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Evaluating city logistics using two-level location routing modeling and SCPM simulation
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Content
Evaluating City Logistics Using Two-Level Location Routing
Modeling and SCPM Simulation
by
Qian An
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)
December 2015
II
Dedication
To my dear father Xichang An, my mother Guangcui He and my husband Dazhao Liu.
III
Acknowledgements
I wish to thank my advisor Dr. James Moore and Dr. Peter Gordon, for all your
encouragement and guidance along the way.
Special thanks to Dr. Maged Dessouky, Dr. Qiang Huang, Dr. Alejandro Toriello,
Dr. Sheldon Ross and Dr. Qisheng Pan for serving my committee and enlightening my
research work.
Finally I would also like to express my thanks to all the other faculty members,
staff and students in ISE and Viterbi School of Engineering. It has been my great
pleasure to work with you!
i
Table of Contents
Dedication II
Acknowledgements III
List of Tables 1
List of Figures 2
Abstract 6
Chapter 1: Introduction 8
Chapter 2: Literature Review 14
2.1 Overview of City Logistics ································ ···························· 14
2.2 Location Routing Problem (LRP) ································ ····················· 19
2.2.1 LRP Heuristics ································ ································ ··· 19
2.2.2 Two-Echelon Location Routing Problem (2E-LRP) ························ 21
2.3 The Southern California Planning Model (SCPM) ································ · 23
Chapter 3: Methodology 28
3.1 2E-LRP Modeling and Heuristics ································ ····················· 29
3.1.1 2E-LRP Modeling ································ ······················ 29
ii
3.1.2 Heuristics ································ ································ 35
3.1.3 Computational Tests ································ ···················· 42
3.2 SCPM Simulation ································ ································ ······· 44
3.2.1 Trip Generation ································ ································ ···· 47
3.2.2 Trip Distribution ································ ································ ··· 47
3.2.3 Trip Assignment ································ ································ ··· 47
3.3 Linking the Two Modeling Systems ································ ················· 51
Chapter 4: Los Angeles Case Study 53
4.1 Clustering ································ ································ ················ 57
4.2 CPLEX Optimal Cluster Route ································ ······················· 63
4.3 3-optimal Clustering Improvement ································ ·················· 63
4.4 Selection of Potential Satellites and Assignment Cost ···························· 65
4.5 Optimal Locations of Satellites ································ ······················· 67
4.6 Objective Functions in the SCPM Simulation ································ ······ 71
4.7 Experiment Result ································ ································ ······ 73
4.7.1 2E-LRP Simulation Result ································ ······················· 75
4.7.2 Improvement of 2E-LRP versus Random Satellites ·························· 92
4.8 Case Study Summary ································ ································ ··· 94
Chapter 5: Conclusions and Discussions 97
Bibliography 99
1
List of Tables
2.1 The Sum of Freight Trips Attractions/Productions in AM peak by USC Sector
(Pan, 2007) ································ ································ ···················· 26
2.2 Employment, Population, and Household in the Five County Los Angeles
Region, 2000 (Pan, 2007) ································ ································ ··· 27
3.1 Instances of Lower Bound by CPLEX and Upper Bound by the Heuristics ········ 43
4.1 Freight Centers in SCPM ································ ································ ··· 54
4.2 SCPM Simulation Results. Columns 6 to11 are in Million Hours. Columns 12
to14 are in Million Gallons ································ ································ · 74
4.3 Output of SCPM Simulation ································ ······························· 95
4.4 Comparison of 2E-LRP Impact and Random Satellite Impact ························ 96
4.5 Average Impact Improvement of 2E-LRP with SCPM Feedback vs. Static
Network Link Cost ································ ································ ··········· 96
2
List of Figures
1.1 Example of a Current City Goods Movement System (Single Level
Distribution Centers and Movements with the City) ································ · 10
1.2 Two Level Distribution Network for a Metropolitan Area ························· 12
3.1.a Step 1: Cluster Customers into Groups ································ ················ 36
3.1.b Step 2: Calculate Allocation Cost ································ ······················ 36
3.1.c Step 3: Locate Hubs, Satellites, Design the 1
st
Level Route and the 2
nd
Level
Allocation ································ ································ ·················· 36
3.2 3-optimal Local Search Procedure (Branco and Coelho, 1990) ···················· 40
3.3 Assigning a Cluster to a Satellite ································ ······················· 41
3.4 SCPM Simulation Flow Chart ································ ·························· 46
3.5 Differences Between Baseline Freight Movement (left) and City Logistics
Freight Movement (right) ································ ································ 49
3.6 Iteration between SCPM and 2E-LRP Solutions ································ ····· 52
4.1.a Population Distribution of TAZs (Pan, 2007) ································ ········· 54
4.1.b Freight Distribution of TAZs (Pan, 2007) ································ ············· 55
3
4.2 City Logistics Simulation Full Feedback Loop ································ ······· 56
4.3 Clustering Algorithm Flow Chart ································ ······················· 58
4.4 TAZs Demand Distribution ································ ······························ 59
4.5.a Step 1 Clustering: 3191 Clusters ································ ······················· 60
4.5.b Step 1 Clustering: 2000 Clusters ································ ························ 61
4.5.c Step 1 Clustering: 1000 Clusters ································ ························ 61
4.5.d Step 1 Clustering: 350 Clusters ································ ························· 62
4.5.e Step 1 Clustering: 150 Clusters ································ ························· 62
4.6 3-optimal Code Flowchart ································ ······························· 64
4.7 Improvement of Total Cluster Route Length by 3-optimal ························· 64
4.8 Potential Satellites Locations and Hub Locations ································ ···· 66
4.9 Step 4 Assignment Cost Flowchart ································ ····················· 67
4.10.a Candidate Satellites (blue points) and Selected Ones (in red circle) ·············· 69
4.10.b TAZs Satellites Assignment (the close by TAZs with same color are
assigned to same satellite) ································ ································ 70
4.11 Convergence of Object Value for Baseline and City Logistics in SCPM
Simulation ································ ································ ·················· 71
4.12.a Objective of Baseline and Case 1 in Millions ································ ········· 75
4.12.b Objective of Baseline and Case 2 in Millions ································ ········· 76
4.12.c Objective of Baseline and Case 3 in Millions ································ ········· 76
4.13.a Total Travel Time of Baseline and 2E-LRP per AM Peak, Case 1 ················ 77
4.13.b Total Travel Time of Baseline and 2E-LRP per AM Peak, Case 2 ················ 78
4.13.c Total Travel Time of Baseline and 2E-LRP per AM Peak, Case 3 ················ 78
4
4.14.a Total Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 1 ········· 79
4.14.b Total Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 2 ········· 79
4.14.c Total Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 3 ········· 80
4.15.a Passenger Total Time of Baseline and 2E-LRP per AM Peak, Case 1 ············ 81
4.15.b Passenger Total Time of Baseline and 2E-LRP per AM Peak, Case 2 ············ 81
4.15.c Passenger Total Time of Baseline and 2E-LRP per AM Peak, Case 3 ············ 82
4.16.a Passenger Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 1 ··· 82
4.16.b Passenger Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 2 ··· 83
4.16.c Passenger Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 3 ··· 83
4.17.a Freight Total Time of Baseline and 2E-LRP per AM Peak, Case 1 ··············· 85
4.17.b Freight Total Time of Baseline and 2E-LRP per AM Peak, Case 2 ··············· 85
4.17.c Freight Total Time of Baseline and 2E-LRP per AM Peak, Case 3 ··············· 86
4.18.a Freight Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 1 ······· 86
4.18.b Freight Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 2 ······· 87
4.18.c Freight Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 3 ······· 87
4.19.a Total Passenger and Freight Time of Baseline and 2E-LRP per AM Peak,
Case 1 ································ ································ ······················· 89
4.19.b Total Passenger and Freight Time of Baseline and 2E-LRP per AM Peak,
Case 2 ································ ································ ······················· 89
4.19.c Total Passenger and Freight Time of Baseline and 2E-LRP per AM Peak,
Case 3 ································ ································ ······················· 90
4.20.a Total Passenger and Freight Gas of Baseline and 2E-LRP per AM Peak,
Case 1 ································ ································ ······················· 90
5
4.20.b Total Passenger and Freight Gas of Baseline and 2E-LRP per AM Peak,
Case 2 ································ ································ ······················· 91
4.20.c Total Passenger and Freight Gas of Baseline and 2E-LRP per AM Peak,
Case 3 ································ ································ ······················· 91
4.21 Objective of Baseline, 28 Random Satellites Scenarios and Three 2E-LRP
Scenarios in Millions ································ ································ ····· 92
4.22 Objective of 28 and 30 Random Satellites in Millions ······························· 93
4.23 Total Time, Passenger Time, Freight Time of 28-Satelites Scenarios and
Three 2E-LRP Scenarios per AM Peak in Million Hours per AM Peak ·········· 94
4.24 Total Gas, Passenger Gas, Freight Gas of 28-Satellites Scenarios and Three
2E-LRP Scenarios per AM Peak in Million Gallons per AM Peak ················ 94
6
Abstract
City logistics is a relatively new research area that focuses on strategies for increasing the
efficiency of moving goods in urban areas, reducing noise and vehicle emissions, and
improving safety in residential areas. City logistics investigates the benefits available
from a consolidated and cooperation-based system. A standard scheme intended to
improve efficiency is to make use of a centralized, two-level distribution system. This
approach excludes large trucks from city centers, relying on smaller, more
environmentally friendly light vehicles to accomplish final deliveries. Our objective is to
formulate a two-level location routing (2E-LRP) model and use efficient heuristics that
give an effectual strategic design for such a two-level distribution. We will estimate the
benefits from this approach by exercising the Southern California Planning Model
(SCPM). The locations of centers and the transportation mode connecting first level
distribution centers (hubs) to second-level distribution centers (satellites) are selected
using two-level location routing model and SCPM, which also produces simulation
results describing how the new network will impact traffic flow and gas consumption.
The outputs of new network link costs are also used as feedback to improve the design of
the City Logistics network.
Research presented in this dissertation is used to develop methodology to design and
7
evaluate a new City Logistics network, with respect to improving traffic level and
reducing private distribution costs. The Los Angeles case study demonstrates an 18%
improvement in network efficiency and a 40% reduction in gas consumption. Moreover,
this study is the first empirically based work that evaluates the effects of a new logistics
system on network link costs and optimality of the logistics system design itself.
8
Chapter 1
Introduction
Cities around the world compete globally for investments and trade opportunities,
knowing that an efficient transport system is essential for sustained economic growth
(Gillen, 1996). Furthermore, congestion levels in large and growing urban areas have
been rising as the demand for personal and freight transportation increases. Energy
consumption is another important concern, as are major environmental issues caused by
traffic in many cities. In addition, trucks moving through residential areas are a
significant source of noise and vehicle emissions, as well as a threat to pedestrian and
driver safety. Therefore, we expect that cities willing to identify problems and impose
more efficient and environmentally friendly logistics systems will become more
competitive with respect to economic development (Taniguchi, Thompson, Yamada, and
Duin, 2001).
City logistics research has seen substantial development in the past 15 years. The
Institute for City Logistics was established in Kyoto, Japan, in 1999, as a center of
excellence for research and development in City Logistics and urban freight transport.
9
Researchers have been searching for ideas to meet increasing transportation demand and
various consumer needs, especially in metropolitan areas with large populations and
high-demand densities.
The United States population continues to urbanize. Although not true of all
metropolitan areas in the United States, many, like the Los Angeles region, continue to
grow and face intensified transportation and environmental challenges. While private
freight carriers and shippers concentrate on reigning in the cost of shipping, those in the
public sector are greatly concerned about protecting the environment and mitigating
traffic problems. Research to be presented here points to a way to design a City Logistics
system that considers the public costs and benefits as well as impacts on the private
sector.
Consolidated shipping strategies are a cost-efficient and effective approach to
achieving those public and private objectives. Currently, goods movement in cities,
especially for retailers/consumers, involves widely dispersed transportation patterns.
Large retailers/consumers might have their own, one-level distribution centers. However,
medium-sized, and small retailers/consumers typically rely on third party freight
providers or their own vehicles to move goods. Thus, many vehicles are dedicated to
only a small number of shippers/consignees, and many vehicles are lightly loaded.
Moreover, freight carriers face a downward trend in vehicle load factors as they compete
to respond to a wider range of consumer needs (Turnquist, 2006). These circumstances
tend to elevate traffic congestion, pollution, and energy consumption. In addition, some
companies are using large trucks to distribute products in residential areas, even during
the day, which brings noise, emission, and safety concerns to communities (See figure
1.1).
10
Figure 1.1: Example of a Current City Goods Movement System (Single Level Distribution Centers
and Movements within the City).
The fundamental premise that underlies most City Logistics initiatives is to stop
considering each shipment, firm, and vehicle individually. Rather, public authority
should recognize that all stakeholders and movements are components of an integrated
logistics system. This approach offers opportunities for the coordination of shippers,
carriers, and movements, as well for as the consolidation of the loads of several
customers and carriers into the same (hopefully greener) vehicles. The term “City
Logistics” encompasses these ideas and goals and explicitly refers to the optimization of
such an advanced urban freight transportation system (Crainic, Ricciardi, and Storchi
2009c). Optimization of such a system could possibly deliver greater efficiencies than
can be achieved in the current market for freight services.
The two-level distribution network in figure 1.2 is a recent research framework that
has attracted attention from logistics scholars. This approach provides the means to
generate efficiencies while also prohibiting large trucks from entering the city center.
Smaller, more environmentally friendly light vehicles execute the last leg of the delivery
requirements (Crainic, Ricciardi, and Storchi 2009c; Benjelloun and Crainic 2009). The
City Boundary
Customer zone
Single level
distribution center(DC)
Truck routes
Goods movement
within the city (about
2/3 of total goods
Movement in 1990’s;
more now)
11
first-level DCs are located at the outskirts of urban areas. Goods are shipped to first-
level DCs via trucks, trains, ships, or aircraft and then transported inside the city in a
consolidated fashion to second-level DCs (satellites) using truck express lanes or trains.
Goods are delivered to and collected from customer zones using smaller, lighter vehicles.
Goods movement within the city, which typically accounts for around two-thirds of total
transportation movements in terms of tonnage (Bureau of Transportation Statistics, 2002
and 2013), could also be shifted to satellites using truck or train expressway facilities. In
addition, the satellites could also serve as connecting centers for the movements that have
both the origin and destination inside the city.
The new system has the potential to move goods into and out of the city and from
one zone to another inside the city in a more efficient and cost-effective manner than can
be achieved by existing service configurations. The key is that both needs are satisfied in
a consolidated fashion that focuses on full truckloads, which could significantly reduce
traffic demand and fuel consumption. Moreover, goods movement in residential areas
(from satellites to customer zones) relies on light vehicles, which keep communities clean,
quiet, and safe.
12
Figure 1.2: Two Level Distribution Network for a Metropolitan Area.
Research in City Logistics has been growing since about 2000. Various new
projects and experiments are underway. In fact, more countries and cities around the
world are introducing City Logistics policies and systems. Both research and practice in
North America, however, are still relatively limited, in part because of the mathematical
complexity of the of the problem, and in part because of the standing difficulty associated
with representing system level choices in environments in which economic agents will
compete in the presence of externalities. There is a growing body of empirical work on
various aspects of City Logistics, yet comparatively little formal modeling work.
Operations research methodology is lagging behind practice. This presents challenges
and opportunities for transportation and logistics science.
At the City Logistics strategic planning level, decision makers need to
simultaneously select the best locations for the network of two-level distribution centers
First level DC
Second level DC
(Satellites)
Customer zone
Environmental friendly light
vehicle
Truck express lane/Railway
13
and the transportation modes and routes needed to connect first-level DCs and satellites.
The standard location and routing problem for the two-level distribution network is
known to be NP-hard (Prdhon and Prins, 2014). That is, optimal solutions cannot be
consistently obtained except by explicit enumeration, which ensures that realistically
large problems cannot be solved optimally. Researchers need better heuristic modeling
techniques and more efficient algorithms for treating problems on a metropolitan scale.
More importantly, we want to know to what degree the new distribution system
based on the City Logistics approach will benefit the public good. That is, to what
degree would it reduce traffic congestion and emissions? We will address these
questions by applying the current version of the Southern California Planning Model
(SCPM).
14
Chapter 2
Literature Review
2.1 Overview of City Logistics
City Logistics research has seen substantial development in the past fifteen years. Some
researchers focused on City Logistics policies and case studies, while others concentrated
on modeling City Logistics problems. In 2001, Taniguchi et al. published the book City
Logistics: Network modeling and Intelligent Transport Systems, which provides the
framework for City Logistics research.
Taniguchi et al. (1999) defined City Logistics as “the process for totally optimizing
the logistics and transport activities by private companies in urban areas while
considering the traffic environment, traffic congestion, and energy consumption within
the framework of a market economy.” They state, too, that “The aim of City Logistics is
to globally optimize logistics systems within an urban area by considering the costs and
benefits of schemes to the public as well as the private sector. Private shippers and
15
freight carriers aim to reduce their freight costs while the public sector tries to alleviate
traffic congestion and environmental problems.”
Benjelloun and Crainic (2009) described City Logistics in this way:
“The fundamental idea of City Logistics is to stop considering each
shipment, company, and vehicle in isolation, but rather as components
of an integrated logistics system to be optimized. Coordination and
consolidation are at the basis of this idea: Coordination of shippers
and carriers and consolidation of shipments of different shippers,
carriers, and customers within the same energy-efficient and
environmentally-friendly vehicles. The goals are to reduce con-
gestion and increase mobility; reduce emissions, pollution, and
noise; contribute to reach the Kyoto agreement targets; improve
the life conditions of the city inhabitants; avoid penalizing the city
center activities such as not to „„empty” it.”
Some actual City Logistics systems have been developed, especially in Europe and
Japan. Carriers in Germany and a number of Swiss cities cooperated in consolidation and
distribution activities with very light government involvement. The Dutch ministry of
transportation and public works introduced a strict licensing policy. It imposes
restrictions on vehicle loads and the total number of vehicles entering the city. This
policy leads carriers to collaborate and consolidate shipments. Monaco made freight
delivery part of the public sector. Large trucks are banned from the city. These trucks
need to deliver goods to a CDC (City Distribution Center), which is a single carrier who
takes charge of the final distribution using special vehicles.
Benjelloun and Crainic (2009) discussed the potential benefits of a two-tier logistics
system for large cities. In their discussion, the first-level city distribution centers (CDCs)
are located on the outskirts of the urban zone. The second-level system is called
16
satellites, where the freight coming from CDCs is transferred to and consolidated into
vehicles adapted for utilization in dense city zones. In more advanced systems, satellites
do not perform any vehicle-waiting or warehousing activities; instead, using vehicle
synchronization and trans-dock transshipment is the operational model (Gragnani,
Valenti, Valentine, 2004).
The two-tier system is connected by two types of vehicles. Urban trucks move
goods between CDCs and satellites, possibly by using routes specially selected to
facilitate access to satellites in order to reduce the impact on traffic and the environment.
City freighters connecting satellites and customers are of relatively small capacity and
can travel among any street in the city. Both vehicles are supposed to be environmentally
friendly. The objective of the two-tier system is to have urban trucks and city freighters
on a “need-to-be-there” basis, meanwhile providing timely delivery of goods to
customers through economically and environmentally efficient operations.
The concepts of City Logistics have been proposed. However, there are few
literature sources related to the design, evaluation, planning, management, and control of
a City Logistics system.
Barcelo et al. (2007) presented a City Logistics modeling framework supported by a
Computer Decision Support System whose core architecture consists of several parts: a
database, to store all the data required by the implied models; location of logistic centers
and customers, capacities of warehouses and depots, transportation cost, operational costs,
fleet data, etc.; a Database Management System for the updating of the information
stored in the database; a Model Base, containing the family of models and algorithms to
solve the related problems of discrete location, network location, street vehicle routing
and scheduling, etc.; a Model Base Management System to update, modify, add, or delete
models from the Model Base; and a Graphic User Interface.
Gentile and Vigo (2007) proposed two demand models, one for movement
generation and the other for trip distribution of the freight movement in traffic zones.
17
The movement generation model was addressed through a particular category index
model, which considers the hierarchy and similarity among the categories identified by
the official tree-based classification of the economic activities. Trip distribution was
addressed through a gravity model, which takes into account that pick-ups and deliveries
are organized into tours that begin and end at given portals.
The main issues and technological challenges of City Logistics were reviewed by
Crainic, Gendreau and Potvin (2009a), who illustrated how the introduction of better
operations research-based decision support software could significantly improve City
Logistics performance. Crainic, Ricciardi and Storchi (2009c) investigated the main
issues related to the integrated short-term scheduling of operations and management of
resources for the general case involving a two-tiered distribution structure. Both a
general model and formulations for the main system components were proposed, and
promising solution avenues were identified.
Several investigations related to the two-echelon vehicle routing problem have been
completed. Crainic et al. (2008) presented several meta-heuristics based on separating
the first- and second-level routing problems. They solve iteratively the two resulting
routing subproblems while adjusting the satellite workloads linking them. Two main
meta-heuristics use a clustering and a multi-depot approach, respectively. They
presented experimental results comparing the meta-heuristics and exact methods, along
with an examination of the impact of different customers and satellites spatial
distributions on the performance of the methods and the total cost. The experiments
showed that the clustering-based metaheuristics perform very well and that a two-echelon
system may significantly reduce the cost of distribution.
Crainic et al. (2009b) studied the impact of instance parameters on the global cost of
a two-echelon vehicle routing problem (2E-VRP). The results of a large body of
experimentation was presented in order to analyze the impact on the total cost of several
parameters, including customer distribution, satellites-location rules, depot location,
number of satellites, mean accessibility of the satellites, and mean transportation cost
18
between the satellites and the customers. The computational results showed that opening
satellites reduces the global cost until a minimum cost is reached. The two-echelon VRP
approach produced better performances relative to the classical VRP, in which a depot is
located externally with respect to the customer area. The results showed the benefits of
two-echelon city logistic systems for large urban areas where distribution centers are far
from the controlled zone. They further showed that different sets of cost and distribution
of satellites has significant impact on the global cost. Therefore, additional research on
the cost parameter study and location routing modeling is timely.
Several studies on the City Logistics two-echelon location routing problem (2E-LRP)
have been completed recently (Crainic, Sforza and Sterle, 2011; Contardo, Hemmelmayr
and Crainic, 2011; Nguyen, Prins and Prodhon, 2011; Hemmelmayr, Cordeau and
Crainic, 2012; Contardo, Hemmelmayr and Crainic 2012; Govindan, Jafarian,
Khodaverdi and Devika, 2014). These studies proposed different formulations of the 2E-
LRP problems and heuristics that could solve the problem efficiently with a good,
feasible solution. More details of 2E-LRP literature are presented in Chapter 2.2.2.
The existing research in City Logistics assumes the network link cost is static. This
is a reasonable but limited perspective that focuses on the interests of private sector
actors and ignores public sector concerns. Strategic planning design decisions would
simultaneously involve the location of distribution centers and the definition of routes,
which will impact transportation network links. This extension of City Logistics system
design into the public sector context motivates us to address these methodological topics.
19
2.2 Location-Routing Problem (LRP)
Location-Routing Models solve the joint problem of determining the optimal number and
location of facilities serving customers/suppliers and finding the optimal vehicle routes
(Min, 1998). The classical location-allocation problem ignores tours when locating
facilities and, consequently, may lead to increased distribution cost (Salhi and Rand,
1989). In contrast, the location routing problem considers tours and then seeks the
optimal location and route design simultaneously.
Practitioners are aware of the danger of risk caused by separating facility location
and vehicle routing (Rand, 1976, p. 248). Facility locations are normally for a long
period and routes can be re-calculated and re-drawn frequently; however, combining
location routing in the same planning framework would be beneficial (Nagy and Salhi,
2007). It was found that the use of location-routing could decrease costs over a long
planning horizon, considering which routes are allowed to change (Salhi and Nagy, 1999).
The benefits of combining location and routing extend to two-echelon systems.
Crainic, Mancini and Perboli (2009b) did a satellite location analysis for a two-echelon
vehicle routing problem. Their analysis showed that different location patterns have a
significant impact on the total distribution cost. Thus, a two-level location-routing
framework would pave the way for planning an efficient City Logistics system.
2.2.1 LRP heuristics
There has been substantial research on the location-routing problem in the past twenty
years. Researchers have been working on efficient formulations and algorithms to solve
a variety of extensions of the problem. One example is the location-routing problem with
route capacity, or with customer time window constraints. It has proved to be an NP-
hard problem, and thus much more difficult to solve than single-level location-routing
problems. Exact methods exist to solve the problem optimally. On the other hand, due to
20
the complexity, only relatively small instances can be solved. The exact methods include
these: direct tree search/branch and bound; dynamic programming; and integer/nonlinear
programming (Min, 1998). General location-routing instances with up to 40 potential
depot locations or 80 customers have been solved to optimality (Laporte et al., 1983,
1988).
Realistic problems cannot be solved optimally with an efficient amount of time.
Fortunately, the fact that a problem has been shown to be NP-hard does not diminish its
practical relevance.
Nagy and Salhi (2007) classified LRP heuristics into sequential methods, clustering-
based, and iterative and hierarchical heuristics. Sequential methods solve the location
problem first and routing second. It can lead to sub-optimality but is still a good method
for benchmarking. Clustering-based methods start with grouping customers into clusters.
The next step is to locate the depots and solve the VRP for each cluster, or solve the
transportation salesman problem (TSP) for each cluster first and then locate the depots.
Iterative heuristics reduce the problem to location and routing and solve the two
subproblems iteratively. Its advantage over sequential heuristics is that it passes
feedback from one subproblem to another. But this is also the most difficult part of the
approach. In contrast to iterative heuristics, hierarchal heuristics treat the location as the
main problem and routing as a subordinate problem. Most of these heuristics use
searches to locate depots with add/drop/shift procedures, and these moves are supported
from the information of the routing part.
Among clustering-based, iterative, and hierarchical heuristics, clustering-based is
most efficient, gives very good upper bound, and is easy to implement. Barreto et al.
(2007) integrated several hierarchical and non-hierarchical clustering techniques in a
sequential heuristic algorithm. All the versions using different grouping procedures were
tested and the results compared. The results showed that a one-phase hierarchical
method and a direct assignment non-hierarchical method are better, compared with a two-
phase hierarchical method and a sequential assignment non-hierarchical method.
21
2.2.2 Two-Echelon Location Routing Problem (2E-LRP)
A two-level location-routing newspaper delivery problem was first introduced by
Jacobsen and Madsen (1980) and Madsen (1983). Newspapers are delivered from the
factory to transfer points and then to customers. The problem occurs with the number
and locations of transfer points, the tours originating at the printing office to serve the
transfer points, and the tours emanating from transfer points to serve retailers.
Literature which deals with two-level distribution systems is limited. Min (1996)
considered a consolidation terminal location-allocation problem, solving the problem by
using a three-phase sequential heuristic solution procedure. The first step was to cluster
customers into groups. The second step treated the cluster centroid as a customer and
solved the two-level location-allocation problem optimally. The final step designed the
optimal route.
The road-tree routing problem, or a vehicle routing problem with accessibility
constraints, can also be viewed as a two-level LRP. Most of the literature failed to allow
for more than one subtour originating from the root (which can be viewed as a second-
level distribution center). Moreover, the road tree-routing problem did not consider the
goods movement among customer zones.
Some literature deals with the location of first- and second-level distribution centers
but consider only the vehicle routing at the second level. Wasner and Zapfel (2004)
looked at a parcel service problem which determined the number and locations of hubs
and depots and their service areas. The second-level distribution between depots and
demand points was treated as a vehicle routing problem, but the first level did not have
route planning included. An iterative solution heuristics was developed to solve the
problem.
Perboli, Tadei and Vigo (2011) considered a two-level vehicle routing problem.
Location analysis was not included in this problem. A math-based heuristics was
22
developed and compared with the lower bound by linear relaxation. Cuts were proposed
and tested to improve lower and upper bound.
The most complex problem yet might be a four-level LRP by Ambrosino and
Scutella (2005). It involved facility location, warehousing, transportation, and inventory
decisions. In their problem, level one is the plant, level two includes distribution centers,
level three consists of transfer points and some customer zones, and level four contains
the rest of the customer zones. Commercial software was used to solve very small cases
optimally and to show computation time and gap between lower and upper bound for
larger cases.
Lin and Lei (2009) formulated a three-echelon distribution system with two-level
routing considerations. The first echelon was comprised of the plants, with locations
given. The second echelon consisted of distribution centers and some of the big clients.
The third echelon was made up of the rest of the big and small clients. Decisions
included the number and location of distribution centers and which big clients should be
part of the first-level routing. The model also designed the first-and second-level routing.
A genetic algorithm was used to find near optimal solutions. Some small test cases with
one plant were used to compare the heuristic solutions and optimal solutions. This
problem is similar to the City Logistic two-level location routing problem. The difference
is that the City Logistic LRP problem also includes the decision of the first-level nodes
locations and considers the location of external logistic centers.
An increase in City Logistics research over the past decade has brought the two-
echelon location-routing problem to the attention of more researchers. There has been
no research prior to 2011 that combines the location and routing decision for a two-
echelon distribution network. Recent years have seen several studies on the two-echelon
location routing problem. Crainic, Sforza and Sterle (2011) proposed three Mixed-
Integer formulations and compared the advantages and disadvantages of each. They
proposed a three-index formulation, a two-index, and a single index formulation. The
three-index formulation is most flexible and can be easily extended to cases like multi-
23
commodity, time window, and heterogeneous fleets. Nevertheless, it is hard to solve
since it includes a large number of variables and constraints. Compared with three-index
formulation, two-index has fewer variables but more constraints. The single-index
formulation, on the other hand, requires a huge number of variables, but the formulation
is flexible and compact. Nguyen, Prins and Prodhon put forth a multi-start local search
with tabu list and path relinking heuristics (2011a), plus a grasp reinforced by a learning
process and path relinking heuristics (2011b). A two-index formulation was used by
Contardo, Hemmelmayr and Crainic (2011 and 2012) to produce the lower bound and
basis for a branch-and-cut algorithm. Additionally, they proposed an adaptive large-
neighborhood search (ALNS) method. ALNS, compared to the heuristics by Nguyen,
showed superiority in regard to the quality of the upper bound. Several sets of tests
performed on the branch-and-cut method showed that ALNS provides tight lower bounds
and is able to solve small and medium-sized instances to optimality.
A two-echelon location-routing problem with time-windows model was proposed by
Govindan, Jafarian, Khodaverdi and Devika (2014). A hybrid of multi-objective variable
neighborhood search and multi-objective particle swarm optimization algorithm was
developed. And experimental results showed the hybrid approach out formed other
existing algorithms.
2.3 Southern California Planning Model (SCPM)
The Southern California Planning Model (SCPM) is designed to measure regional
economic impacts in the TAZ level. The current version has the data for the five-county
region of Los Angeles. The first version (SCPM 1) was developed in the 1990s
(Richardson, Gordon, Jun and Kim, 1993; Gordon, Richardson and Davis, 1998). It is
primarily a regional input-output model designed to trace all economic impacts, usually
at a certain sectoral and geographical disaggregation level.
24
SCPM2, developed in the late 1990s (Cho, Gordon, Moore, Richardson, Shinozuka
and Chang, 2000 and 2001; Gordon, Moore, Richardson, Shinozuka, An and Cho, 2004),
uses Traffic Analysis Zones (TAZs) to measure traffic flows from one node to another.
The input-output component generates indirect and induced impacts. These impacts are
allocated by a gravity model using travel cost calculated from a transportation network
model. The current version, SCPM 2005, is a combination and upgrade of SCPM 1 and
SCPM 2.
The current version of SCPM, SCPM 2005, is a combination and upgrade of SCPM
1 and SCPM 2 It incorporates a new regional freight database that the USC research
group developed from other projects. Most data in SCPM was updated to create a 2001
base year model. . SCPM 2005 has been used to evaluate economic impact of terrorist
attack on ports (Gordon, Moore, Richardson and Pan 2007), US theme parks (Richardson,
Gordon, Moore, Kim, Park and Pan, 2008), financial district (Pan, Richardson, Gordon
and Moore, 2009) and impact of large urban earthquake (Chang, Cho, Gordon, Moore,,
Richardson and Shinozuka, 2015).
SCPM can be used to evaluate the urban economic impacts of network-specific
changes. It has recently been used to evaluate the expansion of toll lanes and free lanes
(Richardson, Gordon, Moore, Cho and Pan, 2008 and 2015) and implications of
congestion pricing schemes (Pan, Gordon, Moore, and Richardson, 2011).
SCPM 2005 includes two main components. The first is the input-output model
built upon the Minnesota Planning Group‟s IMPLAN model (2001). It has 209 sectoral
disaggregation and 47 USC sectors for small-scale area impacts. The second component
allocates sectoral impacts across 3,191 geographic zones plus 12 external zones, which
are aggregated to 282 primarily political jurisdictions. The key function of this
component is allocating the indirect and induced impacts generated by the input-output
model spatially.
25
SCPM 2005 endogenizes traffic flows, which ensures that any change in economic
activity that affects the travel behavior of individuals or the movement of freight will
influence how the transportation network is utilized. It also uses explicit distance decay
(decline in the number of trips with increasing distance) and congestion functions (build-
up of traffic congestion and delay costs as particular routes attract more traffic as other
parts of the network are disrupted). Impact on route and destination choice enables more
accurate allocation of indirect and induced economic losses over geographic zones in
response to any direct losses.
26
Table 2.1: The Sum of Freight Trips Attractions/Productions in AM peak by USC Sector (Pan, 2007).
Sector Description Freight
Attraction/
Productions
($1000)
Share of Freight
Attractions/
Productions in
Dollar Value
Freight
Attractions/
Productions
(PCEs)
Share of Freight
Attractions/
Productions in
PCE
USC 1 Live animals and live fish & Meat, fish, seafood,
and their preparations
3,151 2.37% 7,936,756 1.59%
USC 2 Cereal grains & Other agricultural products except
for Animal feed
5,584 4.20% 8,041,228 1,62%
USC 3 Animal feed and products of animal origin, n.e.c 1,062 0.80% 3,267,383 0.66%
USC 4 Milled grain products and preparations, and
bakery products
2,993 2.25% 4,311,610 0.87%
USC 5 Other prepared foodstuffs and fats and oils 6,504 4.89% 21,721,972 4.36%
USC 6 Alcoholic beverages 1,383 1.04% 7,367,124 1.48%
USC 7 Tobacco products 348 0.26% 4.098,207 0.82%
USC8 Nonmetallic minerals (Monumental or building
stone, natural sands, gravel and crushed stone,
n.e.c.)
6,190 4.66% 1.716,723 0.34%
USC9 Metallic ores and concentrates 347 0.26% 305,573 0.06%
USC10 Coal and petroleum products (C0al and Fuel oils,
n.e.c.)
2,985 2.25% 33,283,036 6.69%
USC11 Basic chemicals 887 0.67% 5,133,821 1.03%
USC12 Pharmaceutical products 348 0.26% 10,690,353 2.15%
USC13 Fertilizers 687 0.52% 935,795 0.19%
USC14 Chemical products and preparations, n.e.c. 1,050 0.79% 11,916,049 2.39%
USC15 Plastics and rubber 682 0.51% 14,269,563 2,87%
USC16 Logs and other wood in the rough & Wood
products
4,797 3.61% 5,723,042 1.15%
USC17 Pulp, newsprint, paper, and paperboard & Paper or
paperboard articles
1,729 1,30% 15,313,927 3.08%
USC 18 Printed products 647 0.49% 12,554,275 2.52%
USC19 Textiles, leather, and articles of textiles or leather 1,645 1.24% 48,113,159 9.66%
USC20 Nonmetallic mineral products 17,134 12.89% 9,962,117 2.00%
USC22 Articles of base metal 10,717 8.06% 25,303,931 5.08%
USC23 Machinery 6,293 4,73% 26,907,420 5,40%
USC24 Eletronic and other electrical equipment and
components, and office equipment
12,494 9.40% 86,707,256 17.42%
USC25 Motorized and other vehicles (including parts) 4,862 3,66% 27,335,669 5.49%
USC26 Transportation equipment, n.e.c. 346 0.26% 14,939,466 3,00%
USC27 Precision instruments and apparatus 1,180 0.89% 14,672,171 2.95%
USC28 Furniture, mattresses and mattress supports,
lamps, lighting fittings, and illuminated signs
3,244 2.44% 9,357,420 1.88%
USC29 Miscellaneous manufactured products, Scrap,
Mixed freight, and Commodity unknown
27,297 20.53% 52,836,560 10.61%
27
The baseline version of SCPM 2005 was developed using data from a variety of
reliable sources. They included employment by economic sectors (from SCAG 2000
data), population (from Census 2000 data), households, the number of households (from
Census 2000 data), and other socio-economic data for 3,191 TAZs (Pan, Richardson,
Gordon, and Moore, 2009; Giuliano, Gordon, Pan, Park, and Wang, 2010).
Table 2.2: Employment, Population, and Household in the Five County Los Angeles Region, 2000
(Pan, 2007).
County ID County Name Employment Population Household
1 Los Angeles 5,529,916 9,518,807 3,133,257
2 Orange 1,929,745 2,842,765 933,773
3 Riverside 698,665 1,519,432 500,337
4 San Bernardino 757,565 1,683,813 520,115
5 Ventura 411,268 752,982 243,068
SUM 9,327,159 16,317,799 5,330,550
28
Chapter 3
Methodology
The focus of this research is the strategic design of a City Logistics network for a large
urban area. Los Angeles region is used as a case study. The research consists of two
parts. To be viable, the system design must account for economic choices in both the
private and public sectors. The location, mode, and route choices associated with use of
distribution centers should be cost-effective for shippers and, at the same time, effective
in alleviating traffic congestion and environmental problems. Good designs from the
private sector perspective will be identified by applying the two-echelon location and
vehicle routing heuristics. Then SCPM will be used to evaluate the potential designs
from the more aggregate systems level perspective that captures aggregate results
important to public authority. Therefore, the first part of the work applies the location-
routing model to select a set of potential locations and routing designs to minimize
distribution cost; the second uses SCPM to simulate and compare the economic impacts
associated with the set of potential designs.
29
3.1 2E-LRP Modeling and Heuristics.
In the model, we preselect a set of potential locations for first-level DCs and satellites,
each with its own fixed location cost. The travel costs on each link, whether from first
level DC to satellites, between satellites, or from satellites to customer zones, are known.
The links in this case could be truck expressways or railways. The variable set includes
both binary variables associated with the DCs, satellites, routes, and the variables
describing the volume shipped on each link. The objective is to minimize the total
shipping and fixed costs over choices of DC locations and routes.
The formulation of 2E-LRP is comparatively straightforward. It is a logical
extension of the current literature. What is more important is matching a good
formulation to a computationally efficient heuristic algorithm that can be used to solve
larger problems. This is the focus of our project‟s private sector element. The research
goal is to generate a set of good (optimal is mathematically out of reach) logistics system
designs for the private sector entities, i.e., the distributors. The set of designs generated
constitute the scenarios for the second part of the work, an SCPM simulation evaluating
the system performance level implications of each design
3.1.1 2E-LRP Modeling
The two-level location routing problem considers a three-tier system. The first tier
consists of transfer hubs. Transfer hubs are located outside the city boundary and are
close to major logistics centers like seaports, railways, airports, and highway exits. The
second tier is composed of satellites, which are located inside the city. Hubs and
satellites are connected by truck express lanes or railways. The third tier includes
customer zones. The demand and location at each customer zone is given. Each
customer zone has to be served once and once only.
Here we call the routing among hubs and satellites the first level of routing and the
30
routing among satellites and customer zones the second level of routing. The decision
includes the location of hubs and satellites, and also the first and second level of routing.
The formulation is an extension of the Two-Echelon Vehicle Routing Problem (2E-
VRP) model by Perboli, Tader and Vigo (2011). The differences are that the 2E-VRP by
Perboli considers only a single hub, and we expand the 2E-VRP to a 2E-LRP formulation.
The shipment of goods between hubs and external logistics centers is also considered.
Definitions and Notations:
H = {1, 2,…, n
h
}: set of potential hubs, where n
h
is the number of hubs
S = {1, 2,…, n
s
}: set of potential satellites, where n
s
is the number of satellites
C = {1, 2,…, n
c
}: set of customers, where n
c
is the number of customers
E = {1, 2,…, n
e
}: set of major external logistics centers, where n
e
is the number of major external
logistics centers
K
1
,K
2
: capacity of first, second level vehicles
d
i
: demand at customer i
c
1
ij
, c
2
ij
: cost of travelling on arc (i, j) at 1
st
, 2
nd
level
c
3
ij
: cost of travelling from external logistics center i to hub j
p
e
: proportion of goods at a hub coming from external center e
f
1
h
, f
2
s
: cost of fixed cost at hub h, satellite s
31
Decision variables:
F
1
ijh
: flow passing through a 1
st
level arc (i, j), and originating from hub h
F
2
ijs
: flow passing through a 2
nd
level arc (i, j), and originating from satellite s
x
h
, y
s
: Boolean variable equal to 1 if hub h, satellite s is selected
z
1
hs
: Boolean variable equal to 1 if satellite s is served by hub h
z
2
si
: Boolean variable equal to 1 if customer i is served by satellite s
x
ijh
: Boolean variable equal to 1 if 1
st
level arc (i, j) is used by a 1
st
level route originating from
hub h
y
ijs
: Boolean variable equal to 1 if 2
nd
level arc (i, j) is used by a 2
nd
level route originating from
satellite s
This is a three-index formulation. The advantage of this formulation is that it can be
easily expanded to multi-commodity cases and extensions with time window constraints,
along with pick-up and delivery constraints. The variables z
1
hs
and z
2
si
are not necessary
to maintain validity of the model, but their existence helps the IBO ILOG CPLEX
Optimization Studio (abbreviation CPLEX) to efficiently find the optimal solution or a
good lower bound. To lighten the formulation, let B be a number that is larger than the
sum of demands at all customer zones. Also, let D
s
be the total demand of customers that
a satellite serves.
2
,
s si i
iC
D z d s S
(3.1)
The model to minimize the total cost is formulated as follows:
32
1 2 3 1
, , , ,
12
Min ( )
+
ij ijh ij ijs eh e hjh
h H i j H S i j s S i j S C i j h H e E j S
h h s s
h H s S
c x c y c p F
f x f y
(3.2)
Subject to:
,
hjh jhh
j S j S
x x h H
(3.3)
,,
, ,
ijh jih
j S h j i j S h j i
x x i S h H
(3.4)
1
,
, ,
ijh hi
j S h j i
x z i S h H
(3.5)
1
=1,
hi
hH
z i S
(3.6)
,
sjs jss
j C j C
y y s S
(3.7)
,,
, ,
ijs jis
j s C j i j s C j i
y y i C s S
(3.8)
2
,
, ,
ijs si
j s C j i
y z i C s S
(3.9)
2
=1,
si
sS
z i C
(3.10)
2
22
, ,
if
,
if j is satellite s
sj j
ijs jis
i C s i j i C s i j
s
z d j C
F F s S
D
(3.11)
1 1 1
,,
, ,
ijh jih hi j
i h S i j i h S i j
F F B z B D j S h H
(3.12)
1 1 1
,,
, ,
ijh jih hi j
i h S i j i h S i j
F F B z B D j S h H
(3.13)
33
11
, , , ,
ijh
F K i j h S i j h H (3.14)
22
, , ,
ijs
F K i s C i j s S (3.15)
1
1
,,
, , ,
,
ijh hi h
ijh h
x z x
i j h S i j h H
F B x
(3.16)
1
11
, , ,
, , ,
,,
ijh jih hi i
ijh jih i
x x z y
i S j h S i j h H
F F B y
(3.17)
2
2
,,
, , ,
,
ijs si s
ijs s
y z y
i j s C i j s S
F B y
(3.18)
1
2
1
2
{0,1 }, , , ,
{0,1 }, , , ,
{0,1 }, ,
{0,1 }, ,
0, , , ,
0, , , ,
ijh
ijs
hi
si
ijh
ijs
x i j h S i j h H
y i j s C i j s S
z i S h H
z i C s S
F i j h S i j h H
F i j s C i j s S
(3.19)
The objective function minimizes the total distribution cost, which includes:
distribution cost on the 1
st
level arcs, distribution cost on the 2
nd
level arcs, shipping cost
from external logistic centers to transfer hubs, and fixed cost at transfer hubs and
satellites. Constraints (3.3) ensure that the incoming and outgoing routes at transfer hub
h are equal. Similarly, constraints (3.4) makes sure the incoming route of a satellite i
originating from any hub h equals the outgoing route ending at h. A satellite needs to be
served by one and only one hub, which is enforced by constraints (3.6). If a satellite i is
served by hub h, the total number of routes leaving satellite i to hub h should be equal to
1; otherwise, it should be 0, which is enforced by constraints (3.5). Constraints (3.7) –
(3.10) are similar route constraints for the 2
nd
level routing among satellites and
34
customers.
Subtour elimination is enforced by arc flows. Additionally, the arc flow formulation
makes it easier to impose vehicle capacity constraints. Constraints (3.11) indicates that if
a customer j is served by satellite s, the inflow to j originating from s minus the outflow
of j heading back to satellite s should be equal to the demand of customer j. Further,
constraints (3.11) ensure that the outflow of satellite s minus the inflow equals the total
demands of the customers served by s. In contrast, the inflow and outflow relationship at
the 1
st
level routes could not be formulated in the fashion of the 2
nd
level route. This is
because the demand D
s
at satellite s is a variable, and multiplying it by z
1
hs
would make
the formulation quadratic and extremely hard to solve. An alternative formulation in
constraints (3.12) and (3.13) ensures that when z
1
hs
equals 1, i.e., when the satellite s is
served by hub h, inflow to satellite s coming from hub h minus the outflow heading to
satellite s should be equal to D
s
. Constraints (3.14) and (3.15) are capacity constraints of
1
st
level vehicles and 2
nd
level vehicles respectively.
Constraints (3.16) imposes that x
h
=1 if any arc is assigned to a route belonging to
hub h or has flow coming from or going to hub h. It also ensures that x
h
=1if a satellite is
assigned to hub h. Constraint (3.17) ensures that y
i
=1 if any 1
st
level arc connecting
satellite i is utilized or if satellite i is assigned to a hub. Constraints (3.18) are similar to
constraints (3.16), ensuring that y
s
=1 if satellite s is utilized in the 2
nd
level.
As mentioned above, subtours are eliminated by arc flow. The classical subtour
elimination imposes too many constraints and makes large cases impossible to solve.
However, subtour elimination constraints with set size of two add only a small number of
constraints and help optimization software to more efficiently find the optimal solution or
lower bound.
1, , , ,
ijs jis
y y i j s C i j s S (3.20)
Subtour elimination constraints with set size of three or larger considerably increase
the number of constraints and are not added to the model.
35
3.1.2 Heuristics
Various heuristics have been proposed for location routing problems. The 2E-LRP
problem can also be solved with modifications of these heuristics. Each heuristics has its
advantages and disadvantages. Among all heuristics, clustering-based heuristics seem to
produce high quality results and are time-efficient.
For the 2E-LRP problem, in general, the size of the set of customers is larger than
the size of the satellite set, and the size of the hub set is the smallest. Thus, the most
difficult part of the 2E-LRP problem is the vehicle routing among satellites and
customers. Each customer has to be served by one and only one route. If customers were
grouped into clusters at the first step, the problem size would be greatly reduced. This is
because after customers are clustered and routes are optimized in the cluster, each cluster
can be treated as a single unit. In this way the second-level LRP will be reduced to a
small size location allocation problem. Also, since the first-level LRP has a
comparatively small size, the subproblem now can be solved optimally and efficiently by
optimization software.
The heuristics for the 2E-LRP problem can be summarized as:
Step 1: Group customers into clusters.
Step 2: Calculate the allocation cost of assigning each cluster to a satellite
Step 3: Solve the subproblem optimally.
Figure 3.1 shows the three steps of the heuristics.
36
Figure 3.1.a: Step 1: Cluster Customers into Groups. Figure 3.1.b: Step 2: Calculate Allocation Cost.
Figurc 3.1.c: Step 3- Locate Hubs, Satellites, Design the 1
st
Level Route and the 2
nd
Level Allocation.
Step 1: Group customers into clusters
Barreto et al. (2007) integrated several hierarchical and non-hierarchical clustering
techniques in a sequential heuristic algorithm. All the versions using different grouping
procedures were tested and the results compared with each other. Results indicated that a
37
one-phase hierarchical method and a direct assignment non-hierarchical method were
better, compared with a two-phase hierarchical method and a sequential assignment non-
hierarchical method. Six proximity measures were used for each method and are listed in
Appendix B – Proximity Measures. The six proximity measures are single linkage,
complete linkage, group average, centroid, ward, and saving. Testing showed that group
average measure produced the most balanced results, followed by centroid, saving,
complete linkage, single linkage, and ward. Barreto advised to use several versions of
the grouping procedures and several versions of the proximity measures and then choose
the best solution. Based on the conclusions by Barreto, the one-phase hierarchical
method and direct assignment non-hierarchical method are used as the grouping strategy;
group average, centroid, saving, complete linkage, and single linkage are used as the
proximity measures. The clustering procedure is summarized as:
(1) Group customers into clusters with the second level vehicle capacity limit.
(2) Determine the route in each customer cluster.
(3) Improve the route using a 3-optimal local search procedure by Branco and Coeho
(1990).
In the first step, the one-phase hierarchical method and direct assignment non-
hierarchical method are used as the grouping strategy. The one-phase hierarchical
method performs an iterative merging of the nearest two groups if the merged cluster
does not violate the capacity limit. The direct assignment non-hierarchical method first
decides the number of routes:
2
i
iC
d
r
K
(3.21)
Where d
i
is the demand at customer i and K
2
is the capacity of the second vehicle.
Next r customer sources are established using a farthest neighbor proximity measure to
select the customers located on the boundary. The remaining customers are assigned to
38
the r groups with closet proximity measure to a source until the group reaches capacity
limit.
For each cluster generated in procedure (1), route in a cluster is optimized using
CPLEX 12.6. If optimal route cannot be found within a certain time limit, the best
solution is used. The optimal route is found by using the formulation below:
Without loss of generality, an arbitrary node in the cluster is selected as node 0. Let
the other nodes in the cluster be node 1, node 2, …, node n.
Definitions and Notations:
N={0, 1, … , n}, set of nodes in a cluster
D
ij
, distance between node i and node j
Variables:
X
ij
, binary variable equals 1 if arc (i, j) is selected
T
i
, “time” the route arrives at node i, used to avoid subtour
The model to minimize total traveling distance is formulated as:
,
ij ij
i N j N j i
Min D X
(3.22)
,,
..
, i N
ij ji
j N j i j N j i
st
XX
(3.23)
,
1, i N
ij
j N j i
X
(3.24)
0
0 T (3.25)
, i N, ,
j i ij
T T X j N j i (3.26)
39
{0,1 }, i N, ,
ij
X j N j i (3.27)
0, i N
i
T (3.28)
Constraints (3.23) ensure that the incoming and outgoing arcs are equal for each
node. Constraints (3.24) indicate that each node can be visited once and only once.
Constraints (3.25) indicate that the route starts at node 0. Subtours are eliminated by
constraints (3.26).
Because of the capacity constraints, the grouping procedure could sometimes group
together two nodes located far away. A modified 3-optimal local search procedure is
used to improve the clustering. The original procedure considered the number of
clusters to be a constant. In this heuristics, when a cluster has only one node left, node is
inserted into another cluster if total distance would be reduced. Detail of the procedure is
described in figure 3.2 below. This procedure helps to improve the set of clusters.
However, since it does not take the location of satellites into consideration, this step
sometimes increases the overall total cost. It was found in several computational tests
that the original set of clusters has smaller overall cost than the one after the 3-optimal
local search. In several computational tests, both the cluster sets before and after the 3-
optimal local search is outputted to Step 2.
Branco and Coeho‟s (1990)3-optimal procedure starts with a feasible solution.
Changes involving three links are systematically considered to obtain a better solution,
which will then replace the previous ones, until no further improvements are possible.
The procedure is summarized as:
(1): Select three links from the existing circuits. Two links are picked from a circuit
and the other is selected from a different one.
(2): Switch the circuits according to the five different ways shown below.
(3): If improvements are achieved, change the two routes.
40
(4): Go back to step 1 to reselect three links. Stop is no improvements could be made.
Figure 3.2: 3-optimal Local Search Procedure (Branco and Coelho, 1990).
Step 2: Calculate the allocation cost of assigning each cluster to a satellite
Step 1 outputs several possible sets of clusters. Each set of clusters is a candidate
solution. Steps 2 and 3 calculate the total cost for each set of clusters and select the best
one. Step 2 calculates the allocation cost between each satellite and cluster. When
assigning a cluster to a satellite, the best route between the satellite and the cluster is
calculated.
41
Figure 3.3: Assigning a Cluster to a Satellite.
As shown in figure 3.3, when assigning a cluster to a satellite s, one arc in the route is
broken. Let cost (i, j) = dis + dsj – dij. Select the arc (i, j) in the cluster where cost (i, j) is
minimum. Next the distance of the rest of the route and the distance between the satellite
and the cluster are summed up to provide the allocation cost between the cluster and the
satellite.
Step 3: Solve the subproblem optimally
Step 1 group customers into clusters and each cluster can be treated as a single unit.
The cost of assigning the cluster to a satellite is calculated in step 2. Thus the second
level location routing among the satellites and customers is reduced to a small size
location-allocation problem. For a City Logistics problem, the number of satellites is
limited to medium or small size, which enables optimization software to solve the rest of
the problem optimally and efficiently.
The subproblem formulation is a reduction of the problem defined by equation (3.2)
to equation (3.20). Some new notations and variables are added or modified:
CL = {0, 1, … , ncl}, the set of clusters, where ncl is the number of clusters.
A
si
, allocation cost of assigning cluster i to satellite s.
z
2
si
, Boolean variable equal to 1 if cluster i is served by satellite s
d
i
, demand at cluster i
The definition of Ds also changes to:
j
i
s
42
2
,
s si i
i CL
D z d s S
(3.29)
The rest of the variables and notations are defined the way same as the original
problem. The subproblem is formulated as follows:
1 2 3 1
,,
12
Min ( )
+
ij ijh si si eh e hjh
h H i j H S i j s S i CL h H e E j S
h h s s
h H s S
c x A z c p F
f x f y
(3.30)
Subject to:
2
=1,
si
sS
z i CL
(3.31)
2
, ,
Constraints (3.3) - (3.6), (3.12) - (3.14), (3.16) - (3.17) and (3.19)
si s
z y i CL s S
(3.32)
The subproblem is solved optimally by CPLEX 12.6 in numerical cases. In the
instances tested, the longest running time of this subproblem is less than 2 seconds.
3.1.3 Computational Tests
Numerical cases of several recent studies in 2E-LRP were generated from existing CLRP
(Capacitated Location Routing Problem) cases. Eight numerical instances generated
from CLRP were used to test the clustering-based heuristics. The CLRP instances were
obtained or adapted from the literature (Gaskell, 1967; Chrstofides and Eilon, 1969; Perl,
1983; Min et al., 1992; Daskin, 1995). Details about the data are downloadable from
http://sweet.ua.pt/~iscf143/. Distribution cost on the first level arc is set up to be 2.5
times of the second level arc cost. Hub locations are generated randomly, and fixed cost
at the hub is set up to be five times the average fixed cost of the satellites.
The numerical test results are shown in table 3.1. The second column, “Size,” shows
43
the number of customers by the number of potential satellites by the number of potential
hubs for each instance. “LB” is the best lower bound found by CPLEX 12.3. “UB” is
the upper bound found by the heuristics. The lower bound or upper bound with the “*”
sign means it is the optimal solution. The “Gap” column is calculated as (UB-LB)/LB,
which shows the quality of the lower and upper bound.
Table 3.1: Instances of Lower Bound by CPLEX and Upper Bound by the Heuristics.
Instance Size LB UB Gap
1 22 x 5 x 2 930* 930* 0.00%
2 27 x 5 x 2 4928* 4983 1.12%
3 29 x 5 x 2 843* 870 3.20%
4 36 x 5 x 2 725* 734 1.24%
5 50 x 5 x 2 823 873 3.36%
6 55 x 15 x 5 3183 3301 3.71%
7 85 x 7 x 2 4803 4910 2.23%
8 88 x 8 x 3 910 981 7.78%
The lower bounds of the eight instances were solved by CPLEX 12.3 using the
formulation from equation (3.2) to equation (3.20). Optimal solutions were found for
instances 1 to 4. In instances 5 to 8, CPLEX was unable to find the optimal solution
before the computer ran out of memory. Often, when lower bound is extremely hard to
find, we fix the number of utilized satellites and select the one with the smallest lower
bound. The gap between the best lower bound and best upper bound given by CPLEX,
for example, 5 to 8, are 1.18%, 2.78%, 3.65%, and 14.92% respectively. Here, lower
bound 8 is the worst result, which might explain the 7.78% large gap between the UB by
44
the heuristics and the LB by CPLEX. For cases with more than 100 customers and 15
satellites, there is not enough memory for CPLEX to load the model.
The heuristics are implemented by C++ and CPLEX. Except for instance 8, the
heuristics can find a feasible solution within a 3% gap relative to the lower bound on
average. The most time-consuming part of the heuristics might be looking for the
optimal route in a cluster. Generally, the optimal route is found within one second. But
for some special cases, when the demand at customer zones is very small, the number of
customers in a cluster might be very large. Under such special circumstances, it takes a
long time for CPLEX to find an optimal route. However, considering that we have a 3-
optimal local search step after the CPLEX route seeking step, we could stop CPLEX after
a good solution (within 1% gap for instance) is found. In general, CPLEX could find a
very good route with less than 10% gap relative to the lower bound in a very short time.
For all instances, the last step, optimizing the sub problem by CPLEX, took less than
two seconds. So, in general, the heuristics are very efficient and produce good solutions
within a small gap relative to the optimal solution. More cases will be tested using the
samples from recent 2E-LRP literature, and the clustering heuristics will be compared
with known heuristics both in solution quality and running efficiency.
3.2 SCPM Simulation
Strategic, system-level design of a City Logistics network requires answering the
question, “Will the new system improve traffic conditions, and to what degree?” Ideally,
this question would also account for improvements in other aspects of urban life
impacted by the indirect cost of vehicles, such as environmental quality and safety. We
will answer this initial question by applying the SCPM, which is designed to measure
45
regional economic impacts in, but not limited to, the five-county Los Angeles region.
SCPM is numerical implementation of a spatial input-output model of the urban economy.
The model gives special attention to network congestion costs but has (at present) no
emissions component. However, emission can be estimated based on network link
volume and speed. More detail is presented in Chapter 4.6.
The new network configuration will directly affect freight trips associated with
specific sectors and indirectly affect and impose induced effects on other sectors. SCPM
approximates the detailed Los Angeles road network by relying on traffic analysis zones
(TAZs), which are small geographical units appropriate for characterizing traffic flows.
Travel costs calculated from the SCPM transportation network model were employed by
a gravity model to allocate transportation flows and thus impacts generated by the input-
output model. The model includes a high degree of simultaneity and feedback but is
numerically convergent, and the values calculated for endogenous variables are brought
to constituent values via iteration (Moore, Little, Cho, and Lee 2006).
Based on the set of designs provided by the City Logistics problem, SCPM is used
to simulate and compare the impacts of those different designs. These will be a more
dramatic set of network changes than the congestion pricing exercise (Pan, Gordon, Moore
and Richardson, 2011), but SCPM is able to estimate associated changes in travel demands
and routes. The resulting comparisons give public authority a means to identify and
select the design that offers maximum benefit with respect to traffic and other costs.
The steps in figure 3.4 are the activities central to simulating the impact of each City
Logistics design.
46
Trip Distribution
Update passenger
work trip productions and
attractions
Calculate changes in
origins and destinations
of inter mediate freight
movement
Total impacts by zone
Update link volumes, travel
times, and zone-to-zone
travel times
Distribute indirect and
induced impacts
Initialization
Change?
Yes
No
Stop
Figure 3.4: SCPM Simulation Flow Chart.
The simulation outputs the change in traffic (and delay) on each link. Aggregated,
these results show whether and how a City Logistics system improves traffic and
environmental conditions in the metropolitan area. This is a comprehensive research
effort that designs and estimates the public and private benefits of implementing a City
Logistics system. High-level principles of SCPM are covered in the following sections.
47
3.2.1 Trip Generation
The freight and passenger trips originated from and destined to each TAZ for each
economic sector is generated by input/output model. The freight amount at a certain
TAZ and certain sector is proportional to the sector transaction ratio and employment
ratio. For instance, the total freight trip destined at zone z for economic sector i, denoted
by D(i)(z), is calculated by equation (3.33):
'
'
zones
ij
j All sectors ik
k All Sectors z All
m emp j z
D i z SumOutput i
m emp j z
(3.33)
Where
is the input-output matrix multiplier, ( )( ) denotes the number of
employees for economic sector j at zone z, and ( ) is the sum of output for
economic sector i.
3.2.2 Trip Distribution
In the freight distribution step, the freight destined to a certain TAZ is distributed to all
other TAZs by a distance decay function. The less the employment and the longer the
distance, the fewer the number of trips. For instance,
exp( )
Freight o d i
exp( )
i
i
o All Zones
travelCost o d
D i z
travelCost o d
(3.34)
Where ( )( )( ) is the amount of the freight trip from zone o to zone d for
economic sector i,
is a multiplier that minimizes the difference between estimated and
observed trips for economic sector i, and ( )( ) is the travel time from zone
o to zone d.
48
3.2.3 Trip Assignment
The freight assignment is a most important step in the transportation network
simulation. In this step, the passenger and freight trips between each Origin-Destination
(OD) pair finds its shortest path route. We model the Los Angeles network with 89,356
links and 65,535 nodes. Each link has a certain speed limit (free-flow speed) and
capacity. The actual travel time on a certain link depends on the link volume, capacity,
and free- flow speed (speed limit), as illustrated in equation (3.35).
4
1 0.15
LinkVolume
Actual travel time Free flowtravel time
Link Capacity
(3.35)
After we find the shortest path for each OD pair by applying the Label-Correcting
Algorithm, the trip volume of each OD pair is then added to the links on their shortest
paths. This will change the link travel time by the equation (3.35) above. We iterate
through this process until we reach the network equilibrium.
The differences of the freight movement between baseline and City Logistics are
illustrated in figure 3.5 below. The graph on the left shows the baseline freight
movement. For any of the TAZs and external zones (hubs), freight is shipped to any
other zones directly in a dispersed fashion. The City Logistics freight movement is
shown on the right figure. In this example, two zones are selected as satellites. External
zones and hubs are connected by specialized express lanes. Any freight into/out of a
TAZ would be shipped via its satellite. This manner is organized, consolidated, and
environmental friendly. It is obvious from this figure that the City Logistics system
reduces freight in the existing transportation network by the specialized freight lanes
connecting satellites and external zones (hubs). By utilizing an electricity-supported
transportation system for the freight movement, gas consumption and emissions will also
be reduced substantially.
49
SCPM does not use routes in the 2E-LRP model. Instead we assume the freight
demand/origin in each TAZ are delivered to or picked up from directly its satellite via the
shortest path. First of all, most TAZs will have greater than a truckload and freight will
be shipped directly from satellites. More details about TAZ demand in Los Angeles Case
study is presented in Chapter 6.1. Second, the demand is not fixed but fluctuating. That
is, for frequent deliveries, the demand will be a fraction of the total morning peak volume,
adding more fluctuations in demand. This means that the true route will be always
changing, might be clockwise, counterclockwise, or missing some nodes, each one with
similar probability. Actually, then, the route from satellite to TAZ might be starting from
any nodes. Moreover, we want to make comparisons between 2E-LRP model selected
satellites and randomly selected satellites locations. 2E-LRP model outputs the freight
delivery route, while creating random delivery routes would divert from optimal in a
large degree. Thus SCPM simulation with freight delivery routes will make the
comparison extremely biased.
H
H
S
S
H
H
Figure 3.5: Differences Between Baseline Freight Movement (left) and City Logistics Freight
Movement (right).
50
The pseudo-codes for baseline and City Logistics network freight assignment are
summarized below. Here we define the following notation:
, -, -
, -, -
In the baseline simulation, the trip assignment step is:
*
, -, - , -, - .}
Now, if we use the City Logistics system illustrated in figure 1.2, within the 3,191
TAZs, a subset of them will be selected as satellites, denoted by set S. Each of the 3,191
TAZs will be served by one and only one satellite. The set of external zones which now
function as hubs we denote as H. Every external zone is linked to all the satellites by
express lanes. This means that the freight movement among hubs and satellites will no
longer be in the existing network. The trip assignment simulation step now becomes:
*
, -, - +
*
, -, - , -, -
51
, -, -
, -, - ∑ , -, -
, -, - ∑ , -, -
+
3.3 Linking the Two Modeling Systems
The potential locations of distribution centers are selected from a set of logistics system
locations that are advantageous from the perspective of private sector entities. These will
be incorporated into the SCPM network as external stations, i.e., as locations where
exogenous demands for freight transportation are imposed on the system, appearing in
addition to the existing external demands imposed by ports, airports, rail yards, and
highway entry-exit points. SCPM will report the economic impacts and the change in
network traffic conditions associated with adding the distribution centers. This presents
an opportunity for iteration. Modeling results generated by SCPM, such as congestion
information, can loop back to the Location-Routing model, which can then improve the
selection of distribution center locations. See figure 3.6.
52
SCPM Data Inventory Initialization
System level impacts,
including changes in freight
demand
Change?
Stop
Yes
No
Two-echelon location and
vehicle routing (2E-LRP)
model specification
2E-LRP specification for the
Los Angeles Network
2E-LRP candidate solutions
SCPM modified to include
2E-LRP solutions
Figure 3.6: Iteration between SCPM and 2E-LRP Solutions.
Further policy discussions can be based on these iterative exercises and results. In
particular, whether a City Logistics system deserves public financing or encouragement
depends in large part on how costs and benefits are distributed across sectors and space
and how sensitive 2E-LRP solutions (and potential benefits) are to the urban economic
responses that would follow from implementing such a scheme.
53
Chapter 4
Los Angeles Case Study
Los Angeles is often ranked as the most congested city in United States (Schrank, Eisele
and Lomax, 2012). The population in the five-county Los Angeles area is close to 20
million in 2015 (California Department of Finance, 2015). Port Long Beach and Port
Los Angeles supply freight for Los Angeles and the rest of the nation. There are multiple
highways and railways into and out of the metropolitan area. LAX and Ontario airports
serve as major centers for express freight movement. Consequently, the scale and
complexity of the freight network made it an excellent metropolitan area to conduct the
City Logistics Network impact study.
The SCPM simulation incorporates data from all five parts of the county of Los
Angeles. There are overall 3,191 TAZs, including seaports, airports, and railway stations,
plus 12 highway exits. Table 4.1 lists these logistics centers. They will serve as hubs in
the City Logistics network.
54
Table 4.1: Freight Centers in SCPM.
Seaport Port Los Angeles, Port Long Beach
Airport Ontario, LAX, Burbank, Long Beach, John Wayne
Rail LANUS (N.Union), ICTF (Carlson), HYF (Hobart_LAIF)
Highway exit
US-101NW, SR-58, I-15N, I-40, I-5N, SR-62, I-10E, SR-86, SR-14, I-15S,
I-5S, US-395N
The figures below show the distribution of population and freight amount of the
3191 TAZs.
Figure 4.1.a: Population Distribution of TAZs. (Pan, 2007).
55
Figure 4.1.b: Freight Distribution of TAZs. (Pan, 2007).
Later in this chapter we will introduce the 2E-LRP and SCPM feedback simulation
model applied to the Los Angeles case. See figure 4.2 for the overall flowchart. Chapter
4.1 shows the clustering algorithm of 3191 TAZs combining to 2000, 1000, 350 and 150
clusters. The improvement of clustering algorithm by 3-optimal is shown in Chapter 4.3.
Selection of satellite locations by reduced 2E-LRP model is described in Chapter 4.4 and
4.5. Chapter 4.6 introduces the detail of SCPM simulation. Lastly, the simulation result
is presented and discussed in Chapter 4.7 and 4.8.
56
Figure 4.2: City Logistics Simulation Full Feedback Loop.
The feedback model applies real world data for 2E-LRP, and the output of 2E-LRP
will impact current transportation network equilibrium. New travel costs on network
links will generate new solutions of the 2E-LRP model. During this iteration, feedback
information will help to improve the selections of locations, thus reducing overall delay
57
in the current transportation network. To the author‟s knowledge, this is the first study
that incorporates the impact of transportation network equilibrium to the selection of
distribution centers itself.
4.1 Clustering
The first step of the simulation is to group TAZs into clusters in order to reduce problem
size. The second level LRP problem is reduced from a 3191-node routing problem to a
350-cluster assignment problem. The hierarchical clustering algorithm agglomerates
nodes into clusters and combining close-by clusters one by one. The clustering flowchart
is displayed in the figure 4.3 below.
One key parameter at the clustering step is cluster capacity. From the complexity
point of view, a large capacity will make more nodes in one cluster and a smaller cluster
number, meaning a bigger reduction in 2E-LRP problem size but more computation in
finding an optimal route in each cluster. On the other hand, a small capacity will limit
the number of nodes in each cluster, making it easier to find an optimal route in each
cluster but difficult to achieve global optimality in the 2E-LRP step.
58
Figure 4.3: Clustering Algorithm Flow Chart.
Realistically, vehicles need to pick up and deliver freight within a limited time
period. This requires the cluster size be reasonably small. The smaller it is, the more
efficient it is to pick up from or deliver freight to TAZs. This leads to an important issue:
to ensure delivery in a timely manner, freight needs to be transferred from satellites to
TAZs directly without a routing. However, that will consume too many vehicles
containing less than a full truckload. Figure 4.4 shows the distribution of freight demand
in the 3191 TAZs. The total demand of most TAZs ranges from 1 to 1000 k$ in one
morning peak. The conversion for 1000$/PCE ranges from 0.2 to 13 for each USC sector.
59
This means that if freight is picked up from satellites every 15 minutes, the average pick-
up volume for each TAZ could have a huge variation, from 2% of a truckload to
thousands of loads. Considering the fact that some commodities can be shipped together
and some cannot, the variation would be even more. In other words, some TAZs would
have more truckloads and others can be served along with another 10 or 20 TAZs.
Figure 4.4: TAZs Demand Distribution.
Another practical factor is that demand does not come fixed. The delivery route will
always be changing. Moreover, as discussed above, the number of TAZs sharing a route
would be small. So the second-level routing serves more as a method to evaluate best
0 0.5 1 1.5 2 2.5 3 3.5 4
0
50
100
150
200
250
300
350
400
450
ln(demand+1), demand in 1000$
# of TAZs
60
locations of satellites rather than designing the everyday routes from satellites to TAZs.
And thus SCPM simulation does not incorporate 2E-LRP routes but freight is assigned on
shortest path between TAZs and satellites.
With the above considerations, the final cluster should be an area where TAZs have
a similar distance to satellites and which might be served either separated or together
with close-by TAZs in the same cluster. In this sense, the capacity of cluster is set to 250
and the upper limit of number of TAZs in a cluster is set to 15. These parameters are
adjusted based on an actual experimental run. It will result in 350 clusters, as shown in
figure 4.5.d. It serves best to reduce 2E-LRP size, while the cluster size is small enough
for TAZs in the clusters to be treated similarly while satellites deliver/pick up freight.
The different sizes of clusters are shown from figure 4.5.a to figure 4.5.e.
Figure 4.5.a: Step 1 Clustering: 3,191 Clusters.
61
Figure 4.5.b: Step 1 Clustering: 2,000 Clusters.
Figure 4.5.c: Step 1 Clustering: 1,000 Clusters.
62
Figure 4.5.d: Step 1 Clustering: 350 Clusters.
Figure 4.5.e: Step 1 Clustering: 150 Clusters.
63
4.2 CPLEX Optimal Cluster Route
Once nodes are grouped into clusters, CPLEX finds an optimal route in each cluster.
Most of them finish instantly, and some large cases finish in a few minutes. The total
running time could range from five minutes to thirty minutes, depending on the clustering
step.
4.3 3-optimal Clustering Improvement
The clusters produced by the hierarchical clustering algorithm can be further improved
by 3-optimal algorithm. It iteratively tries to exchange nodes of two clusters and will
keep the changes if it reduces route distance. The flowchart of 3-optimal is shown in
figure 4.6. It continues to switch clusters until there is no further improvement. Total
route distance decreases in each search iteration, as shown in figure 4.7. The Los
Angeles case demonstrates that 3-optimal can improve the hierarchical algorithm by 7%,
and most are achieved in the first two searches. Considering time efficiency, three
searches are run each time.
64
Figure 4.6: 3-optimal Code Flowchart.
Figure 4.7: Improvement of Total Cluster Route Length by 3-optimal.
65
4.4 Selection of Potential Satellites and Assignment Cost
The key to an effective strategic design is a good set of candidate satellites for CPLEX.
All the TAZs are candidate satellites. Optimally, CPLEX will select the best locations
from these 3,191 potential choices. In practice, only a set of locations is presented to
CPLEX for computational efficiency. The potential set should a) cover the whole of
five-county Los Angeles and close-by subcenters, and b) be proportional to population
density and congestion level. First, there should be at least one or two potential satellites
near dispersed subcenters. This is obvious, since a satellite too far away would lead to
excess freight pick-up/delivery travels. For population-dense areas, reduced freight trips
would be a tremendous remedy to relieve congestion. Hence, because Los Angeles
County has a higher population and TAZ density, there should be more candidate
satellites.
With the above two criteria, selection of potential satellites can be achieved with a
very simple method: pick a potential satellite from the 3191 TAZs with equal probability.
Since 3,191 is a fairly large number, picking up TAZs randomly will ensure that potential
satellites satisfy criteria b. After this step, if no potential satellites are selected for
dispersed subcenters, one TAZ in these areas will be manually selected.
An important factor to consider is the number of potential satellites. Obviously the
range would be from 22 to 350, i.e., the number of hubs and the number of clusters.
Figure 4.8 displays 40 randomly selected potential satellites based on the above method.
It covers the five counties within the Los Angeles region. More potential selections
would be a repetition, adding to more computation time and leading to very minimal
benefit. This is verified by experimental runs. With an experimental run of 50 potential
satellites, the total objective of 2E-LRP decreased only by 0.2%, which almost same with
the iteration convergence threshold.
66
Another set of experiments is to select different groups of candidate satellites based
on the above approach. Shown for different sets, the total objective value would have a
variance between -0.5% and 0.5%. Results indicate that the methodology provides a
solid selection of potential satellites.
Figure 4.8: Potential Satellites Locations and Hub Locations.
After satellites locations are selected, assignment costs from each satellite to each
cluster are calculated (figure 4.9). To improve computation efficiency of step 5, for each
satellite, only the 100 nearest clusters‟ assignment costs are actual costs; the farther-away
clusters‟ assignment costs are set to a large number.
67
Figure 4.9: Step 4 Assignment Cost Flowchart.
4.5 Optimal Locations of Satellites.
With all the preparation for the previous steps, the large-scale 2E-LRP problem is
reduced to a two-level location-allocation problem that could be solved optimally within
an efficient amount of time. The input to this step is the candidate satellites plus the
assignment cost of each satellite to each cluster.
Although the model has the ability to select from potential locations of hubs, the
Los Angeles region has existing logistics centers, like highway exits, airports, and
seaports. Freight is shipped into and out of the system from these logistics centers.
Accordingly, the case study treated these 22 logistics centers as already selected hubs.
For an under developing urban land, though, potential locations of hubs can be provided
and selected by this model.
68
One important parameter at this step is the operating cost of satellites, which
indirectly impacts how many satellites will be selected. With a high operating cost, it is
more efficient to have vehicles make longer trips and have fewer satellites. Conversely,
when the operating cost is low, the best strategy would be to have as many satellites as
possible to have shorter delivery/pick-up trips. Estimating costs is difficult, since the
satellite is a brand new idea and there is no data available. However, an important fact is
that the fixed cost has a high correlation with the number of clusters a satellite serves.
The more clusters a satellite serves, the larger the scale of the satellite. In short, the
number of clusters it serves decides the operating cost, not the other way around. As
discussed in Chapter 4.1, the capacity of a cluster is set to 250. Since the average
assignment cost between satellites and ten close-by clusters is two hours, and average
cluster demand is 150, the average cost of serving one cluster is around 300. If one
satellite serves between 10 to 20 clusters, the vehicle travelling cost would be between
3000 and 6000. The operating cost of a satellite should be one scale less than the vehicle
travelling cost, because it just serves as a transfer point for light vehicles to pick up from
or deliver to trains on express lanes. Hence, a set of values between 300 and 600 was
tried, and 30 to 25 satellites were selected correspondingly. 500 operating cost was
selected to run for all scenarios in this case study. Figure 4.10 below displays the
satellites selected by CPLEX.
69
Figure 4.10.a: Candidate Satellites (blue points) and Selected Ones (in red circles).
2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
x 10
5
3.65
3.7
3.75
3.8
3.85
3.9
3.95
x 10
6
70
Figure 4.10.b: TAZs Satellites Assignment (the Close by TAZs with same color are assigned to same
satellite).
Upon optimal solution of CPLEX, the assigned satellites for each TAZ are passed to
SCPM. This frames the structure of the City Logistics network, and impact to traffic will
be simulated in SCPM. The running time of this two-echelon location-allocation model
falls within an efficiently range and is approximately one hour in average.
3 3.5 4 4.5 5 5.5 6 6.5
x 10
5
3.65
3.7
3.75
3.8
3.85
3.9
3.95
x 10
6
71
4.6 Objective Functions in the SCPM simulation
With the City Logistics network, SCPM can start to simulate the impact of moving most
freight out of the current system. For all scenarios, the objective value that is used to
check equilibrium drops quickly after ten iterations. After 30 iterations the objective only
decreases by 0.2% per iteration. 50 iterations are run for the trip assignment step in this
study, where objective value gap between two iterations is less than 0.1%. The
convergence step of the objective function is shown in figure 4.11.
Figure 4.11: Convergence of Object Value for Baseline and City Logistics in SCPM Simulation.
City logistics takes part of the freight movement out of the baseline network. It
enables freight to move in a specialized and non-congested network and leaves capacity
for passenger trips in the existing network. It is in our interest to see how much delay
72
and gas consumption it reduces. When the simulation reaches equilibrium, we calculate
the following objective values:
Total Delay =
All links
Actual travel time Free flow travel time Link Volume (4.1)
Total Gas Consumption =
()
All links
All links
Link Length Link PassengerVolume
Passenger car fuleeconomy actual speed
Link Length Link FreightVolume
Freight fuleeconomy actual speed
(4.2)
Total Free Flow Gas Consumption =
()
()
All links
All links
Link Length Link PassengerVolume
Passenger car fuleeconomy free flow speed
Link Length Link FreightVolume
Freight fuleeconomy free flow speed
(4.3)
The fuel efficiency for passengers and freight are estimated by the regression
equations below, based on fuel efficiency data from EPA/FHWA‟s MOVES model
equations (Federal Highway Administration, 2010). A validation study showed that the
difference of gasoline consumption between MOVES model and FHWA estimates were
less than 2% in the national level and 11% for California.
2
Passenger Car Fuel Economy 0.0066 0.823 6.1577 speed speed (4.4)
Truck Fuel Economy 1.4898 ln 0.2554 speed (4.5)
These equations are also used to calculate fuel economy in the Texas Transportation
Institute‟s well-known and widely cited Urban Mobility (Schrank, Eisele and Lomax
2012) and Congested Corridors report (Schrank, Eisele and Lomax 2012).
The total delay cost can also be estimated. We assume the average vehicle
occupancy for cars is 1.59 passengers per car same as Congested Corridors report
73
(Schrank, Eisele and Lomax 2012). The delay cost for each passenger is $16.30 per hour
and $88.12 per hour for freight. Thus,
Total Delay Cost (1.59 16.30
88.12 )
All links
Actual free flow travel time
Link PassengerVolume Link Freight Volume
(4.6)
4.7 Experimental results
Three 2E-LRP scenarios where performed with different sets of candidate satellites. Five
scenarios with 28 randomly selected satellites and another five scenarios with 30
randomly picked satellites were also simulated in SCPM. TAZs are assigned to its nearest
satellite in these 10 scenarios.
74
Table 4.2: SCPM Simulation Results. Columns 6 to 11 are in Million Hours. Columns 12 to 14 are in Million Gallons.
Total Obj P Obj F Obj Total
Time
P Total
Time
F Total
Time
Total
Free
Time
P Total
Free
Time
F Total
Free
Time
P Gas P Free
Gas
F Gas F Free
Gas
Baseli
ne
2.46E+08 10.25 1.48 11.73 10.25 1.48 2.18 1.98 0.20 4.65 1.56 3.28 1.85
30
Rando
m Sat.
Case 1
2.05E+08 8.85 0.12 8.97 8.85 0.12 2.03 2.00 0.03 4.34 1.57 0.34 0.21
Case 2
2.01E+08 8.64 0.10 8.74 8.64 0.10 2.01 1.98 0.03 4.28 1.56 0.30 0.18
Case 3
2.01E+08 8.64 0.10 8.74 8.64 0.10 2.01 1.98 0.02 4.26 1.55 0.26 0.16
Case 4
2.01E+08 8.67 0.09 8.76 8.67 0.09 2.01 1.98 0.02 4.27 1.55 0.27 0.17
Case 5
2.03E+08 8.73 0.13 8.86 8.73 0.13 2.01 1.99 0.03 4.29 1.56 0.28 0.17
28
Rando
m Sat.
Case 1
2.05E+08 8.88 0.12 9.00 8.88 0.12 2.02 1.99 0.03 4.34 1.56 0.34 0.22
Case 2
2.03E+08 8.75 0.12 8.86 8.75 0.12 2.02 1.99 0.03 4.31 1.56 0.34 0.21
Case 3
2.04E+08 8.79 0.09 8.89 8.79 0.09 2.03 2.00 0.03 4.33 1.57 0.32 0.22
Case 4
2.04E+08 8.81 0.12 8.93 8.81 0.12 2.02 1.99 0.03 4.31 1.56 0.35 0.21
Case 5
2.06E+08 8.94 0.14 9.08 8.94 0.14 2.03 1.99 0.03 4.36 1.56 0.41 0.26
Case 1 Iter 1
2.03E+08 8.76 0.09 8.86 8.76 0.09 2.02 1.99 0.03 4.32 1.56 0.33 0.23
Iter 2
2.00E+08 8.57 0.08 8.65 8.57 0.08 2.01 1.98 0.02 4.27 1.55 0.27 0.18
Iter 3
2.00E+08 8.55 0.07 8.62 8.55 0.07 2.00 1.98 0.02 4.25 1.55 0.26 0.18
Iter 4
2.00E+08 8.56 0.08 8.64 8.56 0.08 2.00 1.98 0.02 4.26 1.55 0.27 0.19
Case 2 Iter 1
2.02E+08 8.71 0.09 8.80 8.71 0.09 2.02 1.99 0.03 4.31 1.56 0.33 0.23
Iter 2
2.01E+08 8.61 0.08 8.69 8.61 0.08 2.01 1.98 0.03 4.28 1.55 0.29 0.21
Iter 3
1.99E+08 8.53 0.09 8.61 8.53 0.09 2.00 1.98 0.03 4.25 1.55 0.29 0.20
Iter 4
1.99E+08 8.48 0.08 8.57 8.48 0.08 2.00 1.98 0.02 4.23 1.55 0.25 0.16
Iter 5
1.99E+08 8.51 0.11 8.62 8.51 0.11 1.99 1.97 0.02 4.22 1.54 0.32 0.18
Case 3 Iter 1
2.03E+08 8.77 0.09 8.86 8.77 0.09 2.02 1.99 0.03 4.32 1.56 0.31 0.21
Iter 2
1.99E+08 8.50 0.11 8.60 8.50 0.11 2.00 1.97 0.03 4.23 1.55 0.31 0.19
Iter 3
2.01E+08 8.61 0.09 8.69 8.61 0.09 2.01 1.98 0.03 4.28 1.55 0.29 0.19
75
4.7.1 2E-LRP Simulation Results
The first observation is that 2ELRP-SCPM iteration converges and decreases. This
means that the iteration has fulfilled its purpose to improve the City Logistics system
through feedback network link cost. The fact that objective value converges means that
equilibrium has been achieved. This does not necessarily imply optimality. However, it
should be very close. We will argue with the proof of contradiction: the passenger OD
flow does not change; the only flow that changes is freight OD flowing from satellites to
TAZs. Suppose there is another set of satellite locations that have a much smaller total
objective. There must be low traffic from unselected satellites to nearby TAZs so that
when accommodating freight flows there will not be congestion. If this is true, 2E-LRP
would have selected these satellites. They‟re not being selected implies that the network
load must be high for those unselected satellites and, therefore, that the equilibrium set of
satellites is near optimal. To further enforce optimality, three different sets of potential
satellites are randomly selected by the rules described in Chapter 6.1.4. In all cases, they
converge to similar total objective value, ranging from 198.8 million to 199.6 million.
And the variation is less than 0.5%.
Figure 4.12.a: Objective of Baseline and Case 1 in Millions.
245.6
203.1
200.1 199.6 199.8
150
170
190
210
230
250
270
Baseline Iter One Iter Two Iter Three Iter Four
Objective
76
Figure 4.12.b: Objective of Baseline and Case 2 in Millions.
Figure 4.12.c: Objective of Baseline and Case 3 in Millions.
245.6
202.5
200.7
199.4 198.8 199.2
150
170
190
210
230
250
270
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Objective
245.6
203.1
199.1
200.7
150
170
190
210
230
250
270
Baseline Iter 1 Iter 2 Iter 3
Objective
77
The second observation is that the 2E-LRP model-selected locations of satellites
have a 25% less total travel time than baseline. This is expected because removing 10%
of current network flow should lead to an improvement of more than 10% total time for a
congested city. 55% of the savings comes from passengers and 45% comes from freight.
Figure 4.13.a: Total Travel Time of Baseline and 2E-LRP per AM Peak, Case 1.
11.7
8.86
8.65 8.62 8.64
6
7
8
9
10
11
12
Baseline Iter One Iter Two Iter Three Iter Four
Total trave time (million hours)
78
Figure 4.13.b: Total Travel Time of Baseline and 2E-LRP per AM Peak, Case 2.
Figure 4.13.c: Total Travel Time of Baseline and 2E-LRP per AM Peak, Case 3.
The City Logistics network also saves 45% of gas consumption compared with
baseline. 90% of these savings comes from freight and 10% comes from passengers.
11.7
8.8
8.69
8.61
8.57
8.62
6
7
8
9
10
11
12
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Total travel time(million hours)
11.7
8.86
8.6
8.69
6
7
8
9
10
11
12
Baseline Iter 1 Iter 2 Iter 3
Total travel time (million hours)
79
Figure 4.14.a: Total Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 1.
Figure 4.14.b: Total Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 2.
7.93
4.65
4.54 4.51 4.53
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
Baseline Iter One Iter Two Iter Three Iter Four
Total gas consumption (million gallons)
7.93
4.64
4.57 4.54 4.49 4.54
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Total Gas Consumption (million gallons)
80
Figure 4.14.c: Total Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 3.
A similar observation holds for passenger-related objectives. City logistics reduce
passenger total time by 18% and gas consumption by 10%. Since in City Logistics the
remaining freight distribution on baseline network is only 1% of passenger trips, the
iteration with best overall objectives is also the iteration with best passenger objectives.
7.93
4.63
4.53 4.56
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
Baseline Iter 1 Iter 2 Iter 3
Total Consumption (million gallons)
81
Figure 4.15.a: Passenger Total Time of Baseline and 2E-LRP per AM Peak, Case 1.
Figure 4.15.b: Passenger Total Time of Baseline and 2E-LRP per AM Peak, Case 2.
10.3
8.76
8.57
8.55 8.56
7
7.5
8
8.5
9
9.5
10
10.5
Baseline Iter One Iter Two Iter Three Iter Four
Passenger total time (million hours)
10.3
8.71
8.61
8.53
8.48
8.51
7
7.5
8
8.5
9
9.5
10
10.5
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Passenger total time (million hours)
82
Figure 4.15.c: Passenger Total Time of Baseline and 2E-LRP per AM Peak, Case 3.
Figure 4.16.a: Passenger Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 1.
10.3
8.77
8.5
8.61
7
7.5
8
8.5
9
9.5
10
10.5
Baseline Iter 1 Iter 2 Iter 3
Passenger total time (million hours)
4.65
4.32
4.27
4.25
4.26
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Baseline Iter One Iter Two Iter Three Iter Four
Passenger gas consumption (million
gallons)
83
Figure 4.16.b: Passenger Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 2.
Figure 4.16.c: Passenger Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 3.
4.65
4.31
4.28
4.25
4.23
4.22
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Passenger gas consumption (million
gallons)
4.65
4.32
4.23
4.28
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
Baseline Iter 1 Iter 2 Iter 3
Passenger gas consumption (million
gallons)
84
There are two main reasons for the proportions not being the same: 1) gas
consumption is exponentially rather than linearly correlated with speed; and 2) not all
network links are subject to a similar decrease in congestion. Although most network
links have a substantial relief of congestion, a few uncongested ones might have some
increase in traffic for the local freight pick-up and delivery. Feedback iteration also
improves gas consumption by another 2%.
Freight-trip delay and gas consumption have a significant impact on the baseline
transportation network. Based on table 4.2 and figure 4.17, the remaining freight in the
City Logistics network free travel time is 11% of baseline network (0.023 million hours
of 0.2 million hours); and total actual travel time reduces to only 5% of baseline network
(0.08 million hours of 1.48 million hours). Of course, 5% is less than half of 11%, which
means that City Logistics removes freight from the most congested part of an existing
network and highly utilizes the less congested links. Gas consumption by freight also
drops to 8% of baseline. Considering that freight consumes 40% of gas in the baseline
network, this 37% drop in gas consumption in the whole five counties of Los Angeles
results in greatly reduced pollution and noise. The freight transportation on City
Logistics special lanes are assumed to be using environmentally friendly energy, like
electricity, which, according to research (Federal Transit Administration 2007 ), causes a
CO
2
emission level of only 30% of what is caused by gasoline.
85
Figure 4.17.a: Freight Total Time of Baseline and 2E-LRP per AM Peak, Case 1.
Figure 4.17.b: Freight Total Time of Baseline and 2E-LRP per AM Peak, Case 2.
1.48
0.093
0.080 0.073 0.079
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Baseline Iter One Iter Two Iter Three Iter Four
Freight total time (million hours)
1.48
0.089
0.080 0.087 0.082
0.115
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Freight total time (million hours)
86
Figure 4.17.c: Freight Total Time of Baseline and 2E-LRP per AM Peak, Case 3.
Figure 4.18.a: Freight Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 1.
1.48
0.095
0.107
0.086
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Baseline Iter 1 Iter 2 Iter 3
Freight total time (million hours)
3.28
0.33
0.27 0.255 0.271
0
0.5
1
1.5
2
2.5
3
3.5
Baseline Iter One Iter Two Iter Three Iter Four
Freight gas consumption (million
gallons)
87
Figure 4.18.b: Freight Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 2.
Figure 4.18.c: Freight Gas Consumption of Baseline and 2E-LRP per AM Peak, Case 3.
The freight travel time on the City Logistics network drops to 5% compared with
baseline. The other legs of freight transportation are performed by express lanes or, more
likely, railways. The traveling time on these lanes should be similar to free-flow travel
3.28
0.326
0.294 0.29
0.253
0.318
0
0.5
1
1.5
2
2.5
3
3.5
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Freight gas consumption (million
gallons)
3.28
0.314 0.307 0.288
0
0.5
1
1.5
2
2.5
3
3.5
Baseline Iter 1 Iter 2 Iter 3
Freight gas consumption (million
gallons)
88
time on baseline. However, considering that they are transferring times from these lanes
to final pick-up/delivery light vehicles and that the pick-up/delivery could involve
multiple legs to TAZs, the total freight travel time on City Logistics lanes would be
similar to that of baseline.
The most important finding in the iterations between 2E-LRP and SCPM is the
feedback information that helps improve the overall objective quite significantly. For all
three cases, the iteration saves 3% of the total travel time and 2% - 4% of gas. This is a
¼ improvement in the City Logistics network.
The figure below shows how much the objective would divert from optimal if
ignoring the impact of freight on the transportation network. In the first iteration, the
total passenger time is not much better than even randomly selected satellites. This is
because the 2E-LRP selected satellites‟ locations were based on static baseline network
cost. With feedback information, the model has learned the impact of the light vehicle
freight distributions. Consequently, it discards the locations of satellites that are causing
substantial traffic and selects alternatives. In this way, the second-round iterations
always have a shorter total passenger travel time. Furthermore, although the freight total
time would decrease most of the time, it would sometimes increase to achieve a much
lower passenger total time (see figure 4.19.c).
89
Figure 4.19.a: Total Passenger and Freight Time of Baseline and 2E-LRP per AM Peak, Case 1.
Figure 4.19.b: Total Passenger and Freight Time of Baseline and 2E-LRP per AM Peak, Case 2
Baseline Iter One Iter Two Iter Three Iter Four
Total 11.70 8.86 8.65 8.62 8.64
Passenger 10.30 8.76 8.57 8.55 8.56
Freight 1.48 0.093 0.080 0.073 0.079
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
Travel time (million hours)
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Total 11.70 8.80 8.69 8.61 8.57 8.62
Passenger 10.30 8.71 8.61 8.53 8.48 8.51
Freight 1.48 0.09 0.08 0.09 0.08 0.12
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
Travel time (million hours)
90
Figure 4.19.c: Total Passenger and Freight Time of Baseline and 2E-LRP per AM Peak, Case 3.
Figure 4.20.a: Total Passenger and Freight Gas of Baseline and 2E-LRP per AM Peak, Case 1
Baseline Iter 1 Iter 2 Iter 3
Total 11.70 8.86 8.60 8.69
Passenger 10.30 8.77 8.50 8.61
Freight 1.48 0.09 0.11 0.09
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
Travel time (million hours)
Baseline Iter One Iter Two Iter Three Iter Four
Total 7.93E+00 4.65E+00 4.54E+00 4.51E+00 4.53E+00
Passenger 4.65E+00 4.32E+00 4.27E+00 4.25E+00 4.26E+00
Freight 3.28E+00 3.30E-01 2.70E-01 2.55E-01 2.71E-01
0.00E+00
1.00E+00
2.00E+00
3.00E+00
4.00E+00
5.00E+00
6.00E+00
7.00E+00
8.00E+00
9.00E+00
Gas consumption (million gallons)
91
Figure 4.20.b: Total Passenger and Freight Gas of Baseline and 2E-LRP per AM Peak, Case 2.
Figure 4.20.c: Total Passenger and Freight Gas of Baseline and 2E-LRP per AM Peak, Case 3.
This experiment brings up the question of the significance of considering the impact
of baseline traffic for any time-related problem. In the City Logistics case study, freight
Baseline Iter 1 Iter 2 Iter 3 Iter 4 Iter 5
Total 7.93E+00 4.64E+00 4.57E+00 4.54E+00 4.49E+00 4.54E+00
Passenger 4.65E+00 4.31E+00 4.28E+00 4.25E+00 4.23E+00 4.22E+00
Freight 3.28E+00 3.26E-01 2.94E-01 2.90E-01 2.53E-01 3.18E-01
0.00E+00
1.00E+00
2.00E+00
3.00E+00
4.00E+00
5.00E+00
6.00E+00
7.00E+00
8.00E+00
9.00E+00
Gas consumption (million gallons)
Baseline Iter 1 Iter 2 Iter 3
Total 7.93E+00 4.63E+00 4.53E+00 4.56E+00
Passenger 4.65E+00 4.32E+00 4.23E+00 4.28E+00
Freight 3.28E+00 3.14E-01 3.07E-01 2.88E-01
0.00E+00
1.00E+00
2.00E+00
3.00E+00
4.00E+00
5.00E+00
6.00E+00
7.00E+00
8.00E+00
9.00E+00
Gas consumption (million gallons)
92
volume is 10% of passenger in baseline, and in the City Logistics network it is only 1%
of passenger volume. Different distribution of this 1% freight could impact passenger
total time up or down by 5%. The selection of satellite locations also varies greatly from
iteration 1 to converged locations. And freight total time could change up and down by
20% for better passenger travel time. In this sense, any transportation problem that
makes changes to more than 10% or even more than 1% of network volume level should
consider the impact of traffic changes on network link time. Or else the objective and
solution would divert far from optimal.
4.7.2 Improvement of 2E-LRP Versus Random Satellites
Ten sets of randomly selected satellites were simulated in SCPM. Five cases have 30
satellites and another five have 28 satellites. The 2E-LRP model selects 28 satellites in
most cases and 27 satellites in one iteration. As a result, the 28-satellites scenarios are
comparable to 2E-LRP selected satellites and provide a good benchmark. Additionally,
the 30-satellites scenarios show that adding more satellites would have only 1% -2%
improvements in total objective.
Figure 4.21: Objective of Baseline, 28 Random Satellites Scenarios and Three 2E-LRP Scenarios in
Millions.
246
205
203
204 204
206
200
199 199
180
190
200
210
220
230
240
250
Baseline Rand 1 Rand 2 Rand 3 Rand 4 Rand 5 Case 1 Case 2 Case 3
Objective
93
Figure 4.22: Objective of 28 and 30 Random Satellites Scenarios in Millions.
The most important conclusion from the figure above is this: freight and passenger
trips benefit tremendously from 2E-LRP modeling and feedback iterations. Primarily, the
first iteration of 2E-LRP reduces total freight time by 1.5% from the average of randomly
selected satellites. The following iteration further reduces total trip time by around 3%.
For one reason, 2E-LRP selected satellites have lower freight distribution costs. Better
selection of satellites means less congested roads can be selected to serve freight, leading
to lower passenger travel time. Secondly, the feedback information from SCPM re-
evaluates the impact of freight and makes better selections of satellites and allocations of
TAZs. This further improves the total objective.
Another expected observation is that the 2E-LRP solution has a 3% - 4% less gas
consumption than randomly selected satellites. Randomly selected satellites are able to
reduce gas consumption by 40%, and the 2ELRP model can improve that to around 44%.
205
203
204 204
206
205
201 201 201
203
198
200
202
204
206
208
Rand 1 -
28
Rand 2 -
28
Rand 3 -
28
Rand 4 -
28
Rand 5 -
28
Rand 1 -
30
Rand 2 -
30
Rand 3 -
30
Rand 4 -
30
Rand 5 -
30
Objective
94
Figure 4.23: Total Time, Passenger Time, Freight Time of 28-Satellites Scenarios and Three 2E-LRP
Scenarios in Million Hours per AM Peak.
Figure 4.24: Total Gas, Passenger Gas, Freight Gas of 28-Satellites Scenarios and Three 2E-LRP
Scenarios in Million Gallons per AM Peak.
4.8 Case Study Summary
The impact of City Logistics is summarized in the table below. To get an estimate of the
annual impact, we conservatively multiply AM peak data by two to get a daily value and
then multiply by 260 days/year. Gasoline price is assumed to be $4 per gallon
(California Energy Commission, 2015).
11.70
9.00
8.86 8.89 8.93
9.08
8.62
8.57 8.60
7.00
8.00
9.00
10.00
11.00
12.00
Baseline Rand 1 Rand 2 Rand 3 Rand 4 Rand 5 Case 1 Case 2 Case 3
Total travel time (million
hours)
7.93
4.68 4.65 4.65 4.66
4.77
4.51 4.49 4.53
0.00
2.00
4.00
6.00
8.00
10.00
Baseline Rand 1 Rand 2 Rand 3 Rand 4 Rand 5 Case 1 Case 2 Case 3
Total gas consumption
(million gallons)
95
TABLE 4.3: Output of SCPM Simulation.
Baseline
(one AM peak)
City Logistics
(one AM peak)
Impact
(one AM peak)
Annual
Impact
Total Passenger Time
(hour)
10.3 million 8.5 million 1.8 million 0.93 billion
Total Gas Consumption
(gallon)
7.9 million 4.5 million 3.4 million 1.8 billion
Total Cost ($) 60 million 31 billion
City logistics saved 0.93 billion hours per year, helping to save approximately 100
hours per driver per year (assuming that there are 9 million drivers in AM peak) and 12
minutes per AM peak. This is a significant improvement for all peak period commuters.
California consumes 14 billion gallons of gas for Motor per year (United States
Energy Information Administration 2013). This is consistent with the estimation of 7.9
million gallons consumption per AM peak above. Considering California had close to 40
million population in 2014 (United States Census Bureau 2014), the five county Los
Angeles region with 16 million population in SCPM should consumed 5.6 billion gallons
of gasoline approximately. If we multiply 7.9 million by 250 work days and 2 peaks per
day, the annual consumption is 4 billion. Considering the non-peak hour and weekend
gas consumption is not included in the 4 billion, the two numbers adds up very well.
Almost 90% of the 3.4 million gallons of gasoline saved comes from freight trips. It
was assumed that the City Logistics network utilizes environmentally friendly energy
sources, e.g., electricity. Such energy sources are much cheaper and, more importantly,
generate much lower emissions than gasoline (Federal Transit Administration 2007).
The noise in neighborhood areas is also greatly reduced, and both drivers and residents
are safer.
The 2E-LRP designed City Logistics network also makes a substantial improvement
over randomly selected satellites. The table below displays the average performance of
random scenarios (28 satellites) compared with average 2E-LRP solutions. The 2E-LRP
96
and SCPM feedback models, which basically just redesign 1% of total trips, have made a
15% improvement in annual impact.
Table 4.4: Comparison of 2E-LRP Impact and Random Satellite Impact.
2E-LRP
(one AM peak)
Random
(one AM peak)
Improvement
(one AM peak)
Annual
Improvement
Total Passenger Time
(hour)
8.51 million 8.83 million 0.32 million 0.16 billion
Total Gas
Consumption (gallon)
4.51 million 4.68 million 0.17 million 0.1 billion
Total Cost ($) 9 million 4.5 billion
Further, the feedback loop between 2E-LRP and SCPM also improves City
Logistics strategic design substantially. Another $3.4 billion could be saved if we link the
private sector logistics network design with public sector benefits. It demonstrates the
importance of incorporating network link cost impact into the decision making of large
scale logistics system design.
Table 4.5: Average Impact Improvement of 2E-LRP with SCPM Feedback vs. Static Network Link
Cost.
Static
(one AM peak)
SCPM Feedback
(one AM peak)
Improvement
(one AM peak)
Annual
Improvement
Total Passenger Time
(hour)
8.75 million 8.51 million 0.24 million 0.12 billion
Total Gas
Consumption (gallon)
4.64 million 4.51 million 0.13 million 0.065 billion
Total Cost ($) 7 million 3.4 billion
97
Chapter 5
Conclusions and Discussions
The impact of City Logistics in the case study provides a basis for City Logistics
researchers, policy makers, and city residents to evaluate, make decisions on, or vote for
City Logistics alternatives. Simulation estimates that the total impact of City Logistics,
including reduced passenger travel time and saved gasoline, is at least $31 billion per
year. Considering the 15.2 mile Expo Light Rail phase 1 cost $1 billion and phase 2
expected to cost $1.5billion (Expo, 2015), $31 billion savings per year would greatly
exceed the cost of constructing and maintaining a new City Logistics infrastructure.
This study also provides an empirical evaluation of the extent to which large-scale
logistics network trips could affect the logistics network design itself. To the author‟s
knowledge, it is the first study that takes the impact on transportation network congestion
into the location selection of LRP problems. Simulation shows that feedback network
cost is a key to finding the overall best locations compared with the static 2E-LRP
solutions. Even when the remaining legs of freight trip are only 1% of total trips in the
98
City Logistics network, the location of satellites could have a substantial influence on
network link cost. Initial selection of locations based on static link cost could lead to
severe congestion near selected satellites, and feedback network cost helps to adjust the
selections. In this case study, the static solution is just as good as randomly selected
satellites. But feedback information has improved the total time and gas consumption by
around 5% on average and improved the total impact by 15% and 4.5 billion in dollars.
The research work can be furthered along the following directions:
(1) Scenarios with a less than 100% freight transferring through a City Logistics
network: This research work assumes that all freight goes through City Logistics. In
reality, most likely some freight will remain in its original format of shipment. In
this sense, a simulation study with different proportions of freight moving through a
City Logistics network would be valuable to assess the impact of City Logistics
under different levels of applications.
(2) Multiple commodities and multiple time windows: Some commodities may be
shared in a single vehicle and some may not. Practically speaking, the freight is
picked up and delivered with certain frequency. With these specifications, 2E-LRP
design with routing would show further improvement against randomly selected
satellites.
(3) Simulation of network cost against employment change and other economic sectors:
This study does not incorporate the change of employment and impact of network
link costs on each economic sector in each TAZ. A further simulation could be
performed to investigate the impact of City Logistics by sector and by zone.
99
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Abstract (if available)
Abstract
City logistics is a relatively new research area that focuses on strategies for increasing the efficiency of moving goods in urban areas, reducing noise and vehicle emissions, and improving safety in residential areas. City logistics investigates the benefits available from a consolidated and cooperation-based system. A standard scheme intended to improve efficiency is to make use of a centralized, two-level distribution system. This approach excludes large trucks from city centers, relying on smaller, more environmentally friendly light vehicles to accomplish final deliveries. Our objective is to formulate a two-level location routing (2E-LRP) model and use efficient heuristics that give an effectual strategic design for such a two-level distribution. We will estimate the benefits from this approach by exercising the Southern California Planning Model (SCPM). The locations of centers and the transportation mode connecting first level distribution centers (hubs) to second-level distribution centers (satellites) are selected using two-level location routing model and SCPM, which also produces simulation results describing how the new network will impact traffic flow and gas consumption. The outputs of new network link costs are also used as feedback to improve the design of the City Logistics network. ❧ Research presented in this dissertation is used to develop methodology to design and evaluate a new City Logistics network, with respect to improving traffic level and reducing private distribution costs. The Los Angeles case study demonstrates an 18% improvement in network efficiency and a 40% reduction in gas consumption. Moreover, this study is the first empirically based work that evaluates the effects of a new logistics system on network link costs and optimality of the logistics system design itself.
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Evaluating city logistics using two-level location routing modeling and SCPM simulation
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12/02/2015
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