incentivized to implement the socially optimal yield rate, a social planner who wants to achieve the socially optimal collection rate needs to offer the government an incentive equal toI G;c =c G;I (y vnet +d): 119 Thus, when the government uses the deposit/refund scheme, achieving the social optimum requires larger subsidies from the social planner. However, the social planner can reduce its cost by using the following model. Suppose that the social planner charges the government a deposit,D, for every unit sold under its jurisdiction, and returns a refund for every unit collected. The first part of the government’s cost function in (3.5) then changes to c (c)+(1c)( l +D), and the government selects a higher collection rate in order to increase the refund obtained from the social planner. Let us denote the government’s optimal collection rate in the model in which the social planner implements the deposit/refund model byc GD . Our last major result establishes that, under this scheme, we can achieve a socially optimal collection rate without additional incentives. Theorem 5. (Incentives for a socially optimal collection rate when the social planner implements the deposit/refund model) Suppose that the government determines the collection rate. If the recycling entity is incentivized to implement the socially optimal yield rate, a social planner who wants to achieve the so- cially optimal collection rate needs to implement a deposit/refund model in which it charges the government depositD =y vnet for each product sold. If we applyd =D to Corrollary 1, we can see that the social planner needs to offer the government an incentive equal toI G;c =c G;I (y vnet D); selectingD =y vnet would achieve a socially optimal col- lection rate without the need for government incentives. Using California as the social planner, and counties or cities as the government, the deposit/refund scheme should achieve better results if the state charged a deposit fee to local municipalities and refunded it for the recycled containers, instead of charging the firms directly. 15 According to our estimates, vnet = 1;733:49 154:19 = $1;579:30 per short ton of PET. Kuczenski and Geyer (2011) estimate that a typical bottle in California contains about 0.5 l of beverage, and 15 Recall that government’s recycling model also applies to the case in which the recycler is responsible for both recycling and landfill. 120 that 1 kg of PET represents 27.9 l of beverage. Thus, we can obtain27:92907:17 = 50;620 beverage con- tainers from a short ton of PET, hence vnet = $0:031 per average PET bottle in California. Consequently, by charging a modest per bottle deposit to local municipalities (lower than the current deposit/refund scheme charged to firms, which is $0.05 for containers less than 0.7 l (24 ounces) and $0.10 for larger containers), California should be able to improve collection rates. Walls (2011) discusses the use of deposit/refund systems for beverage containers, batteries, motor oil, and so forth. She concludes that both theoretical models and real-world application have shown that de- posit/refund schemes outperform alternative waste disposal policies, such as advance disposal fees or recy- cled content standards. However, she also notices that many product upstream systems, in which recyclers receive the refund, may have lower costs and better environmental outcomes than downstream systems, in which the consumers receive the refund. Our results provide theoretical support for this conclusion. Walls and Palmer (2001) show that a traditional deposit-refund system alone cannot achieve full social optimum. Our results suggest that a careful choice of material-specific deposit/refund scheme implemented by a so- cial planner with respect to local governments could achieve an optimal collection rate without the need for additional instruments, as required incentives could be offset by deposits/refunds. 3.7. A Case Study: Minimum Recycled Content Requirement The implementation of minimum recycled content is another approach that may lead to an improvement in collection and yield rates. In March 2015, a California State Assembly bill (AB 1447 2015) was introduced, which would have required “every manufacturer of PET plastic packaging for sale manufactured in the state to include be manufactured with, and empty PET plastic packaging imported into the state to be filled with food or drink in the state for sale in the state to contain, a minimum of 10% of postfilled PET plastic in its PET plastic packaging.” The bill did not pass. 121 If the bill had passed and been implemented, what would have been the impact on collection and yield rates? Consider the following scenario. In the first period, the firm begins with (1cy) unit of primary materials andcy-unit of secondary materials to manufacture 1 unit of product for consumers. After recycling, the firm obtains cy-unit of secondary materials, which can be combined with (1cy) unit of primary materials in the next period to again manufacture 1-unit of the product. Therefore, each product contains cy-unit of recycled content in each period. Assume that the recycler is responsible for product recycling, and that the social planner requires at least-unit of recycled content. Ifcy , the legislation does not have any impact; if the opposite holds, there are not enough secondary materials available and the recycler needs to be incentivized to increase the rates. If secondary materials are cheaper than primary materials, the firm (instead of the social planner) can develop incentives similar to those described in Theorem 4 to achieve this goal. However, if the opposite is true, Proposition 6 implies that the recycler may already use rates that exceed the social optimum, and a push to increase those rates by implementing minimum recycled content may further worsen the situation. Thus, this type of legislation is only effective whency < and the secondary materials are inexpensive. As previously mentioned, PET recycling is undergoing a difficult period due to the low cost of oil. Table 7 in NAPCOR and APR (2015) shows that for U.S. PET data,cy = 22:6% in 2013. Consequently, a minimum requirement of = 10% is not useful; the recycled content should be set to a higher level, >cy = 22:6%, if we want to influence collection and yield rates. In the data we collected for early 2016 shown in Table 3.4, the aggregate cost of the secondary material ($1,237.56) is lower than that of the primary material ($1,974.38), so selecting a higher may be effective. However, if oil prices go down significantly and secondary material becomes costlier than primary material, the minimum recycled content requirement may actually worsen the societal outcome by increasing the rates to undesirable levels. When secondary material is costlier than primary material, there is a range of secondary material prices,1 1++ l v ; 122 however, in this scenario the optimal collection rate is lower than the social optimum, and a minimum recycle content can help keep the recyclers in business. The impact of legislation is different if we focus only on beverage bottles consumed in California. According to Kuczenski and Geyer (2011), the collection rate of beverage containers in California isc = 73%, while the recycled content in bottles iscy = 3:9%, implying thaty = 5:34%: 16 If a minimum recycled content of 10% is imposed, it would represent an increase in the recycling rate,cy, of 156%. If we assume the collection rate remains unchanged, the legislation would require an increase in yield rate toy = 13:7%. Similarly, if we assume that the collection rate could be increased to 85%, the legislation would require a yield rate ofy = 11:8%. This could be obtained by reducing the amount diverted to open-loop recycling. 3.8. Some Extensions 3.8.1 Open-loop recycling: PET beverage containers in California In our previous analysis, we considered PET in general and assumed = 0; we now present a brief open- loop analysis for PET beverage containers in California. Our collection and yield rates are based on Kuczen- ski and Geyer (2011); they assumec = 73:3% andcy = 3:9%, which corresponds toy = 5:32%. They further assume that1y = 94:68% is divided as follows: 60.01% of the total recycled quantity (or 63.38% of the 1-y amount) is sold to foreign markets, 9.20% (9.7% of the 1-y amount) goes to non-food use, 5.48% (5.79% of the 1-y amount) goes to non-bottle food use, and 19.99% ends up in landfills. Hence, = 1 (1)(1y) 1y = 1 19:99% 94:68% = 78:89%. In order to estimate revenue that could be obtained from outside options,s o , we use prices of different grades of pallet and flake material from PetroChemWire (2017) and estimate that we can obtain 32.9% of 16 Kuczenski and Geyer (2011) estimate that 75% of collected material is diverted to open-loop recycling, hence 1kg of primary materials yields 0.547 kg of material sent to outside recycling, while 20% of collected material ends up in landfill. 123 the value of bottle quality resin (estimated at $1,140 per short ton; see section 4.3.3) when selling to foreign markets (i.e., $375), 53.2% (i.e., $604.50) from non-food use, and 67.5% (i.e., $769.50) from non-bottle food use, with landfill cost ofs l 0 = $94:36 per short ton. Combining these values, we derives d (5:32%) = [$94:3621:11%($37563:38%+$604:509:7%+$769:505:79%)](15:32%) =$303:88. In other words, a disposal cost/diversion benefit would generate benefits for PET beverage containers. We want to obtain x s for the open-loop case, so we first need to calculate s r in this instance. For simplicity, we assume that the collection rate is the same as for the PET in general (hence s c (c) remains unchanged), and thats p (y) is linear iny,s p (y) = Cy for some constantC. RDC Environment and Pira International (2003) estimates the cost of recycling 1 metric ton of PET bottles via curbside collection in Europe at around 1,132 euros, which corresponds to around $1,200 per short ton, close to our estimate. They separate this recycling cost into various components and estimate the collection cost to be around 280 euros per tonne, or about 24.7% of total recycling cost. 17 We now apply this estimate to our original closed-loop calculation for PET (withy = 69:7% and = 0) and obtains c (c) = $281:58 andC = $694:82. We can now calculate the cost for PET beverage containers, s r = $281:58+$694:825:32%$364:5894:68% =$26:64. Thus, recycling of PET beverage containers in California generates revenue at any yield rate due to the profitability of open-loop recycling (s d < 0) at the current collection cost,s c = $281:58. If the collection cost increases to $481.16 per short ton, the current yield rate would become the lower boundary,x s = 5:32%. This example shows that open-loop recycling makes recycling desirable even when a lower fraction of primary material is recycled back into the original product. 17 As an alternative, they consider recycling via bring-back collection, which further reduces collection costs to around 20% of the total recycling cost. 124 3.8.2 Effect of the social cost factor, The social cost of emissions is expected to increase over time (U.S. Government 2013), and recent research argues that the cost could be even higher (Moore and Diaz 2015) than estimated. Therefore, we analyze the effect of on optimal decisions,y () andc () for the social planner problem. Recall thaty () andc () minimize aggregate costs. We introduce some new symbols,y e andc e , as minimizers of the social planner’s problem emissions, andy s andc s , as minimizers of the social planner’s problem operational costs. Proposition 8. (Impact of social cost factor on optimal rates) As the social cost factor,, increases, the following holds: 1. minfy s ;y e gy () maxfy s ;y e g. In addition, ify e y s (resp.,y e y s ), then the optimal yield rate decreases (resp., increases) in andy () converges toy e as!1. 2. minfc s ;c e gc () maxfc s ;c e g. In addition,c e c s (resp.,c e c s ), then the optimal collection rate decreases (resp., increases) in andc () converges toc e as!1. Thus, as increases over time, the optimal yield rate either monotonically increases or decreases, and it converges to the optimal yield rate for emissions,y e ; the same holds for the optimal collection rates. These results also hold for all other centralized and decentralized recycling decision problems we discussed in Sections 3.5 and 3.6 as the proof follow the same logic. 3.9. Concluding Remarks and Managerial Insights Whether recycling is overall (environmentally and/or financially) desirable has been a debatable topic for a long time. Our conclusion is that, for most common materials in the U.S., the answer is positive. Nonetheless, recyclers have to carefully select the yield rate of the underlying recycling processes, and a social planner might need to provide appropriate incentives to help them. 125 We first show that recycling is effective in reducing life cycle GHG emissions and operational costs for all the common materials under consideration, except for glass, which is not financially effective. In the case of office paper, recycling reduces the emissions at any yield rate. Our analysis sheds some light on the core reasons behind financial difficulties faced by recycling businesses, and shows that the recycling yield rate is a key metric in determining their financial feasibility. Investment in technology that improves the yield rate is desirable, yet the cost may be high. One implication from our findings is that in areas with higher costs/penalties for disposal of non-recycled materials into landfills, air, or sewer systems, we can expect a higher yield rate. Further, we notice that the collection rate depends on the relative cost of primary materials and landfills. Different entities responsible for recycling will make different choices. When the social planner determines the collection rate, choosing the firm as the recycling entity is the best option, as it selects the same yield rate as the social planner. Among the remaining two options, we find that the recycler is a better choice when the value of the secondary material is high enough. If the government selects the collection rate, its choice approaches social optimum when primary materials are cheap and the recycler or the firm is responsible for recycling; otherwise, the government should undertake recycling as well. One of the common instruments for increasing the collection rate is the deposit/refund model, which encourages the end consumer to recycle. Previous research has assumed price-dependent demand and found that this model is the cheapest instrument that can achieve desired goals. Our analysis shows that when government implements a deposit/refund model with constant demand, it may lead to a reduced collection rate; however, if the social planner implements this model with respect to the government, it may induce the government to make the socially optimal choice. 126 Chapter 4 Technical Details 4.1. Technical Details Related to Chapter 1 Table 4.1: Sewing-Stage Task Name and Description, Applicable Product Types, and Material Codes Sewing Task Name Task Description Products y Materials z Binding Add binding at the hem of the fabric to prevent the fabric from tearing. DC, SC L, M, H Elastic Add elastic on the front and back of cover to provide a snug fit. VC L, M Grommets Add grommets to the sides of cover for fastening with a lock in windy areas. VC L, M Joining Joining dozens of pieces of fabric together. SC L, M, H Logo-Embroidery Add logo via embroidery operation. DC, SC, VC L, M, H Logo-Silkscreen Add logo via silk screen operation. DC, SC, VC L, M, H Overlock Perform overlock operation to prevent de-threading of the fabric across seams. VC L, M Overlock Seaming Assemble all the major panels in cover. VC L, M Pouch Add the molle patch and pouch at the back to mount tactical bags. SC L, M, H Seaming Sew the pieces together to form the basic shape of cover. VC L, M Velcro Zipper ABS Add ABS sheet or Velcro or Zipper at the back of the seat. SC L, M, H Webbing Elastic Add webbing elastic to secure the SC to the seat of the vehicle. SC L, M, H Zigzag Using a special machine to create a ZIG ZAG stitch to join all the panels. DC L, M y DC = Dash Cover, SC = Seat Cover, VC = Vehicle Cover. z L = Low, M = Medium, H = High. Table 4.2: Return Policies of Online Retailers Retailer Return Period Return Authorization Restocking Fee% Return to Brick-and-Mortar Store 1 Unlimited Not Required 0 Allowed 2 30 Days Required Via Calling Customer Service 15 Not Allowed 3 30 Days Required Via Online System 0 Not Allowed 4 30 Days Required Via Online System 20 Not Allowed 5 Unlimited Not Required 0 Allowed 6 90 Days Not Required 0 Allowed 7 30 Days Required Via Online System 15 Not Allowed 8 30 Days Required Via Online System 15 Not Allowed 9 30 Days Required Via Online System 15 Not Allowed 10 Unlimited Required Via Online System 0 Allowed 11 30 Days Required Via Online System 15 Not Allowed 12 30 Days Required Via Calling Customer Service 20 Not Allowed 13 30 Days Required Via Online System 20 Not Allowed 127 Table 4.3: Summary Statistics of Consumer Socio-Economic and Demographic Characteristics at Shipping ZIP5 Mean Std Dev Min Max Median Household Income (unit: $1,000) 64.1 21.7 32.5 125.2 Median Household Size 2.8 0.4 2.3 4.0 Population Density (unit: 1,000 people per square mile) 1.8 2.5 0.0 11.3 Percentage of Male Population (unit: %) 49.4 1.6 46.0 55.0 Age Group (unit: %) Under 18 Years 23.4 4.4 13.0 33.0 18 to 24 Years 9.3 3.3 5.0 23.0 25 to 34 Years 13.1 3.1 7.0 21.0 35 to 44 Years 12.2 2.0 8.0 17.0 45 to 54 Years 13.6 1.9 9.0 18.0 55 to 64 Years 13.0 2.6 8.0 19.0 65 Years and Older 15.4 5.4 6.0 31.0 Education Attainment (unit: %) Less than High School 14.0 8.5 2.0 39.0 High School 27.7 8.2 10.0 45.0 Some College 23.6 4.9 13.0 34.0 Associate’s Degree 8.3 2.4 3.0 14.0 Bachelor’s Degree 16.8 7.8 5.0 36.0 Post Graduate Degree 9.6 6.1 2.0 29.0 Annual Household Expenditures (unit: $1,000) Total (all categories) 57.0 8.0 28.0 90.4 Apparel and Services 1.8 0.2 1.5 2.3 Entertainment 2.8 0.4 1.8 3.8 Personal Care Products and Services 1.7 0.3 1.1 2.4 Household Furnishings and Equipment 0.7 0.1 0.5 0.9 Vehicle Purchases 3.7 0.5 2.5 4.8 128 Summary statistics of categorical variables The breakdown of sales by product type is as follows: dash cover (54.3%), seat cover (38.3%) and vehicle cover (7.4%); and the material codes are low (41.3%), medium (52.7%) and high (6.0%). Any vehicle can be grouped into three broad categories as car (34.5%), truck (61.9%) and van (3.6%) or twenty-five granular categories such as sedan (15.7%), coupe (6.9%) and sports utility vehicles (16.1%) (the full list is available from the authors). Order size equals 1 (81.3%), 2 (17.2%) or 3 (1.5%). The breakdown of sales by retailers with return period is 30 days (51.6%), 90 days (6.4%) and unlimited (42.0%) and further details on the retailer return policies can be found in Table A2 in the online appendix. In the interest of space, we do not provide summary statistics of other categorical variables (e.g., month), but they are available from the authors. Measuring time spent in sewing There is a challenge in accurately measuring time spent in sewing. This is because in the focal firm each sewer scans the barcode for an order upon completion of each task, but not at the beginning of each task. For simplicity, consider a product that completes the cutting task 1 at 9:00 a.m., sewing task 1 at 11:00 a.m., sewing task 2 at 1:00 p.m., and packing at 4:00 p.m. One may estimate the sewing hours as 1:00 p.m. (end of sewing) – 9:00 a.m. (end of cutting) = 4 hours. But this measure includes the backlog time between each task, and next we propose an approach to eliminate or at least minimize backlog time included in the Sewing Hours and thus Lagged Sewing Hours measure. In the focal firm in our study, as discussed earlier, management keeps their workers fully utilized (they are rarely idle). Consider an employee who completes sewing task 1 (11:00 a.m.) on orderi, and sewing task 2 (11:30 a.m.) on orderj on the same day. Because there is almost no idleness, we can assume that sewing task 2 was started at 11:00 a.m. when her task 1 was completed. Thus, we can measure the sewing task 2 time as (11:30 a.m.—11:00 a.m.) = 0.5 hours. Once we have the task time for each employee for each order, we can sum up all the sewing task times for an order to 129 derive the Sewing Hours for each product. We do not include non-working hours as part of Sewing Hours, such as lunch breaks, evening, weekend or holiday hours when the factory is closed when measuring Sewing Hours. Table 4.4: Average Marginal Effect vs. Worker Specialization (WS) WS From WS To Average Marginal Effect WS From WS To Average Marginal Effect 10.4 20.2 0.15% 54.8 58.7 0.03% 20.2 39.7 0.07% 58.7 62.7 0.04% 39.7 45.9 0.03% 62.7 67.3 0.06% 45.9 50.5 0.01% 67.3 73.0 0.08% 50.5 54.8 0.01% 73.0 78.6 0.10% Figure 4.1: Average Marginal Effect (vertical) vs. Worker Specialization (horizontal) -0.20% -0.15% -0.10% -0.05% 0.00% 0.05% 0.10% 0.15% 10.4 14.4 18.4 22.4 26.4 30.4 34.4 38.4 42.4 46.4 50.4 54.4 58.4 62.4 66.4 70.4 74.4 78.4 130 Table 4.5: Robustness Checks on Effect of Worker Specialization, Workload and Personalization on Return Rate y When Worker Specialization is Measured During the Past 1 Week to 6 Months (1 month = 30 days) Model 1 Model 1 Model 1 Model 1 Model 1 (past 1 week) z (past 2 weeks) (past 3 weeks) (past 4 weeks) (past 1 month) Hypothesis 1: Worker Specialization TeamAverage 0.0200 *** 0.0222 *** 0.0209 *** 0.0218 *** 0.0216 *** (0.0032) (0.0034) (0.0036) (0.0036) (0.0036) TeamAverage 2 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00003) (0.00003) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0228 *** 0.0217 *** 0.0222 *** 0.0219 *** 0.0221 *** (0.0035) (0.0035) (0.0035) (0.0035) (0.0035) Hypothesis 3: Personalization (yes vs. no) 0.2420 *** 0.2410 *** 0.2416 *** 0.2410 *** 0.2410 *** (0.0624) (0.0624) (0.0624) (0.0624) (0.0624) Same controls q Included Included Included Included Included Model 1 Model 1 Model 1 Model 1 Model 1 (past 2 months) (past 3 months) (past 4 months) (past 5 months) (past 6 months) Hypothesis 1: Worker Specialization TeamAverage 0.0242 *** 0.0253 *** 0.0252 *** 0.0246 *** 0.0240 *** (0.0037) (0.0038) (0.0039) (0.0039) (0.0039) TeamAverage 2 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0212 *** 0.0205 *** 0.0203 *** 0.0205 *** 0.0208 *** (0.0035) (0.0036) (0.0036) (0.0036) (0.0036) Hypothesis 3: Personalization (yes vs. no) 0.2398 *** 0.2408 *** 0.2424 *** 0.2440 *** 0.2452 *** (0.0624) (0.0624) (0.0624) (0.0624) (0.0624) Same controls Included Included Included Included Included Model 2 Model 2 Model 2 Model 2 Model 2 (past 1 week) (past 2 weeks) (past 3 weeks) (past 4 weeks) (past 1 month) Hypothesis 1: Worker Specialization TeamAverage 0.0217 *** 0.0243 *** 0.0231 *** 0.0240 *** 0.0239 *** (0.0032) (0.0034) (0.0036) (0.0036) (0.0036) TeamAverage 2 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00003) (0.00003) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0219 *** 0.0206 *** 0.0210 *** 0.0207 *** 0.0209 *** (0.0035) (0.0035) (0.0036) (0.0036) (0.0036) Hypothesis 3: Personalization (yes vs. no) 0.2820 *** 0.2808 *** 0.2814 *** 0.2808 *** 0.2808 *** (0.0628) (0.0628) (0.0628) (0.0628) (0.0628) Same controls Included Included Included Included Included Model 2 Model 2 Model 2 Model 2 Model 2 (past 2 months) (past 3 months) (past 4 months) (past 5 months) (past 6 months) Hypothesis 1: Worker Specialization TeamAverage 0.0264 *** 0.0276 *** 0.0274 *** 0.0267 *** 0.0260 *** (0.0037) (0.0038) (0.0039) (0.0039) (0.0039) TeamAverage 2 0.0002 *** 0.0003 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0201 *** 0.0193 *** 0.0191 *** 0.0194 *** 0.0197 *** (0.0036) (0.0036) (0.0036) (0.0036) (0.0036) Hypothesis 3: Personalization (yes vs. no) 0.2794 *** 0.2804 *** 0.2820 *** 0.2838 *** 0.2852 *** (0.0628) (0.0628) (0.0628) (0.0628) (0.0628) Same controls Included Included Included Included Included y Logit coefficients are provided. Standard errors are shown in parentheses. p-value0:001. z (pastt) denotes the past time windowt in which Worker Specialization is measured. q See details on controls in Table 1.4 in the manuscript. Data size isN =179;906 for all model variants shown above. 131 Table 4.6: Robustness Checks on Effect of Worker Specialization, Workload and Personalization on Return Rate y When Worker Specialization is Measured During the Past 1 Week to 6 Months (1 month = 30 days) Model 1 Model 1 Model 1 Model 1 Model 1 (past 1 week) z (past 2 weeks) (past 3 weeks) (past 4 weeks) (past 1 month) Hypothesis 1: Worker Specialization TeamAverage (based on HHI ) 0.0128 *** 0.0141 *** 0.0144 *** 0.0157 *** 0.0152 *** (0.0025) (0.0028) (0.0029) (0.0029) (0.0029) TeamAverage 2 (based on HHI) 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0266 *** 0.0261 *** 0.0259 *** 0.0255 *** 0.0257 *** (0.0033) (0.0034) (0.0034) (0.0034) (0.0034) Hypothesis 3: Personalization (yes vs. no) 0.2518 *** 0.2536 *** 0.2532 *** 0.2532 *** 0.2530 *** (0.0624) (0.0624) (0.0624) (0.0624) (0.0624) Same controls q Included Included Included Included Included Model 1 Model 1 Model 1 Model 1 Model 1 (past 2 months) (past 3 months) (past 4 months) (past 5 months) (past 6 months) Hypothesis 1: Worker Specialization TeamAverage (based on HHI) 0.0146 *** 0.0142 *** 0.0136 *** 0.0133 *** 0.0127 *** (0.0030) (0.0030) (0.0030) (0.0030) (0.0030) TeamAverage 2 (based on HHI) 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00004) (0.00004) (0.00004) (0.00005) (0.00005) Hypothesis 2: Workload WIP (all stages) 0.0260 *** 0.0261 *** 0.0263 *** 0.0265 *** 0.0268 *** (0.0034) (0.0034) (0.0034) (0.0034) (0.0034) Hypothesis 3: Personalization (yes vs. no) 0.2524 *** 0.2528 *** 0.2542 *** 0.2560 *** 0.2574 *** (0.0624) (0.0624) (0.0624) (0.0624) (0.0624) Same controls Included Included Included Included Included Model 2 Model 2 Model 2 Model 2 Model 2 (past 1 week) (past 2 weeks) (past 3 weeks) (past 4 weeks) (past 1 month) Hypothesis 1: Worker Specialization TeamAverage (based on HHI) 0.0139 *** 0.0154 *** 0.0157 *** 0.0170 *** 0.0166 *** (0.0025) (0.0028) (0.0028) (0.0029) (0.0029) TeamAverage 2 (based on HHI) 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0260 *** 0.0254 *** 0.0252 *** 0.0248 *** 0.0250 *** (0.0033) (0.0034) (0.0034) (0.0034) (0.0034) Hypothesis 3: Personalization (yes vs. no) 0.2922 *** 0.2940 *** 0.2936 *** 0.2936 *** 0.2932 *** (0.0628) (0.0628) (0.0628) (0.0628) (0.0628) Same controls Included Included Included Included Included Model 2 Model 2 Model 2 Model 2 Model 2 (past 2 months) (past 3 months) (past 4 months) (past 5 months) (past 6 months) Hypothesis 1: Worker Specialization TeamAverage (based on HHI) 0.0160 *** 0.0155 *** 0.0149 *** 0.0145 *** 0.0139 *** (0.0030) (0.0029) (0.0029) (0.0030) (0.0030) TeamAverage 2 (based on HHI) 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** 0.0002 *** (0.00004) (0.00004) (0.00004) (0.00005) (0.00005) Hypothesis 2: Workload WIP (all stages) 0.0253 *** 0.0254 *** 0.0256 *** 0.0259 *** 0.0262 *** (0.0034) (0.0034) (0.0034) (0.0034) (0.0034) Hypothesis 3: Personalization (yes vs. no) 0.2926 *** 0.2932 *** 0.2946 *** 0.2964 *** 0.2980 *** (0.0628) (0.0628) (0.0628) (0.0628) (0.0628) Same controls Included Included Included Included Included y Logit coefficients are provided. Standard errors are shown in parentheses. p-value0:001. z (pastt) denotes the past time windowt in which Worker Specialization is measured. HHI denotes Herfindahl-Hirschman Index. See details on how this measure is derived in section 3.2.1 in the manuscript. q See details on controls in Table 1.4 in the manuscript. Data size isN =179;906 for all model variants shown above. 132 Table 4.7: Effect of Worker Specialization, Workload and Personalization on Return Rate y using IV Model 2 y Model 2i z Model 2j z Model 2k y Model 2l z Hypothesis 1: Worker Specialization TeamAverage 0.0240 *** 0.0249 *** 0.0212 *** 0.0231 *** 0.0257 *** (0.0036) (0.0037) (0.0041) (0.0037) (0.0038) TeamAverage 2 0.00021 *** 0.00022 *** 0.00018 *** 0.00021 *** 0.00022 *** (0.00004) (0.00004) (0.00004) (0.00004) (0.00004) Hypothesis 2: Workload WIP (all stages) 0.0207 *** 0.0209 *** 0.0220 *** 0.0197 *** 0.0269 *** (0.0036) (0.0045) (0.0060) (0.0036) (0.0037) Hypothesis 3: Personalization (yes vs. no) 0.2808 *** 0.2560 *** 0.2599 *** 0.3094 *** 0.2668 *** (0.0628) (0.0607) (0.0610) (0.0644) (0.0663) Same controls Included Included Included Included Included IntentToPersonlaize Not Included Not Included Not Included Included Included N (data size) 179,906 179,906 179,906 172,284 172,284 y Logit coefficients are provided in Models 2 and 2k. Standard errors are shown in parentheses. p-value 0:001. Model 2k differs from Model 2 in using Intent To Personalize as additional control. z GMM-IVE coefficients are provided in Models 2i, 2j, 2l. Models 2i and 2j instrument WIP by Lagged WIP and Order Volume respectively. Model 2l includes Intent To Personalize as additional control, and instruments Personalization by Lagged Sewing Hours. 133 4.2. Technical Details Related to Chapter 2 We provide an analysis based on de-trended and de-seasonalized data in subsection 4.2.1, discuss how to construct LaggedReturns for test period in subsection 4.2.2, present model calibration details for Random Forest in subsection 4.2.3 and Gradient Boosting in subsection 4.2.4, and finally show prediction results for all retailer product pairs for future 6 months in subsection 4.2.5. 4.2.1 De-trending and de-seasonalizing data The primary reason we use the year and month variables is to capture the trend effect and seasonality. So, it is equivalent to de-trending and de-seasonalizing. The secondary reason we use the year and month variables is that it is slightly easier to implement, as de-trending and de-seasonalizing creates an additional step for an operations manager. That is, including year and month in the regression model implies that all variables are “selected” simultaneously, while de-trending and de-seasonalizing and then running the model is a 2- step or sequential process. To sum up, from the perspective of prediction accuracy alone, we do not see a substantially difference between both approaches. However, as a robustness check we performed a de-trending and de-seasonalizing analysis and the re- sults are in Table 4.9. The results based on the original data is provided in Table 4.8 for comparison. Next, we provide details on how we carried out the analyses for Table 4.9. To de-trend the data, first we checked whether the trend is stationary or non-stationary. This was done by performing the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) test on the null hypothesis of stationary trend. We failed to reject the null hypoth- esis at p-value = 0.10 and concluded that the trend is stationary. Second, we de-trended and de-seasonalized the data by applying ordinary least squares regression using the year and month variables. Then, on the de-trended and de-seasonalized data we built corresponding models (without year and month variables) and 134 obtained the prediction results in Table A2. The predicted values were computed after re-introducing incor- porating seasonality and trend in the estimated models. Note that Model 2 uses the year and month variables in addition to sales as in Model 1, thus on the de-trended and de-seasonalized data Model 2 becomes identi- cal to Model 1. We found that using de-trended and de-seasonalized data leads to similar but slightly lower prediction performance in the test data set for the main effects models 1 to 6, and the Lasso models 7a (more sparse model) and 7b (less sparse model). Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7a Model 7b Data size 1140 1140 1140 1140 1140 1140 1140 1140 Training set R 2 0.864 0.867 0.869 0.908 0.912 0.921 0.958 0.934 MSE 333.524 325.527 319.655 224.186 214.050 192.395 103.754 161.908 Data size 220 220 220 220 220 220 220 220 Test set R 2 0.836 0.838 0.844 0.888 0.895 0.923 0.928 0.930 MSE 402.506 396.787 381.472 275.189 257.709 189.386 177.815 171.824 Table 4.8: Prediction performance using original data (trained on 33 periods and tested on 6 periods). Model 1 Model2 y Model 3 Model 4 Model 5 Model 6 Model 7a Model 7b Data size 1140 1140 1140 1140 1140 1140 1140 1140 Training set R 2 0.852 0.852 0.855 0.896 0.900 0.915 0.960 0.929 MSE 357.893 357.893 352.265 252.101 242.555 206.412 95.934 136.568 Data size 220 220 220 220 220 220 220 220 Test set R 2 0.835 0.835 0.841 0.886 0.892 0.914 0.904 0.926 MSE 404.695 404.695 390.969 280.178 265.518 210.564 235.306 181.286 Table 4.9: Prediction performance using de-trended and de-seaonslized data (trained on 33 periods and tested on 6 periods). Note: y Model 2.2 is reduced to Model 2.1 because trend and month variables are not used in this data set. 4.2.2 How to construct LaggedReturns for test period Recall that we defined LaggedReturns tij := Returns t6;ij +Returns t5;ij +Returns t4;ij in sec- tion 2.3.3 as a predictor for Returns tij for model (2.5), model (2.6) and the LASSO models 7a (more sparse) and 7b (less sparse). Here we discuss how to construct LaggedReturns tij for the test set. Con- sider our main analysis in which the training data set covers periods 1 to 33, and the test data set contains periods 34 to 39. Notice that LaggedReturns 37;ij = Returns 31;ij +Returns 32;ij +Returns 33;ij and 135 Returns 31;ij ;Returns 32;ij ;Returns 33;ij all belong to the training data set, therefore we can use the ac- tual values and do not need to predict these values. However, LaggedReturns 38;ij = Returns 32;ij + Returns 33;ij +Returns 34;ij andLaggedReturns 39;ij =Returns 33;ij +Returns 34;ij +Returns 35;ij . Thus, we needReturns 34;ij ;Returns 35;ij from the test period. Because our data contained the actual re- turns for the test periods, we tried using actual as well as predictedReturns 34;ij ;Returns 35;ij to derive the correspondingLaggedReturns. But we did not find a noticeable difference in the prediction performance as we show in Table 4.10. Model 6 y Model 6 z Model 7a y Model 7a z Model 7b y Model 7b z Data size 220 220 220 220 220 220 Test set R 2 0.923 0.924 0.928 0.927 0.930 0.929 MSE 189.386 187.322 177.815 178.300 171.824 173.602 Table 4.10: A comparison of prediction performance between models using actual returns y in the test periods and models using predicted returns z in the test periods to derive the predictor variable LaggedReturns. 4.2.3 Calibrating the Random Forest model Minimum node size 5 10 20 30 50 Data size 1140 1140 1140 1140 1140 Training set R 2 0.990 0.984 0.971 0.956 0.918 MSE 25.036 38.628 70.673 108.410 199.480 Data size 220 220 220 220 220 Test set R 2 0.878 0.888 0.877 0.872 0.846 MSE 298.208 275.470 302.689 312.910 377.176 Table 4.11: Prediction performance with respect to different values of the minimum node size forB = 500. B 500 1000 1500 2000 2500 Data size 1140 1140 1140 1140 1140 Training set R 2 0.990 0.989 0.989 0.989 0.989 MSE 25.036 26.528 25.709 27.138 26.125 Data size 220 220 220 220 220 Test set R 2 0.878 0.886 0.884 0.888 0.885 MSE 298.208 278.390 284.321 275.541 281.734 Table 4.12: Prediction performance with different values ofB for the minimum node size = 5. 136 4.2.4 Calibrating the Gradient Boosting model Table 4.13: Gradient Boosting model performance by tuning learning rate with default subsampling rate 0.5. Note y :, learning rate, is also referred to as the shrinkage parameter. Note z :B , early stopping, is also called the optimal number of iterations. , learning rate y 0.1 0.05 0.01 0.0075 0.005 0.0025 0.001 0.0005 , subsampling rate 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 B , early stopping z 1234 1768 4881 4881 4881 4994 5000 5000 Data size 1140 1140 1140 1141 1140 1140 1140 1140 Training set R 2 0.990 0.987 0.981 0.968 0.971 0.961 0.942 0.893 MSE 23.956 31.095 46.793 76.472 70.215 94.303 142.228 261.575 Data size 220 220 220 221 220 221 220 220 Test set R 2 0.902 0.905 0.910 0.911 0.912 0.909 0.897 0.839 MSE 241.513 233.231 221.634 219.187 216.601 223.926 252.313 396.001 Table 4.14: Gradient Boosting model performance using grid-search through tuning parameter space (;). , learning rate y 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 , subsampling rate 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 B , early stopping z 994 4242 3440 3308 1234 903 528 1362 1127 539 Data size 1140 1140 1140 1140 1140 1140 1140 1140 1140 1140 Training set R 2 0.897 0.981 0.993 0.996 0.990 0.988 0.984 0.992 0.990 0.980 MSE 251.699 45.423 17.467 10.606 23.956 28.391 39.245 20.451 25.482 48.249 Data size 220 220 220 220 220 220 220 220 220 220 Test set R 2 0.768 0.893 0.890 0.882 0.902 0.908 0.921 0.913 0.912 0.909 MSE 568.795 263.135 269.080 290.564 241.513 226.329 194.700 214.133 215.876 222.903 , learning rate y 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 , subsampling rate 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 B , early stopping z 1653 4617 4629 4879 1768 1682 1544 4183 1935 908 Data size 1140 1140 1140 1140 1140 1140 1140 1140 1140 1140 Training set R 2 0.898 0.972 0.990 0.994 0.987 0.988 0.987 0.994 0.988 0.978 MSE 249.853 67.233 25.419 14.509 31.095 29.882 32.032 13.745 28.857 53.488 Data size 220 220 220 220 220 220 220 220 220 220 Test set R 2 0.787 0.891 0.896 0.898 0.905 0.912 0.918 0.904 0.916 0.907 MSE 521.632 268.119 255.166 250.774 233.231 215.392 200.052 236.421 205.196 228.224 , learning rate y 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 , subsampling rate 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 B , early stopping z 4991 4998 4881 4880 4881 4502 4869 4945 4942 4994 Data size 1140 1140 1140 1140 1140 1140 1140 1140 1140 1140 Training set R 2 0.887 0.944 0.969 0.977 0.981 0.981 0.982 0.983 0.982 0.979 MSE 274.974 137.198 75.348 56.179 46.793 45.940 42.791 42.447 43.699 51.354 Data size 220 220 220 220 220 220 220 220 220 220 Test set R 2 0.801 0.883 0.899 0.904 0.910 0.915 0.915 0.913 0.914 0.912 MSE 488.958 286.661 247.022 235.212 221.634 209.279 209.381 212.631 210.568 216.460 137 4.2.5 Prediction results for all retailer product pairs for future 6 months Figure 4.2: Observed vs. predicted returns by models 5, 6 and LASSO for 6 future periods. Missing data indicate no sales, e.g., (Retailer 1, Product 3) for all test periods. 138 4.3. Technical Details Related to Chapter 3 4.3.1 Proofs The following Lemma is used in Section 3.4.3; the proof is easy and is omitted. Lemma 1. Letb> 0;d> 0; and > 0. Then, a b > a+c b+d iff a b > c d , and c d > a+c b+d iff a b < c d . The following Lemma is used to prove Propositions 2 to 7; the proof is easy and is omitted. Lemma 2. Letf(x) be an increasing, strictly convex function forx2 [0;1]. Then, the following unique minimizerx is non-decreasing (increasing when interior solution) with respect tos. x = argmin x2[0;1] f(x)sx = 8 > > > > < > > > > : 1; f 0 1 (s); 0; ifs> f 0 1 (1); ifs2 f 0 1 (0); f 0 1 (1) ; ifs< f 0 1 (0): Proof of Proposition 2: Because the optimization problem (3.3) is separable inc andy, we first minimize 2 (y) = p (y) + d; (y)y vnet = p (y) + ( l 0(1) o )(1y)y vnet , and obtain y = argmin y2[0;1] p (y) y l 0(1) o + vnet . Because s p (y);e p (y) are both strictly increasing convex functions, the same is true for p (y) =s p (y)+e p (y) for > 0. Therefore, Lemma 2 implies that we can write the optimal yield rate of the social planner’s problem as y = 8 > > > > < > > > > : 1; 0 p 1 ( l 0(1) o + vnet ); 0; if l 0(1) o + vnet > 0 p 1 (1); if l 0(1) o + vnet 2 0 p 1 (0); 0 p 1 (1) ; if l 0(1) o + vnet < 0 p 1 (0): Second, we usey derived above and minimize 1 (c)+c 2 (y ) = c (c)c[ l tc ]+c 2 (y ), which yieldsc = argmin c2[0;1] c (c)c[ l tc 2 (y )] = c (c)c[ l 2 (y )]+, given tc = c . 139 Since c (c) is a strictly increasing convex function, we can use the same argument as above for c (c) and derive the optimal collection rate of the social planner’s problem as c = 8 > > > > < > > > > : 1; 0 c 1 ( l 2 (y )); 0; if l 2 (y )> 0 c 1 (1); if l 2 (y )2 0 c 1 (0); 0 c 1 (1) ; if l 2 (y )< 0 c 1 (0): Notice that we allow a rather general functional form for collection, c (c), and production, p (y), cost functions—our requirements were only that they should be strictly increasing and convex. Thus, we cannot derive explicit closed-form solutions for the optimal collection rate, c and the optimal yield rate, y . However, when the social planner has the information about the collection and production cost functions—for example, c (c) = 1 c 2 and p (y) = 2 y 2 —one may derive the corresponding closed-form solutions, by plugging in 0 c 1 (x) = x 2 1 and 0 p 1 (x) = x 2 2 into the above expressions fory and c . Proofs of Propositions 3, 4, 5 are omitted because they follow the same logic as in the above proof. Proof of Proposition 6: Our proof is based on two parts below. Part I: We claim the optimal recycling decisions of social planner, government and firm as below. The social planner and the firm always choose the same optimal yield rate, andy y F y G : The social planner always chooses a higher collection rate than the firm. In addition, vnet 8 > > < > > : G;2 (y ) G;2 (y G ) y 2 G;2 (y ) G;2 (y G ) y ; l y + G;2 (y ) G;2 (y G ) y l y + G;2 (y ) G;2 (y G ) y 9 > > = > > ; () 8 > < > : c F <c c G ; c F <c G <c ; c G c F <c : (4.1) 140 Proof: To compare optimal solutions of (3.3), (3.5), (3.7), we use the technique from the proof of Proposition 2. One can verify that we compare optimal yield rates below: y y F = argmin y2[0;1] p (y)y l 0(1) o + vnet ; y G = argmin y2[0;1] p (y)y l 0(1) o : and obtainy y F y G because vnet > 0. Because 2 (y) = F;2 (y) = G;2 (y)y vnet , one can verify that we next compare optimal collection rates below: c =argmin c2[0;1] c (c)c[ l G;2 (y )+y vnet ]; c G =argmin c2[0;1] c (c)c[ l G;2 (y G )]; and c F =argmin c2[0;1] c (c)c[ G;2 (y F )+y F vnet ]: (4.2) Because l > 0 andy =y F , we claimc c F by Lemma 2. Thus, wheny F > 0;y > 0, we have c F >c G () G;2 (y F )+y F vnet > l G;2 (y G )() vnet > l y F + G;2 (y F ) G;2 (y G ) y F and c >c G () l G;2 (y )+y vnet > l G;2 (y G )() vnet > G;2 (y ) G;2 (y G ) y : (4.3) Part II: We use the result in Part I to prove Proposition 6. Proof: With some algebra, we can show that y R = argmin y2[0;1] p (y)y l 0(1) o + v tm ; and (4.4) c R = argmin c2[0;1] c (c)c[ G;2 (y R )+y R ( v tm )]: (4.5) Assuming interior solutions (recycling firm stays in business), we have v tm 1 y R r (c R ;y R ) > 0, and l 0 + v tm > l 0 andy R >y G . Hence, we notice thaty G < minfy R ;y y F g and S 1() l 0 + v tm S l 0 + v tm ()y R Sy y F : (4.6) 141 Consequently, we have the following results on the optimal collection rates comparison: 1. When < 1, thenc R <c F , and sincec F <c we concludec R <c F <c . However, we may have different relationships forc R andc G . – First, we showc R <c F as below: l 0 + v tm < l 0 + v tm =) p (y R )y R l 0 + v tm > p (y F )y F l 0 + v tm =) p (y R )+y R l 0 + v tm l 0 < p (y F )+y F l 0 + v tm l 0 =)c R <c F : – Second, we comparec R andc G . Recall the recycling and disposal cost at yield ratey was defined as g;2 (y) := p (y)+(1y) l 0 andy G = argmin q2[0;1] p (y)+(1y) l 0 . Assuming interior solutions, we must have v tm > g;2 (y R ) y R , because v tm 1 y R r (c R ;y R ) 1 c R r;1 (c R )+ p (y R )+(1y R ) l 0 y R > p (y R )+(1y R ) l 0 y R = g;2 (y R ) y R As a result, we have the following two cases: Case 1 : If v tm > g;2 (y R ) g;2 (y G )+ l y R , then p (y R ) + y R l 0 + v tm l 0 > p (y G )+y G l 0 l 0 + l andc R >c G . Case 2 : If v tm g;2 (y R ) g;2 (y G )+ l y R , thenc R c G . Notice that this scenario is only possible when g;2 (y G )+ l > 0, because otherwise v tm g;2 (y R ) g;2 (y G )+ l y R g;2 (y R ) y R , which causes a contradiction. 142 2. When > 1, one can easily check that the first result changes direction toc R > c F , but the second resultc R > c G remains. Next, we comparec R andc . Recally R > y y F > y G from (4.6), and therefore l 0 + v tm > l 0 + v tm () p (y R )y R l 0 + v tm < p (y )y l 0 + v tm : Recall thaty = argmin q2[0;1] p (y)+(1y) l 0 + v tm , thus, p (y R )+(1y R ) l 0 + v tm > p (y )+(1y ) l 0 + v tm , and p(y R )p(y )(y R y )( l 0+vtm ) v > 0: We distinguish the following two cases: Case 1: When > 1 + p(y R )p(y )(y R y )( l 0+vtm ) v + l v , then p (y R ) + y R l 0 + v tm l 0 > p (y )+y l 0 + v tm l 0 + l , andc R >c . Case 2: When 2 (1;1 + p(y R )p(y )(y R y )( l 0+vtm ) v + l v ], then p (y R ) + y R l 0 + v tm l 0 p (y )+y l 0 + v tm l 0 + l andc R c . 3. When = 1, the recycler’s problem and the firm’s problem collapse and we have identical results. Proofs of Proposition 7 and Theorems 1 to 5 follow from Propositions 2—6 and are omitted. Lemma 3. Let f 1 (x);f 2 (x) be both increasing, strictly convex functions for x 2 [0;1]. Define x 1 = argmin x2[0;1] f 1 (x) s 1 x, x 2 = argmin x2[0;1] f 2 (x) s 2 x. Then, for > 0, the following unique minimizer x () = argmin x2[0;1] f 1 (x)s 1 x+(f 2 (x)s 2 x) satisfies the properties below: minfx 1 ;x 2 gx () maxfx 1 ;x 2 g. Ifx 1 Sx 2 , then @x () @ T 0, andlim %1 x () =x 2 ,lim &0 x () =x 1 . Proof of Lemma 3: Notice thatf 1 (x)s 1 x +(f 2 (x)s 2 x) = f 1 (x) +f 2 (x) (s 1 +s 2 ), where f 1 (x) + f 2 (x) is an increasing, strictly convex function for > 0. When x 1 = x 2 , it is trivial that x () =x 1 =x 2 , is independent of, and satisfies both properties. For ease of presentation, we will usex below instead ofx () as needed. 143 Whenx 1 <x 2 , we prove the first property. We claimx x 2 . Whenx 2 = 1, our claim holds trivially. When x 2 < 1, suppose x > x 2 . Since f 1 (x)s 1 x increases when x > x 1 due to strict convexity, f 1 (x )s 1 x >f 1 (x 2 )s 1 x 2 . Becausex 2 is the unique minimizer off 2 (x)s 2 x, we havef 2 (x )s 2 x > f 2 (x 2 )s 2 x 2 . Therefore,f 1 (x )s 1 x +(f 2 (x )s 2 x )>f 1 (x 2 )s 1 x 2 +(f 2 (x 2 )s 2 x 2 ), which contradicts the definition ofx . Thus,x x 2 , and by symmetry,x x 1 . Hence, the first property holds whenx 1 <x 2 ; the proofx 2 <x 1 follows by symmetry. Next, we prove the second property. By definition,x () simultaneously solves equations (4.7) and (4.8) below, and depends on the parameter. FOC :f 0 1 (x)s 1 + f 0 2 (x)s 2 = 0; (4.7) SOC :f 00 1 (x)+f 00 2 (x)> 0: (4.8) Whenx 1 < x 2 , we havex 2 (x 1 ;x 2 ) by the first property. Sincex > x 1 , we havef 0 1 (x )s 1 > 0 which leads tof 0 2 (x )s 2 < 0 from (4.7). By using the formula for derivative of implicit function, (4.7) gives dx d = f 0 2 (x )s 2 f 00 1 (x )+f 00 2 (x ) ; and it then follows from (4.7) that dx d > 0: Hence, lim %1 x = x 2 , lim &0 x = x 1 . Similar analysis can be performed when x 1 > x 2 . Notice that regardless of whether x 1 <x 2 orx 1 >x 2 , we always havelim %1 x =x 2 andlim &0 x =x 1 . Proof of Proposition 8: Follows directly from Lemma 3 after replacingf 1 (x) by corresponding operational cost functions, and after replacingf 2 (x) by corresponding emissions functions. 4.3.2 Emissions estimates Unless otherwise specified, we assume the emissions unit is MTCO 2 E per short ton, as in the EPA emissions reports. All emissions data (unless otherwise stated) are obtained from EPA emissions reports: EPA Plastics (2015), EPA Paper (2015), EPA Metals (2015), and EPA Glass (2015). 144 Emissions from the use of primary materials,e v Except for PET and HDPE containers, total EPA emissions for product made of primary materials (third column in Table 4.15) include emissions related to product manufacturing (fourth column), emissions due to retail transportation (fifth column), in addition to emissions related to the actual acquisition and processing of primary materials (e v , last column). Thus, to obtain e v we subtract emissions in the fourth and fifth column from one in the third column, or directly estimatee v as in tinplate. Note that the emissions in the fourth and fifth columns add up to manufacturing emissions, which we denote bye m . Since EPA’s definitions of products and primary materials slightly differ from one product category to another, further analyses are required to derive estimates fore v based on EPA emissions reports. Total EPA emissions Product EPA retail Product Material for product made of manufacturing transportation e v primary materials emissions emissions PET container PET resin 2.25 0 0.04 2.21 HDPE container HDPE resin 1.58 0 0.04 1.54 Office paper Paper pulp 1 10:45 0.02 0.53 Aluminum cans Aluminum ingot 11.09 3.61 0.02 7.46 Steel cans Tinplate 3.66 0.90 0.02 2.74 Glass container Glass container 0.60 0:370:3 0.03 0.46 Table 4.15: Emissions from primary materials PLASTICS: EPA Plastics (2015) states that “. . . Due to the large number of end applications for plastics (e.g., bags, bottles and other consumer products) and the lack of data specific to the U.S., EPA models HDPE, LDPE and PET as resin form. ” Therefore, we assign the product manufacturing emissions of PET and HDPE containers to be zero as in the fourth column. PAPER: D’Antonio (2003) estimates that paper production emissions account for 45% of total emissions for paper manufacturing process. 145 METALS: According to EPA Metals (2015), aluminum cans are made from aluminum ingot with two ad- ditional processes: aluminum sheet rolling and aluminum can and lid fabrication. Therefore, for aluminum cans, we consider aluminum ingot as primary material. For steel cans, we assume the primary material is tinplate (tin-coated steel) based on JFE Steel Corporation (2014). We estimate the emissions of tinplate as 2,486CO 2 g=kg or equivalently 2.74 MTCO 2 E per short ton based on Figure 5.5 of Beer et al (2003), and further obtain an estimate of 0.90 for steel can manufacturing, which we use in Table to estimate recycling emissions for steel cans. GLASS: We estimate that the production emissions of glass are approximately 30% of total process energy based on Venditti (2015). We define Glass container as a mixture of raw materials for primary input, which we discuss in more details in operational cost analysis fors v . Emissions from consumer’s transportation for recycling,e tc Franklin Associates (2001) estimates that consumer’s transportation of PET and HDPE on average requires (0:81+1:24)2 = 1:027 gallons of gas per 1,000 lbs (see Table 2-7 on p. 29). Using the estimated 18.95 lbs ofCO 2 E per gallon of gas (EIA 2016), we derive1:02718:95 = 19:46 lbs ofCO 2 E per 1,000 lbs, or 0.018 MTCO 2 E per short ton. We observe that PET, HDPE, aluminum and steel cans are commonly accepted for recycling (with or without deposit) in the U.S. (“CRV” 2014, NAPCOR and APR 2015, “All US Bottle Bills” 2014), whereas office paper can be put in a recycling bin in places such as offices, libraries, and homes. Hence, we estimate e tc = 0:018 for PET, HDPE, aluminum and steel cans, and glass (without differentiation between these materials), ande tc = 0 for office paper. 146 Emissions from transporting secondary materials to a manufacturing facility,e tm EPA total EPA retail Product Material transportation transportation e tm emissions emissions PET container PET resin 0.21 0.04 0.085 HDPE container HDPE resin 0.19 0.04 0.075 Office paper Paper pulp 0 0 0 Aluminum cans Aluminum ingot 0.04 0.024 0.008 Steel cans Tinplate 0.32 0.024 0.148 Glass container Glass container 0.05 0.03 0.010 Table 4.16: Emissions from Transportation of secondary materials We estimate that emissions from transportation of secondary materials to the production facility account for 50% of the total transportation emissions of secondary materials excluding retail transportation (i.e., we assume emissions from recycling stations to recycling facilities are approximately the same as emissions from recycling facilities to manufacturing facilities). Our results are given in Table 4.16. Emissions from secondary materials ande r The secondary materials emission estimates from EPA reports include emissions from production of the final product and transportation of secondary materials from recycling stations to the production facility, in addition to the emissions related to the actual processing of secondary materials. We consider emissions from production of the final product and transportation of secondary materials from the recycling facility to the production facility separately (ase m ande tm , resp.), as shown in Table 4.17. Recall that the unit emissions of secondary materials processing is 1 y e r (c;y), therefore,e r =e r (c;y) =ysecondary materials emissions. 147 Total EPA emissions Product Emissions from Actual Product Material for product made of manufacturing e tm recycling yield rate, e r secondary materials emissions operations y PET container PET resin 0.98 0 0.085 0.90 69.7% 0.62 HDPE container HDPE resin 0.54 0 0.075 0.47 81.8% 0.38 Office paper Paper pulp 1.33 10:45 0 0.88 60.3% 0.53 Aluminum cans Aluminum ingot 0.28 0 0.008 0.27 100.0% 0.27 Steel cans Tinplate 1.82 0.90 0.148 0.78 98.0% 0.76 Glass container Glass container 0.28 0:370:3 0.01 0.16 85.0% 0.14 Table 4.17: Emissions from secondary materials ande r Emissions from transportation to landfill and landfill,e l Emissions for transportation to and from the landfill, denoted ase landfill , can be directly obtained from EPA emissions reports. 4.3.3 Operational costs estimates We now describe the methodology for cost calculations, in USD $ per short ton of materials. Costs of primary materials,s v We first derive cost estimates for the acquisition and manufacturing of primary materials; we will derive secondary materials costs in corresponding months for a fair comparison later. PLASTICS: We obtain $1,670.00 for PET resin and $1,285.00 for HDPE resin from from “Current Pricing: Commodity TPs” (2016) by averaging over V olume I and II for April 2016. PAPER: We use a January 2014 cost estimate of $784.92 from “Wood Pulp Monthly Price” (2014) for primary paper pulp. The reason we use January 2014 data is to be consistent with the recycled paper pulp data, for which we could not obtain more recent data than January 2014. 148 METALS: For aluminum cans, we estimate primary material cost as $1,473.20 for from “Aluminum Prices” (2016) (March 2016). For steel cans, we use electro-zinc coil cost, $760.00 from “MEPS steel price” (2016) (April 2016) to approximate its primary material tinplate cost. Tin costs a few times more than zinc based on “Tin Prices” (2016), however, the fraction of tin in tinplate is negligible — estimated as 0.055% by weight (see Chapter 25 in Rollett 2008), we consider $760.00 is a reasonable approximation for tinplate. GLASS: First, we estimate glass container cost as $1,140.67 per ton by considering two products: 12oz beer bottle and 750ml wine bottle. We estimate that a 12oz beer bottle weights 170g and costs $0.20 (Satran 2014) to $0.23 (IBISWorld 2017) which translates to $1,067.29 to $1,227.37 for an average of $1,147.33 per ton; and a 750ml wine bottle weights 400g and costs $0.40 (Hesser 2003) which corresponds to $1,134.00 per ton. Second, we estimate the cost of raw ingredients $37.98 (April 2016) using cost estimates of silica (71% of volume, $7.81, Sandorfi 2006), limestone (14% of volume, $2.80, “Limestone and Fill Sand Price List” 2016), and soda ash (11% of volume, $25.85, Bolen 2015). Third, we estimate the transportation cost as$34:65 by transportation distance (see more details in the next paragraph.) Finally, we can derive the glass container manufacturing cost as $1,140.67 - $37.98 - $34.65 = $1,068.04, which will use to estimate the recycled glass container cost later. Total Retail Transportation Transportation Transportation Acquisition and Product Material transportation transportation emissions for distance cost manufacturing s v emissions emissions manufacturing (miles) cost PET container PET resin 0.11 0.040 0.035 435 $63.49 $1,670.00 $1,733.49 HDPE container HDPE resin 0.19 0.040 0.075 932 $136.05 $1,285.00 $1,421.05 Office paper Paper pulp 0.02 0.020 0 0 $0.00 $784.92 $784.92 Aluminum cans Aluminum ingot 0.07 0.024 0.023 317 $46.31 $1,473.20 $1,519.51 Steel cans Tinplate 0.36 0.024 0.168 2,317 $338.28 $760.00 $1,098.28 Glass container Glass container 0.07 0.030 0.020 237 $34.65 $1,106.02 $1,140.67 Table 4.18: Virgin Material Manufacturing and Transportation Costs Next, we estimate the cost of transporting primary materials to the firm by using travel distances based on EPA emissions reports. There are three components of transportation involved in EPA emissions reports for primary materials: transportation of raw ingredients (e.g., derivatives from petroleum and natural gas) 149 to the manufacturer of primary materials (e.g., plastic resins), transportation of primary materials from their manufacturer to the manufacturer of end product (e.g., plastic bottle), and transportation of finished products to the retailer. We assume that the first two types of transportation emissions are approximately the same, while the last type can be explicitly derived from the EPA emissions reports (referred to as “retail trans- portation”). The abovementioned costs only include the cost for acquisition and manufacturing of primary materials (including transportation of raw ingredients to the primary material manufacturer); therefore, we need to add the costs incurred for transportation of primary materials to the firm. To do this, we estimate emissions for transportation of primary materials to the firm by first subtracting emissions from retail trans- portation from total transportation-related emissions, and then dividing the resulting number by 2 (because of the assumption that transportation emissions to and from the manufacturer of primary material are ap- proximately the same). We then compute the travel distance by dividing the emissions by the emissions factor (0.00008 MTCO 2 E per mile per short ton; see Exhibit 5 in (EPA Plastics 2015). Finally, we derive the transportation costs by multiplying the travel distance by a cost estimate using$0:146 per mile per short ton (Austin 2015). All results are given in Table 4.18. Cost of consumer’s transportation for recycling,s tc Franklin Associates (2001) shows a comprehensive analysis of different ways in which consumers transport products for recycling, and estimate that it takes on average 1.027 gallons of of gas per 1,000 lbs of PET and HDPE. Using the average gas price of $2:642 per gallon (“Annual Gasoline Price Outlook” 2015), we estimate consumers’ transportation costs as $5.43 per short ton. By applying arguments similar to those used in the emissions analysis, we assume the same cost for aluminum and steel cans and glass, as these are typically widely accepted for recycling, and zero cost for office paper, which can be put in recycled bins in offices and homes. 150 Costs of transportation of secondary materials to product manufacturing facility,s tm Product Material e tm Distance s tm (miles) PET container PET resin 0.085 1,056 $154.19 HDPE container HDPE resin 0.075 932 $136.05 Office paper Paper pulp 0.000 0 $0.00 Aluminum cans Aluminum ingot 0.008 110 $16.11 Steel cans Tinplate 0.148 2,041 $298.01 Glass container Glass container 0.010 119 $17.33 Table 4.19: Cost for Transportation of secondary materials to Product Manufacturing Facility We first compute the travel distance, by dividing the transportation emissions from Table 4.17,e tm , by the emissions factor (0.00008 MTCO 2 E), and then derive transportation costs by multiplying the travel distance by cost estimate ($0:146 per mile per short ton; results are shown in Table 4.19). Cost of secondary materials ands r PLASTICS: We obtain $1,140.00 for PET resin and $1,000.00 for HDPE resin from “Current Pricing: Recy- cled Plastics” (2016). PAPER: We estimate the recycled paper pulp cost as $840.00 for office paper from Venditti (2015) for January 2014 data, as this is the latest data we could obtain. METALS: For aluminum cans, note that the cost of manufacturing aluminum cans is estimated as $1,103.20 = $1,473.20 - $370.00, where $1,473.20 is the cost of primary material–i.e.,s v from “Aluminum Prices” (2016) (March 2016)–and $370.00 is the cost of alumina from Bray (2015). We estimate the cost of recycling operation as 5% of primary materials manufacturing, based on the energy consumption from Environmental Benefits of Recycling (2016), thus 5% $1;103:20 = $55:16. We now estimate cost of scrap metal as $600.00 from “Scrap Metal Prices” (2016) and add a $55.16 recycling cost to obtain a total 151 of $655.16 as the secondary materials cost. For steel cans, we obtain the cost of recycled tinplate as $655 from RIM (2016) for April 2016. GLASS: We estimate recycled container manufacturing cost, s r , as $1,148.04 as a sum of two costs: cost of secondary material, i.e., cullet as $80 per ton, and cost of glass container manufacturing $1,068.04 from primary material analysis. According to Janes (2013), it costs between $70 and $90 to process a ton of glass, but then it is sold only for about $10 per ton. It should be noted that this recycling process does not include the actual glass manufacturing process (GPI 2017). Therefore, the market price $10 here is a subsidized cost and should not be considered an actual cost. For this reason, we use $80 (as an average of $70 and $90) as cullet cost. Recall that the unit cost of secondary materials is 1 y s r (c;y), therefore, s r = s r (c;y) = y secondary materials cost (except for glass.) Using estimates of secondary materials costs and the actual yield rate, we estimates r in Table 4.20. Product Material Cost of secondary materials Actual yield ratey s r PET container PET resin $1,140.00 69.7% $794.32 HDPE container HDPE resin $1,000.00 81.8% $818.00 Office paper Paper pulp $840.00 60.3% $506.47 Aluminum cans Aluminum ingot $655.16 100.0% $655.16 Steel cans Tinplate $655.00 98.0% $641.90 Glass container Glass container NA 85.0% $1,148.04 Table 4.20: Cost of secondary materials ands r for Each Material Cost of transportation to landfill and landfill,s l We denote the costs of transportation to landfill and the actual landfill bys landfill , and use A. Goldsmith Resources (2014) to estimate it as the sum of a $45 transportation cost and a $45 tipping fee for a total of $90 as a national average. 152 Summary Finally, we provide a comparison of minimum yield rates from the perspective of emissions, operational costs, and aggregate costs, along with the actual yield rates and collection rates. x e x s (c;y) x (c;y) Actual Actual Product Material (emissions) (operational cost) (aggregate cost) yield rate, collection rate, PET container PET resin 28.29 % 44.94% 42.81% 69.68% 1 31.00% 1 HDPE container HDPE resin 24.44% 57.08% 53.47% 81.80% 1 33.60% 1 Office paper Paper pulp 0 53.06% 33.65% 60.29% 2 68.00% 2 Aluminum cans Aluminum ingot 3.35% 37.95% 25.82% 100.00% 3 66.70% 3 Steel cans Tinplate 28.48% 69.64% 58.90% 98.00% 3 70.00% 3 Glass container Glass container 25.12% 90.67% 88.15% 85.00% 4 50.00% 4 Table 4.21: Minimum Yield Rates vs. Actual Yield and collection rates 1 NAPCOR and APR (2015) and ACC and APR (2015). 2 Sappi (2013) 3 EPA Metals (2015), Aluminum Association (2014), Steel Recycling Institute (2013). 4 ODNR (2011) 153 References A. 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Abstract (if available)
Abstract
With the emergence of the big-data era, there has been an explosion in the amount of private and public data. How can businesses use such data more effectively to improve operational decisions that impact financial outcomes? How can policy makers learn from such data to design environmental policies for long-term sustainability? These are some of the challenging questions that numerous business leaders and policy makers face today and are the motivation for my Ph.D. dissertation in which I specifically address the following three questions that I explain in more detail in the next two subsections. ❧ 1. Can a Manufacturer Reduce Consumer Returns Using its Operational Levers? (Chapter 1, Forthcoming in Manufacturing and Service Operations Management, https://doi.org/10.1287/msom.2019.0836) ❧ 2. Can a Manufacturer Predict Return Volume Using Machine Learning Methods? (Chapter 2, Published in European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2019.05.046) ❧ 3. Can a Policy Maker Implement Mechanisms to Improve Recycling Decisions? (Chapter 3, Published in European Journal of Operational Research, https://doi.org/10.1016/j.ejor.2018.11.010) ❧ Consumer Returns in Online Retail ❧ My work in the area of consumer returns addresses some of the increasing challenges in online retail. Consumer product returns are a major issue for retailers and manufacturers. Returned merchandise in the U.S. was estimated at $369 billion out of sales of $3.7 trillion in 2018. Online retailers experience a higher return rate than brick-and-mortar stores
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Asset Metadata
Creator
Cui, Hailong
(author)
Core Title
Essays on consumer returns in online retail and sustainable operations
School
Marshall School of Business
Degree
Doctor of Philosophy
Degree Program
Business Administration
Publication Date
03/24/2020
Defense Date
02/26/2020
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
Business Analytics,consumer returns,econometrics,environment and climate change,green supply chains,lasso,life-cycle analysis,machine learning,marketing-operations interface,OAI-PMH Harvest,online retail,predictive model,product personalization,production process,recycling rebates,socially optimal recycling,variable selection
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Rajagopalan, Sampath (
committee chair
), Sošić, Greys (
committee chair
), Ward, Amy R. (
committee member
), Yang, Sha (
committee member
)
Creator Email
hailongc@usc.edu,hcui2010@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c89-276562
Unique identifier
UC11673718
Identifier
etd-CuiHailong-8229.pdf (filename),usctheses-c89-276562 (legacy record id)
Legacy Identifier
etd-CuiHailong-8229.pdf
Dmrecord
276562
Document Type
Dissertation
Rights
Cui, Hailong
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
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Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
consumer returns
econometrics
environment and climate change
green supply chains
lasso
life-cycle analysis
machine learning
marketing-operations interface
online retail
predictive model
product personalization
production process
recycling rebates
socially optimal recycling
variable selection