out (2)

Stochastic and Discrete Green Supply Chain Delivery Models

A dissertation submitted to:

Kent State University Graduate School of Management

In partial fulfillment of the requirements for the degree of

Doctor of Philosophy

By:

Jay R. Brown

April, 2013

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ii

iii

Dissertation written by

Jay R. Brown

BBA, Kent State University, 1999

MBA, Kent State University, 2002

PhD, Kent State University, 2013

Approved by:

_____________________________ Chair, Doctoral Dissertation Committee

Dr. Alfred Guiffrida

_____________________________ Member, Doctoral Dissertation Committee

Dr. Eddy Patuwo

_____________________________ Member, Doctoral Dissertation Committee

Dr. Sergey Anokhin

Accepted by:

_____________________________ Doctoral Director, Graduate School of Management

Dr. Murali Shanker

_____________________________ Dean, Graduate School of Management

Dr. Frederick Schroath

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v

TABLE OF CONTENTS

TABLE OF CONTENTS .......................................................................................................................... V

LIST OF FIGURES .............................................................................................................................. VIII

LIST OF TABLES ..................................................................................................................................... X

ACKNOWLEDGEMENTS ..................................................................................................................... XI

ABSTRACT ................................................................................................................................................. 1

CHAPTER 1: INTRODUCTION .............................................................................................................. 3

1.1. BACKGROUND .............................................................................................................................. 3

1.2. MODELING CARBON EMISSIONS IN A SUPPLY CHAIN ................................................................. 5

1.3. LIMITATIONS OF EXISTING GREEN SUPPLY CHAIN AND TRANSPORTATION MODELS ................ 5

1.4. RESEARCH OBJECTIVES ............................................................................................................... 6

CHAPTER 2: LITERATURE REVIEW ................................................................................................ 10

2.1. TRANSPORTATION, TRANSSHIPMENT, AND FIXED CHARGE MODELS ....................................... 10

2.1.1. Transportation Model ....................................................................................................... 10

2.1.2. Transshipment Model ....................................................................................................... 12

2.1.3. Fixed Charge Problem ...................................................................................................... 13

2.2. INTRODUCTION TO THE LAST MILE PROBLEM .......................................................................... 14

2.3. CARBON EMISSIONS MODELING ................................................................................................ 19

2.4. EMISSIONS MODELING IN SUPPLY CHAIN AND TRANSPORTATION MODELS ............................ 21

2.5. MODELING OF LAST MILE SUPPLY CHAIN DELIVERY MODELS ................................................ 26

2.6. DELIVERY IMPORTANCE OF THE LAST MILE PROBLEM IN SUPPLY CHAIN MANAGEMENT ...... 29

CHAPTER 3: TRANSSHIPMENT MODEL ......................................................................................... 33

3.1. FIXED CHARGE MULTIPLIER TRANSSHIPMENT MODEL WITH CARBON FOOTPRINT ................. 33

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3.1.1. Model Objective: Minimize Total Cost ............................................................................. 34

3.1.2. Model Objective: Minimize Carbon Footprint ................................................................. 35

3.1.3. Model Objective: Minimize Carbon Footprint ................................................................. 36

3.2. A NUMERICAL EXAMPLE AND COMPARING RESULTS ............................................................... 37

3.2.1. Minimizing Total Cost ...................................................................................................... 39

3.2.2. Minimizing Carbon Footprint ........................................................................................... 40

3.2.3. Hybrid Solution Minimizing Cost with a Carbon Cost Penalty ........................................ 41

3.3. FIXED CHARGE MULTIPLIER TRANSSHIPMENT MODEL SUMMARY .......................................... 42

CHAPTER 4: LAST MILE DELIVERY MODELS ............................................................................. 44

4.1. DISCRETE LAST MILE MODEL WITH CARBON FOOTPRINT ........................................................ 44

4.2. CONTINUOUS LAST MILE MODEL WITH CARBON FOOTPRINT .................................................. 46

4.3. DISTRIBUTION OF EXPECTED OPTIMAL TOUR DISTANCES........................................................ 48

4.3.1. Stochastic Last Mile Delivery Framework ....................................................................... 49

4.4. FLEET MODEL FORMULATION ................................................................................................... 58

4.4.1. Assumptions and Notation ................................................................................................ 59

4.4.3. Model Definition ............................................................................................................... 60

4.4.4. Model Illustration with a Numerical Example .................................................................. 63

4.5. SUMMARY .................................................................................................................................. 68

CHAPTER 5: CARBON EMISSIONS COMPARISON OF LAST MILE DELIVERY VERSUS

CUSTOMER PICK UP ............................................................................................................................ 70

5.1. STOCHASTIC LAST MILE MODEL DEVELOPMENT ..................................................................... 73

5.2. EXPECTED DISTANCE TRAVELED FOR CUSTOMER PICK UP ...................................................... 75

5.3. EMPIRICAL DATA ON CUSTOMER TRAVEL DISTANCES ............................................................. 79

5.4. BREAK-EVEN ANALYSES AND FINDINGS SUPPORTED BY EMPIRICAL DATA ............................ 84

5.5. CARBON EMISSIONS OF LAST MILE DELIVERY VERSUS CUSTOMER PICK UP SUMMARY ........ 91

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CHAPTER 6: CONCLUSIONS AND FUTURE RESEARCH ............................................................ 93

6.1. SUMMARY OF RESEARCH CONTRIBUTIONS ............................................................................... 93

6.2. SUMMARY OF LIMITATIONS AND FUTURE RESEARCH .............................................................. 95

APPENDICES ........................................................................................................................................... 98

APPENDIX 1: MODEL FORMULATION OF THE EXAMPLE USING LINGO ................................................ 98

APPENDIX 2: DEMAND GENERATION FOR STOCHASTIC LAST MILE DELIVERY .................................... 99

APPENDIX 3: TRAVELING SALESMAN SOLUTION ALGORITHMS EMPLOYED ....................................... 100

APPENDIX 4: SAMPLE MATHEMATICA CODE FOR FINDING THE MINIMUM TOUR ............................... 101

APPENDIX 5: DISTRIBUTION OF OPTIMAL TOURS FOR T=1 WITH VARYING NODE LEVELS ................ 102

APPENDIX 6: DISTRIBUTION OF OPTIMAL TOURS FOR T=2 AT SELECTED NODE LEVELS ................... 114




REFERENCES ........................................................................................................................................ 134

CURRICULUM VITAE ......................................................................................................................... 142

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LIST OF FIGURES

Figure 3.1: Shipment Allocations for Minimizing Total Cost. ................................................................... 39

Figure 3.2: Shipment Allocations for Minimizing Carbon Footprint. ........................................................ 40

Figure 3.3: Shipment Allocations for the Hybrid Model. ........................................................................... 41

Figure 4.1: Demand Region with Last Mile Delivery for N = 10 and T = 1. ............................................. 50

Figure 4.2: Distribution of Single Truck Expected Optimal Tour Distances for N = 50. ........................... 51

Figure 4.3: Demand Sub Regions with Last Mile Delivery for N = 10 and T = 2. ..................................... 52

Figure 4.4: Mean Optimal Tour Distances. ................................................................................................. 55

Figure 4.5: Standard Deviations of Optimal Tour Distances. ..................................................................... 55

Figure 4.6: Fit of Single Truck Mean Tour Distances By Nodes. .............................................................. 56

Figure 4.7: Fit of Single Truck Standard Deviations of Tour Distances By Nodes. ................................... 57

Figure 4.8: The Midpoint, Used In the Calculation of Missed Deliveries. ................................................. 62

Figure 4.9: Missed Deliveries Calculated Individually Vs. the Midpoint Method. .................................... 63

Figure 4.10: Total Cost Results for Alternative Delivery Scenarios........................................................... 64

Figure 4.11: Carbon Emission Weekly Totals for Alternative Delivery Scenarios. ................................... 65

Figure 4.12: Sensitivity Results of CD (cost of missed deliveries). ............................................................ 66

Figure 4.13: Sensitivity Results of H (hours available for delivery per day). ............................................. 67

Figure 5.1: Demand Region with Customer Pick Up for n = 9 Customers................................................. 75

Figure 5.2: Regression Results of Google Map Miles by L1 Distance ....................................................... 81

Figure 5.3: Vehicle Speeds Returned by Google Maps for Customer Trips ............................................... 82

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Figure 5.4: Distribution of L1 Distance from Origin of Trip to Store ......................................................... 83

Figure 5.5: Distribution of L2 Distance from Origin of Trip to Store ......................................................... 83

Figure 5.6: Example CO2 Emissions of Customer Pick Up versus Last Mile Delivery ............................. 89

Figure 5.7: Example CO2 Emissions Saved Through Last Mile Delivery .................................................. 91

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LIST OF TABLES

Table 2.1: Classes of Distribution Models .................................................................................................. 17

Table 3.1: Model Specification and Supporting Data for Numerical Example. ......................................... 38

Table 3.2: Comparison of Different Objective Functions. .......................................................................... 42

Table 4.1: Statistical Information of Model Equations. .............................................................................. 53

Table 5.1: Statistical Information of Model Equations. .............................................................................. 74

Table 5.2: Estimated Delivery Region Radius Based on Mean Distance to Store ...................................... 84

Table 5.3: Break-even Points for CO2 Emissions ....................................................................................... 86

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Acknowledgements

I would like to thank and convey my sincerest gratitude to my dissertation chair, Dr.

Alfred L. Guiffrida. His support, direction, knowledge, and guidance were instrumental in not

only this dissertation but also during my classes and research. I really could not ask for a better

mentor, teacher, and friend throughout this process.

I am also very grateful to my committee members, Dr. Butje Eddy Patuwo and Dr.

Sergey Anokhin, for their insight, support, and guidance.

Next, I would like to thank Dr. David E. Booth for taking an interest in my research,

answering my questions, and providing valuable knowledge and citation information.

I would also like to thank my colleagues and friends, Mr. Maxim A. Bushuev and Dr.

Venugopal Gopalakrishna-Remani, for being so supportive and encouraging during my time at

Kent State University.

Last but certainly not least, I would like to thank my family for their unconditional

support, encouragement, and understanding throughout this entire process.

1

Stochastic and Discrete Green Supply Chain Delivery Models

Abstract

Green supply chain models and carbon emissions tracking have become increasingly

prevalent in the supply chain management literature and in corporate strategies. In this

dissertation, carbon emissions are integrated into cost-based freight transportation models that

can be used to assist operations and supply chain managers in solving the “last mile problem”.

The models presented herein serve to provide the decision maker with choices on which strategy

to implement depending on the strength of the management’s desire to reduce carbon emissions.

By comparing the optimal solutions that result from using different delivery strategies, this

research provides a basis for evaluating an appropriate trade-off between transportation cost and

carbon emissions.

This dissertation contributes to academia and the literature in several ways. The discrete

supply chain models provide a method for decision makers to analyze and compare the lowest

cost delivery option with the lowest carbon footprint option. The stochastic last mile framework

that is introduced provides a method for researchers and practitioners to measure the expected

carbon footprint and compare probabilistic costs, carbon emissions, delivery mileage, and

delivery times in order to make decisions regarding the most appropriate delivery strategy. This

framework is then applied to two different problem settings. The first involves optimizing a

delivery fleet to produce the lowest total cost with carbon emissions integrated into the total cost

equation. The second compares the carbon footprint resulting from last mile delivery

(ecommerce retailing involving a central store delivering to end customers) to customer pick up

2

(conventional shopping at a brick-and-mortar retail location); the break-even number of

customers for carbon emissions equivalence provides a basis for companies to determine the

environmental impact of last mile delivery and to determine the feasibility of last mile delivery

based on objectives related to minimizing carbon emissions.

3

CHAPTER 1: INTRODUCTION

1.1. Background

Modeling containing carbon emissions is a relatively new area and Supply Chain and

Logistics (2009) reported that only 10% of companies are actively modeling their supply chain

carbon footprints and have implemented successful sustainability initiatives. This will change in

the future as Srivastava (2007) notes that “green supply-chain management (GrSCM) is gaining

increasing interest among researchers and practitioners of operations and supply-chain

management.”

There are different reasons companies are interested in reducing carbon emissions. Talk

of government taxes on carbon emissions have been springing up around the globe (Moran,

2010). If countries begin putting these taxes and corresponding enforcement measures into

action, companies will need to rethink the management of the freight transportation component

of their supply chains since this component of the supply chain is directly impacted by carbon

emission legislation. Organizations would need to look at not only their physical freight assets,

but also their methods for determining delivery routes and moving products within these routes.

Traditionally used optimization models and inventory strategies used in support of freight

management and distribution would need to be reviewed and modified to account for the cost of

carbon emissions. For example, firms operating under the just-in-time (JIT) management

philosophy, which advocates frequent deliveries of small delivery quantities, would need to re-

examine and potentially modify operations to maintain cost-effectiveness under the green supply

chain management philosophy.

4

The impact of green supply chain management and related carbon emission legislation

would naturally vary depending on the country where freight transportation is occurring and how

the country enforces taxes on carbon emissions. While laws regulating and taxing carbon

emissions appear to be a possibility in the future, companies are also interested in lowering their

carbon footprint as a general company philosophy.

Going green has been a popular mantra for companies for years. If company philosophy

were to dictate the desire to reduce carbon emissions as either a social responsibility initiative or

as a marketing tool, company executives would want to figure out a trade-off factor of cost

versus carbon emissions. Often times, the lowest cost also produces the lowest carbon dioxide

(CO2) emissions, but this is not always the case so some analysis needs to be done to determine

what the company is willing to spend to reduce its carbon footprint. In other cases, the delivery

strategies can be altered to achieve lower emissions while producing a lower or equivalent

transportation cost.

This dissertation will investigate methods of reducing transportation cost and/or carbon

emissions by exploring different delivery strategies or options. Delivery strategies can have

three different objectives: to minimize carbon emissions regardless of transportation cost, to

minimize cost regardless of transportation cost, or to reduce carbon emissions at the same or

lower overall transportation cost.

5

1.2. Modeling Carbon Emissions in a Supply Chain

Carbon emissions are defined as the CO2 emitted from vehicles. A carbon footprint is

defined as the sum of CO2 emitted over a specified time period or while accomplishing a

specified task or business objective. This research aims to reduce the carbon footprint of

companies through optimizing delivery strategies for motor freight distribution or travel required

for business services.

Instead of tracking and quantifying the carbon emissions from past activities, this

dissertation will specifically focus on reducing it through an acceptable trade-off with

transportation cost and by optimizing delivery strategies by changing other specified variables

(i.e. labor hours, labor schedule, number of delivery vehicles, etc.). In addition, a method of

quantifying a company’s future carbon emissions is presented, which can be used for

measurement and comparing to different delivery alternatives.

1.3. Limitations of Existing Green Supply Chain and Transportation Models

Much of the literature involving carbon emissions in supply chain and transportation

models revolves around quantifying and estimating the CO2 emissions in existing supply chain

and transportation models (see for example El Saadany et al. 2011; Abdallah et al. 2012; Wahab

et al. 2011). The objectives of these models typically address minimizing total transportation

cost. This often results in lowering carbon emissions, which is quantified or calculated, but is

not the main objective of the optimization. The models developed in this dissertation examine

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minimizing carbon emissions and total transportation cost in an integrated supply chain. Each

model or framework explores these aspects in a unique way.

In this dissertation multiple scenarios will be introduced to examine the reduction of

carbon emissions within the setting of green supply chain and transportation models. In one

scenario, decision makers can consider a trade-off between carbon emissions and total

transportation cost. In another scenario, delivery strategies involving changing business

practices can be created that result in a reduction of the carbon footprint while still maintaining a

cost minimal transportation strategy. These scenarios will be explored in this dissertation.

1.4. Research Objectives

The research objectives of this dissertation are as follows:

1) Introduce carbon emissions into the fixed charge multiplier transshipment model and

provide a solution methodology for decision makers with trade-off options between

transportation cost and reducing carbon emissions.

2) Extend the last mile problem to incorporate carbon emissions resulting from freight

transportation. This will involve the development of a stochastic last mile delivery

framework that will determine the expected optimal delivery distance to allow for

planning and the probabilistic assignment of costs and service level.

3) Provide a comprehensive framework for evaluating delivery strategies according to

transportation cost and carbon footprint by altering decision variables such as labor

hours, number of delivery trucks, and/or optimal delivery schedule in order to give

7

the best mix of cost and reduction in carbon emissions. This will also entail a

comparison of last mile delivery to customer pick up to quantify the difference in

carbon emissions and to find the number of customers at which last mile delivery can

provide a reduction in the overall carbon footprint.

The research objectives will be accomplished through the building of each model, the

application of solution methodologies, and through supporting numerical analyses. Solution

methodologies will vary depending on the model in question, but in each case carbon emission

reduction is at the forefront.

Accomplishing the first objective will involve building a mathematical model that

extends the traditional transshipment model to incorporate the cost associated with the carbon

emissions of multiple vehicles. The key features of this model that distinguish it from models

found in the literature are the incorporation of the cost of carbon emissions and the use of a fixed

charge multiplier that assigns a fixed charge for each vehicle used along a route. In addition,

further modifications may be done in order to enhance the realism of the model. The next step of

this objective involves applying a solution methodology to the fixed charge multiplier

transshipment model. The goal of this solution methodology will be to provide the decision

maker with a trade-off function between cost savings and reduction in carbon footprint.

Depending on the decision maker’s preferences, the solution methodology will report an optimal

solution that meets the preferences of the decision maker.

8

The second objective will introduce a carbon emissions component into both a discrete

last mile delivery model and a continuous last mile delivery model. From there, the research will

explore the distribution of optimal solutions in a demand region with randomly distributed

delivery points (customers). The goal will be to provide a distribution of the expected optimal

tour distance to service a region depending on the number of trucks servicing the region. The

distributions will be used to analyze the specifics of a delivery fleet needed to serve the region

along with the application of probabilistic costs such as overtime and late deliveries.

Satisfying the third objective will involve formulating a stochastic last mile model in an

effort to lower carbon emissions through changing the weekly delivery schedule and number of

delivery vehicles while maintaining the same or lower overall transportation cost. The model

will be developed and then a numerical analysis will be conducted to evaluate the impact of these

variables in lowering carbon emissions. In addition, the expected optimal tour distance

distributions will be used to compare last mile delivery to customer pick up in order to quantify

the expected difference in carbon footprint and to find how many customers are needed to realize

a reduction in carbon emissions.

As Section 1.3 pointed out, gaps exist in the literature regarding modeling carbon

emissions in transportation and supply chain networks. The models developed in this

dissertation, which address minimizing a dual objective of total transportation cost and carbon

emissions, will contribute to bridging this gap. As is evident by the literature, modeling carbon

emissions in supply chain management is of high interest to managers and represents a growing

research discipline for the years to come.

9

The research contributed by this dissertation is significant since it provides a set of

decision models for determining the optimal reduction of carbon emissions and transportation

costs in transportation and supply chain networks. While most companies may not be interested

in spending more money to reduce carbon emissions, they certainly would be interested in

reducing carbon emissions while maintaining the same total transportation cost level. The

decision trade-offs between carbon emissions and transportation costs that result from the models

presented in this dissertation will benefit companies in making decisions from a marketing

perspective (distribution), a social responsibility perspective (sustainability), as well as

proactively meeting potential legislation on the reduction of carbon footprint.

10

CHAPTER 2: LITERATURE REVIEW

Four different (yet related) research streams will be reviewed in this chapter. Each stream

is integral in providing the foundation needed to meet the research objectives of this dissertation.

This chapter is organized in sections depending on the literature stream being reviewed. Section

2.1 reviews the historical evolution of the transportation, transshipment, and fixed charge models

and their application to supply chain management. Section 2.2 defines the last mile problem and

reviews the associated literature on this model Section 2.3 covers methods of modeling

emissions and calculating carbon footprints. Section 2.4 reviews how carbon and related

emissions have been modeled in supply chain models.

2.1. Transportation, Transshipment, and Fixed Charge Models

In this section, the transportation, transshipment and fixed charge models will be

reviewed. The historical genesis of each model will be presented followed by an illustration of

the canonical form of the model.

2.1.1. Transportation Model

The transportation problem was first introduced by Hitchcock (1941). The goal of the

optimization is to minimize transportation cost in delivery of goods from points of origin (supply

points) to points of destination (demand points). The flow of goods is one directional, meaning

11

that shipments can only go from a supply point to a demand point. Cost is proportional and

assigned per unit shipped. Hence, total cost is the summation of units shipped along a route

multiplied by the cost of shipping one unit along that route.

The classical transportation problem is as follows:

Minimize

m

i

h

j

ijij xcz1 1

(2-1)

subject to

h

j

iij ax1

for i = 1, …, m (2-2)

m

i

jij bx1

for j = 1, …, h (2-3)

xij ≥ 0 for i = 1, …, m, j =1, …, h (2-4)

m

i

h

j

ji Tba1 1

ai ≥ 0, bj ≥ 0 (2-5)

where

i = 1, 2, … , m starting points (sources)

j = 1, 2, … , h ending points (destinations)

xij = units shipped along route ij

cij = cost per unit shipped along route ij

ai = units of demand at destination i

bj = units of supply at source j

T = sum of demand or sum of supply

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2.1.2. Transshipment Model

The transshipment problem (Orden, 1956) is a more comprehensive extension of the

transportation problem. Unlike the transportation model, which limits shipping to one-way

shipments down the supply chain, the transshipment model allows shipments between

intermediate points. These intermediate points are referred to as “transshipment points” and

allow for lateral shipments to occur between suppliers (or between destinations) in any direction

and within any level. This model is more realistic than the transportation model and can be used

to model multi-echelon supply chains.

The classical transshipment problem is as follows:

Minimize

n

i

n

j

ijij xcz1 1

(2-6)

subject to

n

ijj

iiiij axx1

for i = 1, …, n (2-7)

n

jii

jjjij bxx1

for j = 1, …, n (2-8)

xij ≥ 0 for i = 1, …, n, j =1, …, n (2-9)

cjj = 0 for all j (2-10)

where

i = 1, 2, … , n starting points (sources);

j = 1, 2, … , n ending points (destinations);

13

xij = units shipped along route ij;

cij = cost per unit shipped along route ij;

ai = units of demand at destination i

bj = units of supply at source j

Chiou (2008) provides a thorough review of transshipment problems and applications.

Descriptions, classifications, methodologies, solution procedures, and research directions are

discussed for variations of the transshipment problem and to support further study of

transshipments in the supply chain system.

2.1.3. Fixed Charge Problem

The fixed charge problem, originated by Hirsch and Dantzig (1954), involves optimizing

a system in which there are fixed charges associated with positive level activities. For example,

set-up costs are a common fixed charge and appear in almost any manufacturing or supply chain

activity. The fixed charge problem is also referred to as the product mix problem depending on

the problem setting. The fixed charge problem seems simple, but because it is a nonlinear

programming problem, it can be difficult to solve.

The classical fixed charge problem is as follows:

Minimize

n

j

jjjj ykxcz1

(2-11)

subject to

yj = 1 if xj > 0 (2-12)

14

= 0 if xj = 0

where

j = 1, 2, … , n products

xj = units of product j

cj = cost per unit for producing product j

kj = setup cost for producing product j

yj = 1 if producing product j

= 0 otherwise

In this dissertation, the fixed charge problem is combined with the transshipment problem

in order to formulate a fixed charge multiplier transshipment model. A fixed charge multiplier is

when a fixed charge is applied at certain levels or thresholds of units. This is utilized in order to

account for the use of multiple trucks being used when the units shipped along a route require

more than one truck.

2.2. Introduction to the Last Mile Problem

The last mile problem (LMP) is defined as the optimizing of the last leg of the business-

to-consumer delivery service (Boyer et al. 2009). The last mile part is the least efficient part of

the supply chain due to the high degree of empty running. In addition, not-at-home deliveries

can have extra costs associated with returning to the location several times (Gevaers et al. 2011).

While costs vary with population density, product type, package size, and package weight, last

mile delivery has proven to incur the highest transportation costs in the supply chain according to

Chopra (2003). Naturally these high costs provide an opportunity for companies to achieve

substantial cost reductions with the optimal planning and execution of a delivery plan. Reducing

15

costs anywhere in a supply chain is particularly attractive to companies and the last mile

provides the possibility for even a small percentage savings adding up to a very substantial

amount. A more centralized distribution center, more efficient routings, changing delivery

zonings, or more fuel efficient vehicles are all possible ways for lowering costs as well as

improving a company’s carbon footprint.

The literature of the last mile problem can be broken down into the two subgroups of

discrete and continuous models. Discrete models have known demands and route distances and

seek to find the shortest or most economical way to deliver the goods while satisfying the

associated constraints. Continuous models differ in that they seek to approximate distances

based on region size and shape and demand densities. These models can provide practitioners

with quick and dirty methods for approximating costs and distances and allow zones to be set up

intelligently. Continuous models are no substitute for discrete models as they serve a different

purpose.

Clarke and Wright (1964) introduced their savings algorithm as a solution algorithm to a

problem similar to many discrete LMPs. In their model, vehicle fixed costs and fleet sizes are

ignored, but vehicle capacities are relevant. The Clarke and Wright Savings Algorithm has been

more thoroughly demonstrated by Evans et al. (1990, p. 688). In this algorithm, sij is the savings

associated with linking customers i and j on the same route and tij is the distance or travel time

between customer i and j (note that 0 represents the depot). It can be helpful when working with

the algorithm to construct a table and sort the savings. The algorithm consists of three steps:

Step 1: Compute the savings for all pairs of customers. The savings for linking

customers i and j is sij = ti0 + t0j – tij.

16

Step 2: Choose the pair of customers with the largest savings. If feasible (subject to

constraints), link them. If not, move to the next largest.

Step 3: Continue with Step 2 as long as savings are positive. When all positive savings

have been considered, stop.

In addition, this algorithm can be implemented in two different ways. The first way is

known as sequential and involves completing one route at a time. The second way is known as

the parallel method and allows multiple routes to be constructed simultaneously (instead of

skipping the next sij if not feasible, you open up a new route and work in parallel). Usually the

parallel method will return the better results.

Laporte (1992) presented a review of exact and approximate algorithms applied to the

discrete vehicle routing problem (VRP) under different scenarios. Solution methodologies

discussed include the Clarke and Wright (1964) algorithm, branch and bound (Laporte et al.

1986), dynamic programming (Eilon et al. 1971), and tabu search (Gendreau et al. 1994).

Laporte’s article provides readers with a good overview of approaches to the discrete LMP.

Similarly, Langevin et al. (1996) provides an overview of continuous approximation

models in which the last mile problems are segmented into direct shipping and peddling and

summarized into six different model classifications (see Table 2.1). Direct shipping refers to

vehicle routes from an origin to single destinations. Peddling refers to vehicle routes that make

multiple stops to pick up or deliver goods. Continuous approximation models estimate route

length by functions of the area of the sub region and the spatial density of the stops. This allows

travel distances to be estimated without knowing exact locations of origins, destinations, or

17

transshipment points (in the case of peddling). The paper addresses distances using the

Euclidean (L2) metric, which is as the crow flies, and the Manhattan (L1) metric, which is the

shortest navigable route using streets/city block. Models adopting these metrics are reviewed and

summarized into six classes (see Table 2.1).

Model

Class

Description

I One-to-many distribution without transshipments (direct

shipping)

II Many-to-one distribution without transshipments (direct

shipping)

III Many-to-many distribution without transshipments (direct

shipping)

IV One-to-many distribution with transshipments (peddling)

V Many-to-many distribution with transshipments (peddling)

VI Integrated works

Table 2.1: Classes of Distribution Models

Models found in Classes I and IV are the most applicable to the LMP and to carbon

footprint modeling. Class I is divided into subclasses where Class I-A involves only

transportation costs, Class I-B adds other costs, and Class I-C includes time constraints. In all

classes, carbon emission costs are not included. In addition, models reviewed by Langevin et al.

(1996) are placed nicely into these categories with information on the metric used (L1 and/or L2),

routing strategy (peddling or direct shipping), and key contributions. These models are attractive

to supply chain analysts in solving the LMP since the central output of these models (distance

18

traveled) is the key driver for evaluating vehicle delivery cost and capacity, determining delivery

zones and for estimating the cost of the vehicle carbon footprint.

Punakivi et al. (2001) uses simulation to show that unattended reception of goods reduces

home delivery costs by up to 60%. For groceries, the authors suggest refrigerated reception or

delivery boxes to eliminate the problem of unattended delivery thereby reducing repeated

delivery attempts which add cost and decreases in overall delivery efficiency. The payback

period for the adoption of delivery boxes was about two years.

Kull et al. (2007) performs an empirical study of seven firms and over 4000 customers

using nonlinear regression to examine how order time changes within an online grocery ordering

environment. They compare learning models of on line purchasing with actual data and

determine that learning exists and can be used to enhance the interface between a supply chain

and its customers.

Edwards et al. (2010) introduce carbon footprint analysis to the last mile problem and

compare the environmental effects of online versus conventional shopping. Home deliveries and

typical shopping trips are compared and the findings suggest that home deliveries result in lower

carbon emissions.

Newell (1973) looks at several operations research problems and converts them into a

continuous perspective to find approximate solutions. The problems discussed include the

scheduling problem, design of transportation networks, and the warehouse location problem.

Average distance metrics for different shaped delivery zones for both Euclidean (L2) and

Manhattan (L1) distances are provided. Daganzo (1984), Vaughan (1984), and Stone (1991) also

19

present many average distance results for differently shaped regions in different settings. The

metric presented in these papers provide a basis for modeling the continuous LMP.

Daganzo (1987) focuses on many-to-many distribution (Class III) using break-bulk

terminals (swapping points that enable vehicles to pick up loads for many more destinations than

those ultimately served by one vehicle).

2.3. Carbon Emissions Modeling

Daccarett-Garcia (2009) presents an excellent summary of methods to calculate carbon

emissions for transport trucks and reports that carbon emission calculations can be based on

either the gallons of diesel fuel consumed (which results in 10.1 kilograms of carbon dioxide per

gallon of fuel) or the number of miles traveled (which results in an average of 1.01 kilograms of

carbon dioxide per kilometer). The following equation is for modeling carbon dioxide emissions

(CDE) based upon diesel fuel utilization:

i j k i

jijk

E

DXgalkgCDE 1.10

(2-13)

where

i, j, k = defines the truck type, route and day

ijkX = number of trips made by truck type i to route j in day k

jD, jE

= distance of route j, fuel efficiency of truck type i.

The lead coefficient representing the carbon dioxide emission per gallon of diesel is

determined as follows:

20

Cwm

COwmfactoroxidation

gallon

contentcarbonGallonCO

..

../ 2

2

(2-14)

Entering the following set of parameters to the above equation: oxidation factor for diesel

(0.99) and the molecular weights (m.w.) of CO2 and carbon (44 and 12 respectively) yields:

galkgggalgGallonCO /1.10084,1012

44*99.0*/788,2/2

(2-15)

Kenny and Gray (2009) compared six different models or calculators for estimating the

carbon footprint of a typical family of three in Ireland. The results showed the six different

models produced inconsistent and often contradictory results. Standards for calculating carbon

footprint are not available and estimates are all that exist for these calculations, which make them

an educated guess at best. The paper calls for “an urgent need for comprehensive and reliable

models that can accurately determine individual and household primary carbon footprints.”

Harris et al. (2011) compare costs and CO2 emissions among different logistics designs

using simulation software that allows the decision maker to vary inputs such as number of depots

and location of depots in order to evaluate different supply chain network designs in terms of

costs and carbon emissions. They show that the optimal design of a supply chain network based

on costs does not necessarily equate to an optimum solution for CO2 emissions. They argue

“therefore that there is a need to address economical and environmental objectives explicitly as

part of the logistics design.”

Reed et al. (2010) reviews methods for quantifying carbon emissions and estimating costs

associated with reducing CO2 emissions in select supply chain optimization models. One of the

21

biggest obstacles in incorporating emissions into supply chain optimization models is the lack of

an accepted method for calculating the carbon emissions quantity. This paper provides steps for

calculating carbon emissions for rail carrier and motor carrier transportation and also for

calculating the cost of carbon credits.

2.4. Emissions Modeling in Supply Chain and Transportation Models

In this section, a summary of optimization models reported in the literature for

determining operating policy decisions when green costs (carbon emissions and related

atmospheric pollutants) are included into the model formulations is presented.

Schipper et al. (2008) modeled the total emissions of carbon monoxide (CO), simple

hydrocarbons and their variations, particulate matter, sulfur oxides (SOx), and carbon dioxide

(CO2) for the transportation system supporting the area around Hanoi, Socialist Republic of

Vietnam. Emissions were calculated using a fuel-based, mass-balance approach and were

modeled for each individual pollutant type and then summed over all vehicle and fuel types:

Σ{Total distance (km) traveled by vehicle type}{emission factor (g/km) by vehicle type ).

Cordeiro (2008) studied the emissions resulting from the existing bus network in the state

of Queretaro, Mexico and the expected emission reductions from six different project scenarios

affecting change to the existing network. The vehicle emissions of pollutant p, were calculated

using:

22

vf

vfvfvf

p

EFVKTNE

1000000 (2-16)

where

p = type of pollutant

v = type of vehicle

f = type of fuel

pE= vehicle emissions of pollutant p (tons/year)

vfN= number of vehicles by vehicle and fuel type

vfVKT= annual average km traveled by vehicle model and fuel type (km/year)

vfEF= emission factor for contaminant by vehicle model and fuel type (g/km)

Anciaux and Yuan (2007) construct an intermodal (truck, train, and ship) optimization

model to minimize the total transportation costs for delivering goods from the Peugeot factory in

Paris to Marseille. The model includes a term (Ig) that quantifies the total air emissions from

pollutants (CO2, NOx, SO2, hydrocarbons, and dust) during product shipment. This term in the

model is defined as:

K

k

I

i

J

t

tiiiiiiig VQedBBAQxIkk

1 1 1

, ,1 (2-17)

where

gI= total air emission during the shipment

i = defines the mode of transportation

t = defines the type of pollutant

k = defines the delivery zone

tie , = unit of air pollutant t in weight per unit of weight transported per unit of distance shipped

by transportation model i

kix , = the units shipped to zone k using transportation mode i

Q = total weight of products to be transported

V = total volume of products to be transported

23

A = VQ

kid , = the distance traveled in zone k using transportation mode i

B = the noise cost of the total shipment

= a fit parameter, 10

i = a capacity parameter for transportation model i

Paksoy et al. (2010) presented a multi-objective linear programming model of a closed-

loop supply chain network that minimizes transportation, green, and raw material purchasing

costs. An interesting feature of this model formulation is that penalty costs are levied in the

reverse logistics portion of the model for extra carbon dioxide emissions.

(2-18)

where

i, j, k = the number of suppliers, plants, distribution centers (DC)

l, m, p = the number of customers, collection centers, dismantlers

d, t, r = the number of decomposition centers, trucks, raw materials jtijt COCO 22 = unit CO2 omissions for all trucks serving i, j, k, l

ij

rtX = units of raw material r via truck t from supplier i to plant t

jk

rtY = transported product r via truck t from plant j to DC k

j

rtZ = transported product r via truck t from plant j to warehouse

k

rtQ = transported product r via truck t from warehouse to DC k

l

rtW = transported product r via truck t from warehouse to customer l

kl

rtE = transported product r via truck t from DC k to customer l

2CO

cP = penalty cost for extra carbon dioxide emission ($0.05/gr if > 2000 kg CO2)

24

Sundarakani et al. (2010) investigates the carbon footprint across the supply chain by

examining “heat” transfer across various stationary and non-stationary supply chain processes.

While not specifically focused on freight transportation, the model does support the significant

threat of carbon emissions that warrants careful attention in the design and implementation of

supply chains.

Ramudhin et al. (2010) integrate carbon emissions and total logistics costs into the design

of a transportation problem model using a multi-objective mixed-integer linear programming

(MILP) model that is solved using goal programming. Similar to one of the goals for this

dissertation, the article evaluates the trade-offs between total logistics costs and carbon emissions

under different supply chain operating strategies. The article discusses carbon credits and how

the model can be used by decision makers to evaluate whether they would have a carbon credit

or would need to purchase credits in the carbon market place.

Wang et al. (2011) also propose a multi-objective optimization model with the goal of

capturing the trade-off between total cost and environmental influence. The following model is

presented for a supply chain network.

Parameters

the set of products

the demand of customer for product

the supply of supplier for product

transportation cost for product from facility to facility

setup cost for facility j

the handling capacity for facility j

capacities consumed by handling a unit of product in facility j

25

handling cost of product p in facility j

Decision variables

= 1, if facility j is open;

= 0, if otherwise.

the flow of product p from node i to node j

the environment protection level in facility j

Objective functions:

OBJ1:

(2-19)

OBJ2:

(2-20)

Constraints:

(2-21)

(2-22)

(2-23)

(2-24)

(2-25)

(2-26)

(2-27)

(2-28)

Lee (2011) identifies carbon footprint modeling in supply chain management as an

emerging discipline in supply chain management. Using a case study of Hyundai Motor

Company that highlights the actions of a supplier that delivers front bumpers, empirical evidence

is presented to demonstrate how to measure a carbon footprint and improve environmental

performance with respect to CO2 emissions. Measuring this total carbon footprint burden can

enable companies to reevaluate supply chain practices.

26

2.5. Modeling of Last Mile Supply Chain Delivery Models

Environmental concerns are impacting how organizations design, coordinate, and manage

their supply chains and has generated a huge interest in the topic of “green supply chain

management.” Srivastava (2007) defines green supply chain management (GSCM) as the

integration of environment thinking into supply chain management. This includes product

design, material sourcing and selection, manufacturing processes, delivery of the final product to

the consumers, and end-of-life management of the product after its useful life. A detailed review

of the green supply chain management literature is found in Sarkis et al. (2011). Frameworks for

integrating green and sustainable practices into supply chains may be found in Sarkis (2012,

2003), Carter and Rogers (2008), and Vachon and Klassen (2006). Recent case study based

analyses which detail the integration of GSCM in real-world supply chains are reported by

Ubeda et al. (2011) for Eroski, a Spanish food distributor, and by Lee (2011) for Hyundai, a

Korean automobile manufacturer.

A vast literature on supply chain performance measurement exists. A review of the

strategic, operational and tactical aspects of supply chain performance measurement as well as

the measurement metrics adopted by organizations is found in Gunasekaran et al. (2004, 2001).

Given the high importance placed on GSCM, several researchers have investigated its impact on

supply chain performance (see for example, Green et al. 2012; De Giovanni and Vinzi, 2012;

Hervani et al. 2005; and Rao and Holt, 2005).

27

The importance that the logistical component plays in the performance of a supply chain

is well documented in the literature (Chopra, 2003; Stank et al. 2003; McIntyre et al. 1998). In a

climate of enhanced awareness of environmentally sustainable business practices, the issue of

carbon emissions as a result of freight transportation in supply chains is rapidly becoming a key

managerial concern. Golicic et al. (2010) identify that developing a sustainable supply chain

transportation strategy is a key concern of organizations yet as reported in Supply Chain and

Logistics (2009, p. 42), only 10% of companies are actively modeling their supply chain carbon

footprints and have implemented successful sustainability initiatives.

Of particular concern to supply chain managers is the “last mile problem” (LMP) which

is considered to be one of the most costly and highest polluting segments of the supply chain

(Gevaers et al. 2011). The LMP is defined as the optimizing of the last leg of the business-to-

consumer delivery service, is the least efficient part of the supply chain due to the high degree of

empty running (Boyer et al. 2009). While costs vary with population density, product type,

package size, and package weight, last mile delivery has proven to incur the highest

transportation costs in the supply chain (Chopra, 2003). Naturally these high costs provide an

opportunity for companies to achieve substantial cost reductions through optimal planning and

proper execution of a delivery plan which may involve analyses to redesign the overall

distribution network, establishing more efficient routings, changing delivery zonings, or

upgrading to a more fuel efficient transportation fleet.

In the development of the stochastic model for the LMP presented herein, we draw upon

the literature which is referred to in the operations research literature as “geometric probability”

(see Larson and Odoni, 1981; Ch 3) where models have been developed to determine the optimal

28

distance traveled from a source (or set of sources) which serves a customer base. Models within

this literature can be broken down into the two subgroups of discrete and continuous models.

Discrete models have known demands and route distances and seek to find the shortest or most

economical way to deliver the goods while satisfying the associated constraints and can be

thought of as a subset of the traveling salesman problem (TSP). Continuous models differ in that

they seek to approximate distances based on region size, shape, and demand densities. Distance

is measured using the Manhattan (L1) metric, which is the shortest navigable route using

streets/city block, or the Euclidean (L2) metric, which is as the crow flies. Historically this class

of models has been used in analyses directed at improving the distribution of products to end

customers from a sourcing depot.

In the review of the literature on the LMP we identify only one paper (Edwards et al.

2010) which directly incorporates carbon emissions (CO2) into the LMP. Edwards et al. (2010)

introduces carbon footprint analysis to the last mile problem and compares the level of carbon

emissions resulting from online versus conventional shopping for the non-food retail sector.

Carbon emission from delivery vehicles was defined by the number of grams of CO2 emitted per

kilometer traveled and the rate of emission was estimated based on secondary technical data

sources of vehicle operation. Home deliveries and typical shopping trips were compared based

on the aggregate gram weight of CO2 generated during delivery. The findings suggest that home

deliveries result in lower carbon emissions.

Based upon this review of the literature we note two major limitations. First, distance

estimation models focus only on the average distance of the demand for a given delivery region

and not the exact set of distinct demand points being served. The exact location of customer

29

demand points is more realistic representation of the characteristics of the LMP. Second carbon

emission costs associated with the delivery process are not included in these models. Methods

for estimating the cost associated for carbon emissions in distribution have appeared in the

literature (see for example, Chaabane et al. 2012; Harris et al. 2011) however the modeling

environment was for deterministic demand.

2.6. Delivery Importance of the Last Mile Problem in Supply Chain Management

In this section we present a general overview of the importance that delivery performance

plays in the integration and coordination of a supply chain. Following this overview, we

summarize research on the “last mile problem” in supply chain management, which represents a

class of delivery models pertaining to our stated research objective.

The importance of the delivery and the supporting logistical process is well recognized in

the operations and supply chain literature (see for example, Chopra, 2003; Stank et al. 2003). In

the early 1980s researchers established the link between competitive performance and time-

based measures of performance (see for example Porter, 1980 and Stalk, 1988). Rao et al.

(2011) and Gunasekaran et al. (2004) identify delivery performance as a key metric that serves to

integrate performance measurement throughout a supply chain. As a time-based performance

measure, delivery timeliness has been linked to customer satisfaction (Forslund et al. 2009; Tan

et al. 2002), the selection of suppliers (Anderson et al. 2011; Shin et al. 2009; Ernst et al. 2007),

production planning and control (Lane and Szwejczewski, 2000) and the interrelationship

between sales globalization and supply chain investment (Golini and Kalchschmidt, 2010).

30

Of particular concern to operations and supply chain managers is the “last mile problem”

(LMP) which is defined as optimizing the last-leg of the business-to-consumer delivery service

(Boyer et al. 2009). The LMP implies delivery to the physical address of the end customer from

the location (depot) where the purchased item is maintained and is acknowledged as a key

element of the order fulfillment process (Lee and Whang, 2001; Bromage, 2001). The logistical

burden of the LMP is considered to be one of the most costly and highest polluting segments of

the supply chain (Ülkü, 2012; Gevaers et al. 2011). While costs vary with population density,

product type, package size, and package weight, last mile delivery has proven to incur the

highest transportation costs in the supply chain (Chopra, 2003). Goodman (2005) notes that up

to 28% of all transportation costs are incurred in last mile delivery. Naturally these high costs

provide an opportunity for companies to achieve substantial efficiencies through optimal

planning and proper execution of a delivery plan which may involve analyses to redesign the

overall distribution network, establishing more efficient routings, changing delivery zonings, or

upgrading to a more fuel efficient transportation fleet.

The LMP has been investigated along several research dimensions. Huang et al. (2011),

Stapleton et al. (2009), and Balcik et al. (2008) have adopted a last mile framework in modeling

the delivery of relief supplies from local distribution centers to demand locations requiring aid

due to natural disasters. Boyer et al. (2009) investigated the effect that factors such as customer

density and duration of the delivery window have on delivery efficiency. Kull et al. (2007)

studied how web sites influence the efficiency of the supply chain last-mile via differing learning

rates within the order cycle. Esper et al. (2003) examined the effects of the disclosure and

promotion of carrier information by online merchants on customers’ purchasing behavior and

perceptions of the delivery process. Punakivi et al. (2001) examined the cost and operating

31

efficiencies for home delivery service under conditions of attended and unattended receipt of the

delivered items.

The research cited above demonstrates the importance of the LMP in operations and

supply chain management. Of particular importance to our research herein are treatments of the

LMP that capture how the LMP interacts with environmental sustainability. McIntyre et al.

(1998) identified that traditional time and cost based logistic performance metrics which tend to

support short-term managerial decision making are incapable of supporting the longer-term

logistical decisions that are required under a sustainable and environmentally compatible green

logistics strategy. Golicic et al. (2010) identify that developing a sustainable supply chain

transportation strategy is a key concern of organizations yet as reported in Supply Chain and

Logistics (2009), only 10% of companies are actively modeling their supply chain carbon

footprints and have implemented successful sustainability initiatives.

Siikavirta et al. (2003) examined the greenhouse gas (GHG) emissions of alternative

home delivery strategies for the e-grocery industry and compared these findings to GHG

emissions that would result from customer pick up. Based on a case study of e-grocery

customers in Helsinki Finland, the GHG emissions were measured as a function of the travel

distance incurred under the competing delivery methods. The travel distance resulting from

home delivery was analyzed under a set of conditions in which differing lengths of a promised

delivery window and differing frequencies of home delivery to a household delivery reception

box were offered. Point of sales information and the road infrastructure was used to determine

the travel distances that would be incurred under customer pick up. The results of the simulation

experiments conducted suggest that home delivery service offers the potential for significant

32

traffic reduction over customer self pick up. Depending on the home delivery methods used,

reductions in GHG emissions in the range of 18% to 87% can be achieved over customer pick

up.

Edwards et al. (2010) contribute a comparative study of the CO2 emissions resulting from

home delivery from online shopping and customer pick up (conventional shopping) in the non-

food retail sector. Using established secondary data sources which define the emission factors

for carbon-fuel based vehicles, the CO2 per kilometer traveled under each type of delivery

(online shopping versus conventional shopping) was estimated. Delivery failure rates for home

delivery ranging from 2% to 25% were considered and a subjective estimate of the degree of trip

chaining (picking up multiple items from multiple locations in one trip) was considered under the

conventional shopping option. Given a set of modeling assumptions and acknowledging that

numerous factors influence emissions from home deliveries, when customers buy less than 24

items per shopping trip, it is likely that the CO2 per item purchased will be lower under home

delivery.

In summary, the literature indicates that attempts have been made to introduce CO2

emissions into the logistical delivery component of the supply chain. The studies reviewed have

provided a starting point for comparing the CO2 emissions generated under the alternatives of

home delivery and customer pick up. In the study herein, we extend this type of research

through the incorporation of factors which improve the robustness of the comparison of delivery

options.

33

CHAPTER 3: TRANSSHIPMENT MODEL

This chapter presents a fixed charge multiplier transshipment model in which carbon

emissions is injected and will be used as a basis for providing the decision maker with choices

related to cost and carbon emissions. The fixed charge multiplier transshipment model will be

used as a model for a trade-off function later. Initially the model will be presented with three

different objectives: minimizing total cost, minimizing carbon footprint, and minimizing a

combination of transportation cost and carbon footprint based on a simple penalty cost for the

amount of carbon dioxide emitted. Later, a solution methodology will be applied to the model

that allows the decision maker to predefine preferences on cost savings and lowering carbon

emissions.

3.1. Fixed Charge Multiplier Transshipment Model with Carbon Footprint

The model developed herein combines the transshipment model with fixed charge factors

and integrates a penalty factor for carbon emissions. A fixed charge is applied when products

are shipped along a route. Additional fixed charges are applied for each additional truck used

along a route. For example, if the trucks used along a certain route have a capacity of 100 units,

and 150 units are shipped, then two trucks are needed and two fixed charges are applied. As

expected, additional trucks also increase the carbon footprint.

This model allows the user to dictate the truck capacities for each route. The model also

allows for different rates of carbon emission associated with each route and truck type.

34

The model introduces a penalty factor for carbon emissions, p, which is used in the

objective function as a way to quantify the company’s desire to reduce carbon emissions. The

more inclined a company is to reduce its carbon footprint, the higher the penalty factor. Stated

explicitly, the penalty factor is either the rate of carbon emissions tax per kilo or how much a

company is willing to spend to save one kilo of CO2 emissions.

3.1.1. Model Objective: Minimize Total Cost

In the first form of this model, the objective is to minimize total cost, Ztc. This is the

traditional form of a transshipment model (although adding the fixed charge multiplier) and the

notation herein has been slightly modified from the original formulation by Orden (1956).

Carbon emissions are not part of the equation here, but are recorded for a comparison in the

example.

The objective is to minimize total cost, Ztc.

(3-1)

subject to

j = 1, 2, … , n, (3-2)

xij ≥ 0, i = 1, 2, … , n, j = 1, 2, … , n, (3-3)

yij ≥ xij / tij, (3-4)

tij > 0, (3-5)

n

i

n

j

ijijijijtc ykxcZ1 1

j

n

i

jiij fxx 1

35

kij ≥ 0, i = 1, 2, … , n, j = 1, 2, … , n. (3-6)

where





yij = an integer value = the number of fixed charges along route ij;

kij = fixed setup charge to ship along route ij;

tij = units at which each fixed charge is to be applied along route ij;

fj = net flow (received – shipped) for destination j;

3.1.2. Model Objective: Minimize Carbon Footprint

In this form of the model, the objective is to minimize total carbon footprint, Zcf. Cost,

while recorded for comparison in the example, is not a factor in this objective function.

The objective is to minimize total carbon footprint, Zcf.

(3-7)

subject to

j = 1, 2, … , n, (3-8)

xij ≥ 0, i = 1, 2, … , n, j = 1, 2, … , n, (3-9)

yij ≥ xij / tij, (3-10)

tij > 0, (3-11)

kij ≥ 0, i = 1, 2, … , n, j = 1, 2, … , n. (3-12)

where

n

i

n

j

ijijcf ygZ1 1

j

n

i

jiij fxx 1

36







gij = kilograms of CO2 emitted per truck along route ij;

3.1.3. Model Objective: Minimize Carbon Footprint

In the final form of this model, the objective is to minimize the hybrid objective function,

Zh, which utilizes a carbon emissions penalty factor. The optimization returns a result that is a

combination of cost and a penalty factor for carbon emissions. Total cost and carbon emissions

are both recorded for comparison to the other two objectives.

The objective is to minimize the objective, Zh.

(3-13)

where






kij = fixed setup charge to ship along route ij;



gij = kilograms of CO2 emitted per truck along route ij;

p = penalty factor per kilogram of CO2;

n

i

n

j

ijijijijijijh ygpykxcZ1 1

37

subject to

j = 1, 2, … , n, (3-14)

xij ≥ 0, i = 1, 2, … , n, j = 1, 2, … , n, (3-15)

yij ≥ xij / tij, (3-16)

tij > 0, (3-17)

kij ≥ 0, i = 1, 2, … , n, j = 1, 2, … , n. (3-18)

Net flow, fj, is simply the net inflow or outflow of units from or to each city. Fixed costs,

kij, are applied to each truck used along each route. If the route is not used, no fixed charges are

applied. Cost per unit, cij, is applied to each unit, xij, shipped along each route. Truck capacity,

tij, defines the capacity of the truck(s) used along each route. Kilos of CO2 emissions, gij, are

calculated for each route.

3.2. A Numerical Example and Comparing Results

In order to illustrate the objective differences in the model, a five city two-stage balanced

example is presented with supply points of Boston, Cleveland, and Orlando and demand points

of Columbus and Indianapolis. For the purposes of this example an average of 1.01 kilograms of

carbon dioxide per kilometer is used as introduced by Daccarett-Garcia (2009). If more detailed

data was available, then more exact figures could be used. Finally, the penalty factor for CO2

emissions, p, in this example is set at 1.6, meaning either the government tax is $1.60 per kilo of

CO2 emissions or the company is willing to spend $1.60 for every reduction of one kilo of CO2

n

i

jjiij fxx1

38

emissions. Table 3.1 shows the details of the example. The model was formulated and solved

using LINGO (see Appendix 1).

The objectives in each of the formulations from Section 3.1 are different. Here, these

differences are demonstrated. In this example, the three formulations produce three different

solutions. The most cost effective solution with no regard for CO2 emissions is quite different

from the solution that applies a penalty cost for CO2 emissions and both are different from the

solution that seeks to minimize carbon footprint with no regard for cost.

Table 3.1: Model Specification and Supporting Data for Numerical Example.

TO

Flow Boston Cleveland Orlando Columbus IndianapolisF = -500 -400 -350 500 750

K = Fixed Cost Boston Cleveland Orlando Columbus IndianapolisBoston 0 200 350 225 290Cleveland 200 0 325 50 75Orlando 350 325 0 325 350Columbus 225 50 325 0 55Indianapolis 290 75 350 55 0

C = Per Unit Cost Boston Cleveland Orlando Columbus IndianapolisBoston 0 6 12 8 9Cleveland 6 0 18 1 6Orlando 12 18 0 16 15Columbus 8 1 16 0 8Indianapolis 9 6 15 8 0

T = Truck Capacity Boston Cleveland Orlando Columbus IndianapolisBoston 1 500 500 300 400Cleveland 500 1 500 400 300Orlando 500 500 1 500 300

Columbus 300 400 500 1 300Indianapolis 400 300 300 300 1

G = Kilos CO2 Boston Cleveland Orlando Columbus Indianapolis

Boston 0 1042 2098 1244 1526Cleveland 1042 0 1692 231 515Orlando 2098 1692 0 1549 1584Columbus 1244 231 1549 0 285Indianapolis 1526 515 1584 285 0

FR

OM

39

3.2.1. Minimizing Total Cost

The shipment schedule resulting from the solution of the numerical example is shown in

Figure 3.1. The total cost was $11,240 with CO2 emissions of 6198 kilos. Boston shipped 400

units in one truck to Indianapolis and 100 units in one truck to Cleveland. Cleveland, now with

Boston’s 100 units plus its 400 units of production shipped all 500 units to Columbus aboard two

trucks. Finally, Orlando shipped all 350 of its units to Indianapolis aboard two trucks. This

solution is the most cost-effective solution, but as will be demonstrated later, does not have the

lowest carbon footprint.

Figure 3.1: Shipment Allocations for Minimizing Total Cost.

40

3.2.2. Minimizing Carbon Footprint


Figure 3.2. The total cost was $14,480 with CO2 emissions of 4137 kilos. Boston shipped all of

its 500 units in one truck to Cleveland. Cleveland, now with Boston’s 500 units plus its 400

units of production shipped 300 units to Columbus aboard one truck and the remaining 600 units

to Indianapolis split between two trucks. Orlando shipped all 350 of its units to Columbus

aboard one truck. Finally, Columbus, now with 450 units, shipped its 150 excess units to

Indianapolis in one truck. This solution is not the cheapest solution, but it does produce the one

with the lowest carbon footprint.

Figure 3.2: Shipment Allocations for Minimizing Carbon Footprint.

41

3.2.3. Hybrid Solution Minimizing Cost with a Carbon Cost Penalty


Figure 3.3. The total cost was $14,050 with CO2 emissions of 4367 kilos. Boston shipped all of

its 500 units in one truck to Cleveland. Cleveland, now with Boston’s 500 units plus its 400

units of production shipped 150 units to Columbus aboard one truck and the remaining 750 units

to Indianapolis split between three trucks. Finally, Orlando shipped all 350 of its units to

Columbus aboard one truck. This solution, while not the cheapest solution or the one with the

lowest carbon footprint, provided a compromise between cost and CO2 emissions.

Figure 3.3: Shipment Allocations for the Hybrid Model.

42

In the model comparison of each of these different objectives, Table 3.2 shows the

breakdown of total cost and kilos of CO2. Please note that the addition of one additional model

not discussed involves not allowing transshipments. This would be the classic transportation

model where products can only be shipped from a supply point to a demand point. It is added in

the table to demonstrate the expected superiority of the transshipment model to the transportation

model.

As Table 3.2 shows, the results from the differing objectives are quite different. By

changing the carbon penalty cost factor, p, managers would be able to further change the results.

The selection of p is naturally a crucial step in this process.

Table 3.2: Comparison of Different Objective Functions.

3.3. Fixed Charge Multiplier Transshipment Model Summary

This chapter introduced a carbon penalty factor into a fixed charge transshipment model

and compared results from a numerical example with differing objective functions. The model

presented shows how companies can incorporate a carbon penalty factor into freight

Optimization Method Cost Kilos CO2

Lowest Cost - Transportation $11,315 6169

Lowest Cost - Transshipment $11,240 6198

Lowest Carbon Footprint $14,480 4137

Green Transshipment Hybrid (carbon penalty factor) $14,050 4367

43

transportation planning in order to achieve a desired reduction in carbon footprint or to minimize

costs given the potential for a new government tax on carbon emissions.

In the end, the models have shown how minimizing total cost is not always going to

achieve company objectives in this new age of green initiatives and sustainability. When

deciding on trucking routes and inventory movements, managers can try to strike a balance

between lowest total cost and reducing carbon emissions. Other strategies such as maximizing

freight trailer capacities and avoiding LTL (less than truck load) shipments are other avenues for

managers to meet these new objectives while still keeping an eye on the bottom line.

44

CHAPTER 4: LAST MILE DELIVERY MODELS

In this chapter a model that overcomes limitations found in the current class of LMP

models is presented. The limitations that are overcome in the model development include: 1) the

lack of incorporating stochastic demand into the LMP, and 2) the limited manner in which

carbon emissions that result from the vehicle transportation is incorporated into the LMP. The

stochastic LMP model presented herein improves the quality of information available for supply

chain managers to plan properly and enhances overall decision making due to the ability to

gauge the probabilistic likelihood of the costs associated with solving the LMP.

The remaining sections of this chapter are organized as follows. In Section 4.1, a discrete

last mile model with carbon footprint is presented. In Section 4.2, a continuous last mile model

with carbon footprint is shown. In Section 4.3, the foundation for the development of our

stochastic model for solving the LMP is presented. Section 4.4 involves formulating and

demonstrating a LMP model that has stochastic demand and includes carbon emissions due to

motor carrier freight transport. Conclusions and future research are summarized in Section 4.5.

4.1. Discrete Last Mile Model with Carbon Footprint

In a discrete last mile problem, exact customer locations, distances, and demands are

known with complete certainty. The first model that will be introduced is a discrete LMP

formulation for minimizing carbon footprint in the case where different types of trucks are

available. This allows for a situation where a depot has a number of different trucks and the

45

LMP can be optimized based on the different capacities and fuel consumptions of its different

vehicles. Therefore, each vehicle would have its own capacity and grid of gijk (CO2 emitted from

i to j using vehicle k). The following formulation defines a model for minimizing the carbon

footprint for a discrete LMP. The formulation presented is based upon the description of the

Clarke-Wright algorithm (Clark and Wright, 1964), which did not offer a canonical formulation.

The objective function, equation (4-1), minimizes the carbon footprint.

Minimize

K

k

n

i

n

j

ijkijk yg1 0 0

(4-1)

subject to

yijk = 0, 1 for all i, j, k (4-2)

yi0k = y0jk for all k (4-3)

k

n

i

n

j

ijki bya 0 0

for all k (4-4)

K

k

n

i

ijky1 1

1 for all j (4-5)

11 1

K

k

n

j

ijky for all i (4-6)

where

i = 1, 2, … , n customers or destinations

j = 1, 2, … , n customers or destinations

k = 1, 2, … , K vehicles

n = number of customers or destinations

cijk = cost of travelling in vehicle k along route ij

gijk = kilograms of CO2 emitted from vehicle k along route ij

yijk = 1 if vehicle k uses route ij

= 0 otherwise

bk = capacity of vehicle k

ai = order size of customer (or for destination) i

46

Constraint (4-2) specifies that yijk is a binary variable that is set to 1 if the route from i to j

is used and 0 otherwise.

Constraint (4-3) ensures that each vehicle leaves from the depot and returns to the depot.

Constraint (4-4) makes sure that the vehicle capacities are not violated.

Constraint (4-5) and (4-6) guarantee that each customer is visited once and only once and

note that the summation starts at i=1 and j=1 instead of 0 because these are dealing with

customers and not the depot, which is included multiple times when multiple vehicles are used.

4.2. Continuous Last Mile Model with Carbon Footprint

In the continuous case of last mile problems, there are several options to build upon for a

carbon footprint model. Newell (1973) provides a Euclidean distance metric (L2) basis for

computing expected distances in the continuous case with specified densities in the region.

However, an application of Beardwood et al. (1959) will serve the carbon footprint model better

as the distances involved are Manhattan (L1 metric), which are more appropriate for the last mile

problem. In addition, based on the distance metric constant (call it d) that is used, the

formulation can easily be changed for different strategies. For example, Daganzo (1984) uses d

= 1.15 for this constant in a strip strategy, which divides the region into rectangular strips and

does the tour based on these strips. Stein (1978) uses d = 0.765 for Euclidean (L2) distances.

Finally, Jaillet (1988) uses d = 0.97 for the Manhattan (L1) distances, which is the distance

47

metric employed within this dissertation in the construction of the continuous LMP for carbon

footprint. In addition, it should be noted that a new value for d could be derived here for

multiple trucks in the same region or zone. However, based on a preliminary analysis, the

accuracy of the resulting expected tour distance drops off as the number of trucks increases.

Essentially, these models are all one TSP (traveling salesman problem) per region. The LMP

formulation for minimizing carbon footprint in a continuous case with random demand using a

distance metric constant, d, is as follows.

Minimize

n

j

jjjj gNAd1

(4-7)

where

j = 1, 2, … , n regions

n = number of regions

d = distance metric for region j

Aj = area of region j

Nj = number of customers in region j

gj = average kilos of CO2 emitted per kilometer by the vehicle servicing region j

As (4-7) demonstrates, the objective is to minimize the total distance traveled in the

predefined zones. Doing so will also minimize the carbon footprint. In an ideal scenario, there

would be no restrictions on zones so that total distance traveled could be minimized even further.

In the development of the distribution of optimal solutions for last mile delivery to

follow, it should be noted that the aforementioned method using a distance metric constant is

found to be less accurate for expected travel distance with multiple trucks, but can be used for a

rough estimate nonetheless. In addition, while this formulation is giving an expected tour

48

distance, it is not providing any information on the tour distance variability. This dissertation

addresses this limitation and establishes a framework for modeling the distributions of tour

distances for changing levels of N (nodes, which are the number of customers plus the point of

delivery origination), T (trucks), and R (the delivery region radius). From the simulations

performed in the following section (circular demand region, central depot, and computing area

from delivery region size), using d = 1.055 results in the closest match for 1 truck tours.

Comparisons to multiple truck tours did not produce as accurate of a match. Hence, the

estimation method presented in Section 4.3 is recommended for a better total delivery tour

estimation and for the variability information.

4.3. Distribution of Expected Optimal Tour Distances

In order to generalize the last mile problem and place it in a decision making context for

examining the sensitivity of the expected optimal tours and probabilistic costs, the distribution of

delivery tours needs to be modeled stochastically. Section 4.3.1 explains the process for

developing this framework and discusses how it can be utilized in planning and measuring both

cost and carbon emissions.

This section provides an overview on the development of the stochastic last mile delivery

framework and shows examples of the process at each stage. For full information on this

process, a set of supporting Appendices for the technical details are employed. Appendix 2

details the demand generation process. Appendix 3 provides information on the four algorithms

employed in determining the minimal tour distance of each trial. Appendix 4 shows sample code

49

of the algorithms as used in Mathematica. In addition, Appendices 5 – 9 contain complete

details on the quality of using the Gaussian probability density function to represent the

distributions of tour distances as function of the number of nodes and number of trucks.

4.3.1. Stochastic Last Mile Delivery Framework

For the delivery scenarios, demand points were uniformly and randomly

generated within a circular demand region of radius R with a single depot located at the circle

center (see Figure 4.1). Truck tour distances were evaluated using the Manhattan distance (L1)

distance metric which implies that only north, south, east, and west travel is allowed. Twelve

levels of customer demand ranging from 10 to 160 nodes were used. Note: a node size of N

implies N -1 distinct customer locations and one node reserved for the central depot. Truck tour

distances at each level of customer demand were evaluated for 120 random trials in which the

customer nodes were randomly generated as defined in Appendix 2. The minimum tour distance

traveled in each trial was determined based on the minimum distance resulting from four built-in

traveling salesman problem (TSP) solution algorithms found in Mathematica. Details on how

the simulation trials were solved and descriptions of the TSP algorithms employed within

Mathematica to determine the minimum tour distances are found in Appendices 3 and 4. This

methodology was previously used by Brown and Guiffrida (2012).

50

Figure 4.1: Demand Region with Last Mile Delivery for N = 10 and T = 1.

For each level of N and T, the minimum tour distances resulting from each of the 120

trials conducted was aggregated and analyzed using the SAS statistical package JMP. Goodness-

of-fit testing of the aggregated trial data using the Shapiro-Wilk test supports the use of the

Gaussian probability density function for defining the distribution of the minimum tour distance

traveled in satisfying n customers. Figure 4.2 illustrates the distribution of expected optimal tour

travel distances for N = 50 nodes (n = 49 customers) and T = 1 truck. This analysis was done at

periodic levels of N and T and the Gaussian fit held 91% of the time. Please refer to Appendices

5-9 to see each of these Gaussian fits. Employing four different algorithms allowed for closer

approximation to the optimal solution, particularly as the problem became increasing difficult (as

N increases). Interestingly, when one algorithm alone is analyzed for the best continuous fit over

120 trials, the result tended to be a bit left skewed with slightly more mass concentrated at higher

distance levels. Fitting each of these would result in a skewed fit from a distribution such as the

Weibull distribution. Since the methodology involved taking the minimum of four different

solution methodologies, this issue of a skewed distribution due to non-optimal solutions (that

51

were far enough from optimal to cause the skew) was overcome and the fits proved to be

symmetric and Gaussian.

Figure 4.2: Distribution of Single Truck Expected Optimal Tour Distances for N = 50.

Similar to the trials conducted for single truck tours, additional trials were performed for

T = 2, 3, 4, and 5 trucks. For multiple trucks (T > 1), the circular demand region of radius R was

subdivided into T equally sized and shaped sub regions. Each sub region was assigned one truck,

hence the number sub regions equates directly to the number of individual truck delivery tours.

Figure 4.3 illustrates the demand sub regions for T = 2 trucks. The use of predefined delivery

zones is a universal practice in industry so this method most closely mimics the prevailing

business practice.

52

Figure 4.3: Demand Sub Regions with Last Mile Delivery for N = 10 and T = 2.

Given that the distribution of expected tour distances at each level of N and T, we address

how the mean tour distance and corresponding standard deviation change as N and T change.

For a given radius of the demand region, R, the expected distance traveled per day )|,( TRNM

is a function of the number of trucks T and the number of nodes (customer delivery points plus

the depot), N. Based on numerical analyses where the number of nodes N was varied from 2 to

160 and the number of trucks T was varied from 1 to 5, (T = 1, all nodes within the demand

region serviced by one truck; T = 2, two identical sub regions with one truck serving each sub

region; …; T = 5, five identical sub regions with one truck serving each sub region), the

following general form for the expected tour distance for T = 1, 2,…, 5 was fit.

RNbbTRNM TT 21)|,( (4-8)

where

Tb1 = y-intercept coefficient for T = 1, 2, …, 5

Tb2 = slope coefficient for T = 1, 2, …, 5

53

Fitting (4-8) T from the trial data yielded statistically significant results (p < 0.001)

with R2 in the range of 0.989 to 0.999. The standard deviation )|,( TRNSD of )|,( TRNM was

fit in the general form as shown in equation (4-9).

RNccTRNSD TT )ln()|,( 21 (4-9)

where

Tc1 = y-intercept coefficient for T = 1, 2, …, 5

Tc2 = slope coefficient for T = 1, 2, …, 5

Although, the fits for (4-9) were not as strong as the fits achieved for (4-8), they all

proved to be statistically significant (see Table 4.1). These equations allow for probabilistic

estimation of optimal delivery tour distances and can be used for calculating delivery time, costs,

probability of overtime, etc.

T=

Mean Standard Deviation

Equation TRNM |, R2 Sig. Equation TRNSD |, R

2 Sig.

1 RN871.1017.0 .998 <.0001* RN)ln(064.0990.0 .528 .0075*

2 RN744.1862.1 .999 <.0001* RN)ln(199.0591.1 .832 .0308*

3 RN770.1776.2 .999 <.0001* RN)ln(245.0864.1 .871 .0206*

4 RN706.1721.3 .998 <.0001* RN)ln(367.0336.2 .861 .0229*

5 RN794.1666.4 .989 .0005* RN)ln(434.0789.2 .940 .0063*

Table 4.1: Statistical Information of Model Equations.

54

Using the fitted equations for the mean and standard deviation of the tour distances found

in Table 4.1, we can construct probabilistic estimates of tour distances. For example, by

introducing an average truck speed, a 95% service level for the delivery time could be created.

Figure 4.4 illustrates the changing mean tour distances and Figure 4.5 illustrates how the

standard deviations of the expected tour distances change as the number of nodes increase for T

= 1 to 5 trucks. The change in standard deviations is much more volatile and less predictable

than that of the mean tour distances. However, the downward sloping trend is what was

expected as Beardwood (1959) proved that the standard deviation would fall to 0 with an infinite

number of nodes. Larger sample sizes could help mitigate this volatility to some degree.

In order to determine the presence of potential outliers or influential points, an analysis

was performed using Cook’s Distance (Cook, 1977) and DFFITS (difference in fits

standardized), which is introduced by Belsley et al. (1980). The point associated with one truck

and ten nodes on the standard deviation plot was determined to be an influential point. However,

per Belsey et al. (1980), since this was from valid data and there is a large amount of movement

at this point in the fit, the point is kept and the fit is still considered appropriate.

55

Figure 4.4: Mean Optimal Tour Distances.

Figure 4.5: Standard Deviations of Optimal Tour Distances.

0

5

10

15

20

25

30

10 30 50 70 90 110 130 150

Dis

tan

ce (

Un

its

are

in t

he

Re

gio

n's

Rad

ius)

Nodes

Expected Optimal Tour Distances with Central Depot

1 Truck

2 Trucks

3 Trucks

4 Trucks

5 Trucks

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

10 30 50 70 90 110 130 150

Stan

dar

d D

evi

atio

n (

Un

its

are

th

e R

egi

on

's R

adu

s)

Nodes

Standard Deviations as Nodes Increase

1 Truck

2 Trucks

3 Trucks

4 Trucks

5 Trucks

56

Figure 4.6 shows the fitted model of the mean tour distances for single truck deliveries

found for the changing levels of nodes. The fitted information was presented in Table 4.1, but

this figure expands upon that and gives full details and graphs to show exactly what was done for

each of T = 1 to 5 truck scenarios.

Figure 4.6: Fit of Single Truck Mean Tour Distances By Nodes.

While the fitted information was presented in Table 4.1, Figure 4.7 shows the fitted

model of the standard deviations of the tour distances for single truck deliveries found for the

changing levels of nodes. As mentioned previously, the fits were not as strong as the standard

deviations proved to be much more volatile than the means. Perhaps an area of future research

57

would be to use much larger sample sizes in an effort to come closer to the true population

standard deviation and have less variability across the different levels of N.

Figure 4.7: Fit of Single Truck Standard Deviations of Tour Distances By Nodes.

The presented framework for modeling the distribution of expected tours as a function of

the number of customers and number of trucks provides a generalization that can be used to

compute expected tour distances, probabilities of missed deliveries, overtime, and other

probabilistic costs associated with mileage and time. This stochastic last mile delivery

framework generalizes the last mile problem and places it in a context that can be used for

advanced planning.

58

The stochastic last mile framework that has been developed in this section will be applied

in two problem settings. The first application begins in Section 4.4 and optimizes a delivery fleet

in terms of the number of trucks and number of days to deliver per week in order to minimize

total cost while recording all options so that carbon emissions results can factor in to not only the

objective function, but also to act as a possible deciding factor in breaking near ties. The second

application, which is presented in Chapter 5 uses the stochastic last mile delivery framework to

compare the carbon emissions resulting from last mile delivery (ecommerce retailing involving a

central store delivering to end customers) with customer pick up (conventional shopping at a

brick-and-mortar retail location). The break-even number of customers for achieving carbon

emissions equivalence between last mile delivery and customer pick up is determined.

Knowledge of the break-even point provides a basis for companies to determine the



4.4. Fleet Model Formulation

Using the stochastic last mile delivery framework, an optimization model is formulated to

determine the optimal number of trucks and the optimal number of days to deliver per week

subject to the demand distribution, costs associated with the deliveries, the number of hours

available per day to make deliveries, radius of the demand region, average vehicle speed in the

region, and average number of minutes spent per delivery stop.

59

4.4.1. Assumptions and Notation

The following assumptions are adopted.

a) Distance is measured in miles using the Manhattan (L1) distance metric.

b) A fleet of trucks are available for use from a central depot.

c) Truck capacity is not constrained, but daily number of delivery hours is a constraint.

We define the following notation where T and D are the decision variables.

CD = cost of a missed delivery

EC = CO2 emission cost per mile

MC = mileage cost ($/mile traveled)

CW = labor wage rate per hour

D = number of days making deliveries per week

H = feasible delivery hours per day

P = wage premium for overtime

N = the number of nodes including the depot. The number of delivery points = N – 1

R = the radius (in miles) of the circular demand region

S = average speed of delivery trucks in miles per hour

T = number of delivery trucks

a = average minutes spent at each stop or customer location

DTTC , = total cost as a function of the T and D

M(N,R|T) = expected optimal tour distance for a demand region of radius R with N

nodes given T trucks

SD(N,R|T )= expected standard deviation of M(N,R|T )

m* = S[H – a(N – 1)]; the feasible delivery miles per day per truck

Let f(m) denote the normal distribution function of M(N,R|T) with SD(N,R|T)

Let f(N) denote the demand function, which is subject to D. Weekly demand is the same

regardless of the length of the work week so days working determines how the demand

distribution breaks down on a daily basis. For example, if f(N) is normally distributed and D=2,

the expected daily demand equals weekly demand mean divided by 2 and the expected daily

demand has standard deviation equal to the square root of the weekly demand variance divided

by 2.

60

Let )(1 represent the inverse Gaussian giving the miles associated with the probability

contained within the parentheses where the miles ~ N(M(N,R|T), SD(N,R|T)).

Let p =2

)(

1 *

m

dmmf

; the cumulative probability of the calculated midpoint, which is the point

that bisects the probability of being greater than m*.

4.4.3. Model Definition

The total weekly cost, TC(T,D), is defined as the sum of the mileage cost, labor cost

(regular time plus overtime for more than 40 hours), carbon emission cost, and missed delivery

cost. This total cost function is as follows.

dNNfTRNMCDDTTCN

M )(,))((),(1

dNNfTRNMCDN

E )(,))((1

dNNfNaS

TRNMCD

N

W )(1,

))((1

)(40)(1|,

)(,0))((1

TdNNfNaS

TRNMDMAXCP

N

W

1

1

*

1

)(

)(*

))((N

m

D dNNf

N

p

dmmfmp

CD

(4-10)

Examining the total cost equation (4-10) we note that for a given radius of the demand

region, R, the distance traveled per day M(N,R|T) is a function of the number of trucks, T, and

the node size (customer demand + 1), N. This total cost equation represents the summation of

61

five different costs: mileage cost, carbon emissions cost, regular labor cost, overtime labor cost,

and missed delivery cost (or penalty). Each of these cost components is detailed in the following

paragraphs.

The mileage cost is based on the total expected miles traveled and includes costs such as

fuel and vehicle maintenance. The cost of carbon emissions, which is also directly related to

total mileage, is captured separately.

The total labor cost is defined by the total labor hours expected for the work week and

multiplied by the labor wage. If the weekly hours per truck exceeds the overtime threshold of 40

hours, an overtime cost is applied.

The cost for missed deliveries is estimated by finding the probability (area) of exceeding

m* on a given day and then using the midpoint method (see Figure 4.8) to find the point at which

that area is halved. That midpoint can be thought of as the expected tour distance on a day when

m* is exceeded. The midpoint is then used to calculate the average distance between nodes by

dividing the midpoint by the number of nodes. The difference between the midpoint and the

expected tour distance, M(N,R|T), is then divided by this average distance between nodes to

determine the approximate number of expected missed deliveries when m* is exceeded. Next

multiplying this value of the expected number of missed deliveries on a day when m* is

exceeded by the probability that m* is exceeded gives the overall number of expected missed

deliveries. Finally, multiplying this overall number of expected missed deliveries by the cost of

missed deliveries, CD, provides the probabilistic cost that is assigned for missed deliveries.

62

Figure 4.8: The Midpoint, Used In the Calculation of Missed Deliveries.

Figure 4.9 compares the midpoint method of determining the expected number of missed

deliveries with the computationally arduous method of calculating the expected missed deliveries

for each node individually. Since each node has its own probability as specified by the demand

distribution, the midpoint method is more computationally efficient than the individual method

and produces essentially similar results.

63

Figure 4.9: Missed Deliveries Calculated Individually Vs. the Midpoint Method.

4.4.4. Model Illustration with a Numerical Example

To numerically illustrate the model we assign the following parameter values:

CD = $20.00; CE = $0.002; CM =$0.45; CW = $15.00; D = 3, 4, 5, or 6; H = 12.0; P = 0.5; R = 50;

S = 29.6; a = 0.04; T = 1, 2, 3, 4, or 5; f(N) is derived from weekly demand ~ N(300, 20).

Fitted values of M(N,R|T) and SD(N,R|T) from the equations shown in Table 4.1 are represented

below.

42.56871.1017.0)1|42.56,( NNM

42.56744.1862.1)2|42.56,( NNM

42.56770.1776.2)3|42.56,( NNM

64

42.56706.1721.3)4|42.56,( NNM

42.56794.1666.4)5|42.56,( NNM

42.56)ln(064.0990.0)1|42.56,( NNSD

42.56)ln(199.0591.1)2|42.56,( NNSD

42.56)ln(245.0864.1)3|42.56,( NNSD

42.56)ln(367.0336.2)4|42.56,( NNSD

42.56)ln(434.0789.2)5|42.56,( NNSD

The Excel spreadsheet results from the total cost function for the parameter set identified are

presented in Figure 4.10.

Figure 4.10: Total Cost Results for Alternative Delivery Scenarios.

Examining Figure 4.10 for integer values of the number of trucks, we observe that the

minimum total cost is found to consist of four delivery trucks working three days per week at a

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

0 1 2 3 4 5 6

To

tal W

eekly

Co

st

Trucks

3 Day

4 Day

5 Day

6 Day

65

total weekly cost of $3413. Imposing the missed delivery costs causes infeasible delivery

strategies to be discarded based on the resulting high costs. For each of the delivery strategies,

the cost curve is relative flat between using four and five trucks with the percentage penalty

being between 0.3% and 9.2% across all days. The difference between 4 trucks and 5 trucks

when working 3 days is only $12. However, while there is only a $12 difference, as Figure 4.11

illustrates using 4 trucks results in a reduction of 357.5 kilos of CO2 per week over 5 trucks.

Clearly, the cost and carbon emission results demonstrated are parameter specific. Therefore, a

sensitivity analysis will follow on the key parameters. However, the methodology that has been

demonstrated presents a decision framework for assessing the truck fleet needed in satisfying

customer demand in the context of a stochastic representation of the last mile problem.

Figure 4.11: Carbon Emission Weekly Totals for Alternative Delivery Scenarios.

66

The parameters that were analyzed for their affect on the solution were CD and H. CM

and CW were analyzed as well, but changing the mileage cost and wage cost did not change the

resulting solution even when changing them simultaneously to different levels. All that changed

was the magnitude of the dollar difference between the solutions. While the parameters a, R, and

S are not presented here, it should be noted that each has a similar effect to changes in H as they

all affect the feasibility of making the necessary deliveries in the allotted amount of time.

Varying levels of CD and H were analyzed to see how the optimal solution was affected by each

parameter. To illustrate these, Figures 4.12 and 4.13 can be referenced.

Figure 4.12: Sensitivity Results of CD (cost of missed deliveries).

As illustrated in Figure 4.12, changing CD, the cost of a missed delivery, impacts the

result of the optimal (lowest cost) around CD = $20. The largest range in the changing order of

$2,000

$3,000

$4,000

$5,000

$6,000

$7,000

$8,000

$0 $5 $10 $15 $20 $25 $30 $35 $40

We

ekl

y To

tal C

ost

CD, cost of a missed delivery

T = 1, D = 3

T = 1, D = 4

T = 1, D = 5

T = 1, D = 6

T = 2, D = 3

T = 2, D = 4

T = 2, D = 5

T = 2, D = 6

T = 3, D = 3

T = 3, D = 4

T = 3, D = 5

67

the best solution comes between CD = $0 and $5. Reducing the cost of missed deliveries, CD, to

$0 changes the optimal solution as it eliminates the penalty associated with going over the daily

allotted delivery hours. Since this would cause major business issues, this cost must remain in

place to push out infeasible solutions. When the cost moves to $30, the larger penalty for the

probability of a missed delivery moves the optimal solution from T = 4 trucks delivering D = 3

days per week to T = 5 trucks delivering D = 3 days per week. So while the new weekly cost

difference between the two options is $113, the carbon emissions that are generated does not

change and the minimum still resides at T = 4 trucks delivering D = 3 days per week.

Figure 4.13: Sensitivity Results of H (hours available for delivery per day).

Changing the hours available for delivery, H, has the largest impact on the optimal

solution. As mentioned previously, changing parameters a, R, and S would each have a similar

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

6 8 10 12 14 16

We

ekl

y To

tal C

ost

H, daily hours available for delivery

T = 1, D = 3

T = 1, D = 4

T = 1, D = 5

T = 1, D = 6

T = 2, D = 3

T = 2, D = 4

T = 2, D = 5

T = 2, D = 6

T = 3, D = 3

T = 3, D = 4

T = 3, D = 5

68

effect to changes in H as they all affect the feasibility of making the necessary deliveries in the

allotted amount of time. The change in total weekly cost of each delivery option changes with

the feasibility of H. Changes in H within the infeasibility range do not impact the total cost.

Also, once H passes into the feasible range, the changes of H again do not impact the cost. It is

this small range of H where the probability of not being able to make all the deliveries is

uncertain that results in the total cost residing somewhere between the two extremes.

While the total cost function was found to not be convex, the sensitivity analysis shows

that the parameters most responsible for impacting the optimal solution are those that affect the

feasibility of making the required deliveries within the allotted time available for delivery. As

these parameters change and constrict the feasibility and probability of successfully making the

necessary deliveries, certain delivery combinations of delivery days per week and number of

trucks to employ become inadmissible. The model provides decision makers with the ability to

compare delivery alternatives in order to minimize cost and/or carbon emissions. Another

contribution of this model is the model’s ability to highlight the differences in carbon emissions

among decision alternatives that are similar in total cost.

4.5. Summary

In the last mile delivery fleet model, we have presented a mathematical model which for

a given set of parameters can be used to determine the optimal number of trucks and optimal

number of delivery days per week for delivering a single product to the end customers in a

supply chain. The characteristics of this model have been applied in the environment of the

69

LMP. The model presented herein extends distance based models found in the literature by

adopting a modeling structure that uniquely addresses the set of distant demand points found in

the delivery region. The model also incorporates the cost of CO2 emission into the model

formulation.

70

CHAPTER 5: CARBON EMISSIONS COMPARISON OF LAST MILE

DELIVERY VERSUS CUSTOMER PICK UP

Environmental sustainability is well recognized in the operations and supply chain

literature as a key current and future concern for organizations competing in the global

marketplace (Sarkis, 2012; Tang and Zhou, 2012; Seuring, 2013; Linton et al. 2007; Vachon and

Klassen, 2006; Kleindorfer et al. 2005). Sustainability in an organization is often driven along

the three core dimensions of economic, environmental or social development (Seuring and

Müller, 2008). Whether driven by social responsibility, compliance to pending and future

governmental legislation or attraction to new consumer markets organizations are addressing the

impact of their operational decisions on greenhouse gas emissions as a part of their overall

sustainability efforts. In this climate of enhanced awareness of environmentally sustainable

business practices, the issue of greenhouse gas emissions that result from freight transportation in

the product delivery process is becoming a key concern for operations and supply chain

managers.

Consumers have two basic options when making a retail purchase. E-commerce channels

allow the customer to initiate the purchase electronically without visiting the physical location of

the item to be purchased while conventional shopping methods involve visiting the physical

location of the item. In conventional shopping for retail items, the customer themselves picks up

the purchased item from the retailer and self delivers the item to their home using their own

vehicle; in e-commerce the item is delivered to the customer by the retail seller or by an agent

contracted by the seller to provide a home delivery service. Each of these delivery options

impacts the environment through the generation of greenhouse gas emissions during the delivery

71

of the purchased item. As identified by Ericsson et al. (2006), CO2 which is generated by

transport trucks burning carbon-based fuel represents a serious threat to the environment.

Several researchers have investigated the greenhouse gas emissions and carbon footprint

implications resulting from conventional shopping (customer pick up) versus delivery of the

product to the customers’ residence for e-commerce transactions (see for example, Edwards et al.

2010; Edwards et al. 2010; Siikavirta et al. 2003). The aforementioned studies provide a

baseline for investigating the tradeoff in the carbon footprint associated with product delivery

under conventional shopping and e-commence based online retailing and report the amount of

carbon dioxide (CO2) generated by each shopping option for retail purchases. These studies are

limited in that they do not integrate the carbon footprint burden of the two delivery options into

the logistical decision making process under varying levels of customer demand. This limitation

represents a research gap in the literature and suggests the need for a more comprehensive

analysis of the environmental impact of the logistical component of the supply chain under the

alternative delivery methods for conventional shopping and home delivery under online retailing.

In this chapter we model the carbon footprint resulting from delivery of products to

customers under conventional shopping and e-commence based online retailing. Our research

objectives are to: (i) integrate customer demand based measures of carbon emissions into the

decision making process for delivery of products to consumers, and (ii) provide a decision

making framework that can be used to assist organizations in making decisions involving the

choice of delivery options under a policy where sustainable logistical performance is evaluated.

The research contribution of the chapter herein is twofold. First we integrate carbon emissions

that are generated by customer demand for the delivery of products into the logistical decision

72

process thereby offering a more comprehensive modeling environment for evaluating logistical

performance. Better model development of the environmental aspects of the logistics function in

making deliveries may help to overcome the potential negative effects to the economy of making

suboptimal logistics decisions (Van Woensel et al. 2001). Second, using break-even analysis, we

provide a decision framework that can be used by an organization to identify a delivery option

that has the least harmful impact to the environment in terms of the carbon footprint under the

competing delivery options. The research herein is topical with current trends in the marketplace

as retail and online organizations such as Walmart and Amazon.com are beginning to consider or

are in the process of beta testing same day delivery of selected products to their customers

(Banjo 2012).

Refer to Section 2.6 for a review of the literature on sustainable aspects of delivery,

which provides the foundation for the development of our research modeling. The remaining

sections of this chapter are organized as follows. Section 5.1 involves formulating the model for

last mile delivery whereby product delivery is made to the customer’s home by the seller or an

agent providing delivery service for the seller. In Section 5.2, we formulate a methodology for

quantifying expected travel distances and carbon emissions for conventional shopping involving

self deliveries of a purchased product. In Section 5.3, we introduce empirical data on customer

travel distances and destinations to parameterize the delivery formulations defined in Sections

5.1 and 5.2. In Section 5.4, we do break-even analyses and quantify the carbon emission tradeoff

between conventional shopping and last mile delivery. Conclusions and future research are

summarized in Section 5.5.

73

5.1. Stochastic Last Mile Model Development

Last mile delivery involves the final leg of delivering to end customers in the supply

chain. Generally, trucks depart from a central depot to deliver goods. In order to model this

delivery in the general case, a circular demand region with a radius of R surrounding a centrally

located depot is the starting point. The following assumptions are adopted.

a) Demand is considered to be uniformly and randomly distributed, which is supported

in a review of continuous approximation models in freight distribution by Langevin et

al. (1996).

b) Travel distance is measured in miles using the Manhattan (L1) distance metric.

c) Time available for delivery is a feasibility constraint. For example, in Walmart’s beta

testing of same-day delivery, the available hours for delivery are 4 – 10 PM or 6

hours available for delivery.

While total truck capacity is not considered in the numerical example presented at the end

of this chapter, this could easily be added as a feasibility constraint if the distribution of customer

demand volume (or perhaps weight) was known. If the probability of exceeding available

capacity exceeded a predefined threshold, then more trucks would be required and the

comparison would be based on this number of delivery trucks.

As detailed in Chapter 4, in the development of this delivery model, demand points were

uniformly and randomly generated within a circular demand region of radius R with a single

depot located at the circle center (refer back to Figure 4.1 for an illustration). Details on how

these demand points were generated can be found in Appendix 3. Truck tour distances were

74

evaluated using the Manhattan distance (L1) metric, which implies that only north, south, east,

and west travel is allowed. Truck tour distances at each level of customer demand were

evaluated for 120 random trials. The minimum tour distance traveled in each trial was

determined based on the minimum tour distance resulting from four built-in traveling salesman

problem (TSP) solution algorithms found in Mathematica. Details on the TSP algorithms

employed to determine the minimum tour distance can be found in the Appendix 1 and 3.

Similar to the trials conducted for single truck tours, additional trials were performed for

T = 2, 3, 4, and 5 trucks. For multiple trucks (T > 1), the circular demand region of radius R was

subdivided into T equally sized and shaped sub regions. Each sub region was assigned one truck,

hence the number sub regions equates directly to the number of individual truck delivery tours

(refer back to Figure 4.3 for an illustration of the demand sub regions for T = 2 trucks).

As presented in Chapter 4, Table 4.1 is reproduced as Table 5.1 to show the equations for

the mean travel distance and associated standard deviation as the number of nodes, N, change (as

well as the delivery region radius, R) at each level of trucks, T.

T=

Mean Standard Deviation

Equation TRNM |, R2 Sig. Equation TRNSD |, R

2 Sig.

1 RN871.1017.0 .998 <.0001* RN)ln(064.0990.0 .528 .0075*

2 RN744.1862.1 .999 <.0001* RN)ln(199.0591.1 .832 .0308*

3 RN770.1776.2 .999 <.0001* RN)ln(245.0864.1 .871 .0206*

4 RN706.1721.3 .998 <.0001* RN)ln(367.0336.2 .861 .0229*

5 RN794.1666.4 .989 .0005* RN)ln(434.0789.2 .940 .0063*

Table 5.1: Statistical Information of Model Equations.

75

Using the fitted equations for the mean and standard deviation of the tour distance found

in Table 5.1, we can construct probabilistic estimates of tour distances. For example, by

introducing an average truck speed, a 95% service level for the delivery time could be created.

Calculating expected carbon emissions is a function of total tour mileage and will be discussed

further in Section 5.5.

5.2. Expected Distance Traveled for Customer Pick Up

In this section, we depart from last mile delivery and look at the alternative of customers driving

to the store (depot) to pick up goods and return home. Figure 5.1 illustrates customer pick up

from a store with a circular demand region with radius, R.

Figure 5.1: Demand Region with Customer Pick Up for n = 9 Customers.

76

In the development of the equations in this section, a store is located at the center of the

circular demand region with a radius of R. The following assumptions are adopted.

a) Demand is considered to be uniformly and randomly distributed.

b) Distance is measured in miles using both Euclidean (L2) and Manhattan (L1) distance

metrics.

The expected roundtrip distance that a customer travels in order to purchase goods

(without trip chaining) can be defined mathematically. Using Euclidean distances (L2 distance

metric) with uniformly and randomly distributed customers around the central store with radius

of R, the Euclidean mean distance, ED , of a customer from the store can be defined

mathematically as follows (Weisstein).

RDE3

2 (5-1)

The mean Euclidean distance as defined by (5-1) can be converted to a mean Manhattan

distance through the integration found in (5-2). For example, when the store lies exactly south

from the customer (angle is 0 degrees), the L2 and L1 distances are both R3

2. However, when

the store lies perfectly southwest from the customer (angle is 45 degrees), the L1 distance is

RRDM3

2245cos

3

245sin

3

2

. Hence (5-4) quantifies the expected Manhattan

distance where x equals the angle in radians from 0 to 2π (equivalent to 0 to 360 degrees).

77

3

8

2

)cos(3

2)sin(

3

22

RR

dxxx

D oM

(5-2)

The expected Manhattan round trip distance is MD2 .

In order to find the proportion of customer travel distance that should be applied to the

store due to trip chaining, a distance proportion, P (0 ≤ P ≤ 1), is used to account for trip

chaining. For example, if a customer leaves home, stops at Walmart, then the bank, then the

local grocery store, and then returns home, only a portion of that trip can be attributed to the stop

at Walmart. P is defined in (5-3). In the event that the customer made additional stops, but

would not have made the trip at all if the primary store had delivered the goods, then P = 1.

n

d

dd

P

n

i Oi

ZiXi

1 ,

,,

2 (5-3)

where

i = the index for each customer from 1 to n.

Xid , = the total distance of the trip including other stops.

Zid , = the distance that would have been traveled had the customer not visited the

delivering store, but made the other stops.

Oid , = the distance from the trip origin to the delivering store.

The difference, ZiXi dd ,, , can be thought of as the marginal distance saved due to last

mile delivery.

The expected total mileage, D, traveled for n customers is shown in (5-4).

78

3

16nPRD (5-4)

The distance proportion, P, can be estimated using empirical data. This proportion would

be P = 1 if every customer only went directly to the store and returned home. However, in

reality someone will probably be trip chaining, making other stops at other stores or may be

stopping at the store on the way to or from work. In these cases, the marginal distance that the

stop at the store adds is the true distance that would not have occurred if the customer had the

goods delivered. Empirical data on trip chaining was collected and will be discussed in more

detail in Section 5.

Given (5-4), fuel consumption and total kilos of CO2 emissions can be determined using

(5-5) and (5-6).

f

nPR

f

DF

3

16 (5-5)

where

F = total gallons of fuel consumed.

f = average fuel economy in miles per gallon (MPG).

D = expected total mileage for n customers.

n = number of customers.

P = proportion of customer travel distance that is devoted to the depot.

R = radius of demand region around depot.

f

cnPR

f

cDcFC

3

16 (5-6)

where

C = carbon footprint defined as total kilos of CO2 emitted.

c = average CO2 emitted per gallon of fuel.

79

The EPA (2011) estimates that the average gasoline vehicle on the road in 2011 has a fuel

economy of around 21 MPG. Kodjak (2004) states vehicles typically used in delivery (platform

trucks, delivery vans, super-duty pickups, etc) average 7.8 MPG, which is generally diesel, and

estimates fuel economy in 2015 could rise to 10.1 MPG. However, 7.8 MPG may be a better

estimate for all delivery vehicles on the road today with an understanding that fuel economies of

both passenger vehicles and delivery vehicles are on the rise due to the introduction of more fuel

efficient vehicles and the retiring of older vehicles.

5.3. Empirical Data on Customer Travel Distances

As mentioned in Section 5.2, one of the biggest issues in assessing the reduction of

carbon emissions resulting from last mile delivery is determining P, the proportion of distance

that a customer travels that is devoted to the store offering delivery. A survey of all customer

stops when engaging in conventional shopping involving a Walmart or Target was conducted to

gather data on P. These two stores, considered the primary or delivering store henceforth, were

chosen since they are both representative of conventional shopping retail outlets.

In all, 80 responses (out of 140 possible) were received of which 55 were useable.

Responses that contained incomplete or duplicate information were discarded. Responses were

analyzed as follows.

Determining P, the proportion of customer travel distance that is devoted to the depot

Comparing L1 distances to real world road distances

Estimating average vehicle speed of customers

80

Finding average distance from customers to the depot and using this to determine the

estimated radius of the demand region

As discussed, determining P was the primary motivation for collecting this data. Using

equation (5-5), P = 0.6368. The data was comprised of 42% of respondents that would not have

made the trip to the other locations if home delivery had been provided. Only 5% of respondents

did not engage in trip chaining. The remaining 53% of respondents would still have made the

trip to visit the other stops had the primary store delivered.

Another use of this data is comparing L1 distances to road distances. All the addresses

for each response were converted to a point of latitude and longitude. From there, the great-

circle distance formula was used to calculate L1 distances. For the road distances, Google Maps

was used to route the quickest trip between the addresses. Figure 5.2 shows that the correlation

between road distance and L1 distance for these observations is quite strong with an R2 of

0.97647 and statistical significance of p < .0001. While we use L1 distances throughout our

estimations, the equation (Google Map Miles = 0.437 + 1.026* L1 Distance) can be used to

convert these L1 distances into expected road distances. Naturally, since this data was mostly

Ohio suburban areas, the correlation may differ in more rural or more urban areas, particularly if

there are extensive barriers such as rivers or mountains.

81

Figure 5.2: Regression Results of Google Map Miles by L1 Distance

Road distances and travel times were obtained from Google Maps in order to establish

average vehicle speed, which is needed for determining the radius of the demand region that can

be serviced for a given number of trucks. Figure 5.3 shows a mean vehicle speed of 27.68 miles

per hour (MPH) with a 95% confidence interval of 27.68 ± 1.55 MPH (26.13, 29.23).

Interestingly enough, this correlates almost exactly to the 27.6 MPH national average traffic

speed as represented by the EPA (EPA 2008).

82

Figure 5.3: Vehicle Speeds Returned by Google Maps for Customer Trips

In Section 5.4, average distance to the delivering store becomes important. Using

Walmart as an example, Holmes (2005) found that the average distance of a customer to the

nearest Walmart varied by the region’s population density, but the average distance, weighted by

population was 6.7 miles. The range of this distance estimate runs from a minimum of 3.7 miles

in medium density (1273-3183 people per square mile) regions to 24.2 miles in sparsely

populated regions. Using our survey data, the average distances to the delivering store under the

Manhattan and Euclidean distance metrics are reported in Figures 5.4 and 5.5, respectively.

83

Figure 5.4: Distribution of L1 Distance from Origin of Trip to Store

Figure 5.5: Distribution of L2 Distance from Origin of Trip to Store

Although these average distances can be converted to an expected delivery radius using

equations (5-1) or (5-2), we opt to use Euclidean distances (5-1) because it offers more precision

in the estimate of the delivery radius. Table 5.2 lists possible mean distances to stores based on

our survey data and from Holmes (2005).

84

Source Population Density (1,000 in 5

mile radius)

Mean Distance

to Store (miles)

Calculated Delivery

Radius (miles)

Holmes (2005) 5-10 11.3 16.96

10-20 7.2 10.80

20-40 5.1 7.65

40-100 4.0 6.00

100-250 3.7 5.55

250-500 4.2 6.30

500 and above 6.9 10.35

Population weighted average 6.7 10.05

Our Data 20-250 (estimated) 4.27 6.40

Table 5.2: Estimated Delivery Region Radius Based on Mean Distance to Store

5.4. Break-even Analyses and Findings Supported By Empirical Data

This section will analyze break-even points for the number of customers (n) and the

distance proportion (P) in terms of CO2 emissions for last mile delivery versus customer pick up.

The break-even points for the number of customers are analyzed for delivery feasibility based on

the results and our empirical data.

Setting (5-6) equal to a modified (4-8) yields (5-7), which establishes the break-even

points for CO2 emissions for n = N – 1 and P.

D

TTD

G

G

f

RNbbc

f

PRNc 21

3

)1(16

(5-7)

where

Gc Average kilos of CO2 emitted per gallon of gasoline

Dc Average kilos of CO2 emitted per gallon of diesel

Gf Average fuel economy for a passenger vehicle in miles per gallon (MPG)

Df Average fuel economy for a delivery vehicle in miles per gallon (MPG)

85

Examining equation (5-7), we note that the demand region radius R does not impact the

break-even point for N or P. However, R does impact how many customers can be serviced

through last mile delivery in a given time period. Equation (5-8) gives the break-even equation

for P and (5-9) gives the break-even equation for N, the number of nodes where the number of

customers n = N – 1. While the break-even P is not illustrated in the example, it could be useful

for determining feasibility.

)1(16

3 21

Ncf

NbbcfP

GD

TTDG (5-8)

2

1

2

22

32

3166493

Pfc

fcbPfcPfcfcbfcbN

DG

GDTDGDGGDTGDT (5-9)

The expected break-even point for the number of customers, n = N – 1, can be established

by parameterizing (5-9) using the following values found in the literature and through our

empirical analysis: (i) average fuel economy for a passenger vehicle is Gf = 21 MPG of gasoline

(EPA 2011), (ii) average fuel economy for a delivery vehicle is Df = 7.8 MPG of diesel (Kodjak

2004), (iii) the EPA estimated the average CO2 emitted per gallon of gasoline as Gc = 8.887

kilos, and (iv) for diesel Dc = 10.180 kilos (EPA 2011). From Section 2, Tb1 and Tb2 vary

depending on how many trucks are doing deliveries. For T = 1 truck, 11b = 0.017 and 21b =

1.871. Finally, as initially stated in Section 5.3, P was estimated to be 0.6368 from our empirical

data.

Employing the parameterized equation (11), Table 5.3 gives the break-even points

involving the number of customers for CO2 emissions for 1 to 5 trucks, T. As the number of

86

trucks increases, the break-even number of customers rises because fewer trucks will always

cover less distance to service the same number of customers. The way in which a circular region

divides for different numbers of trucks explains why the gap between the break-even point for

different numbers of delivery trucks is irregular. If the number of customers requiring delivery

on a day is less than the break-even point, then last mile delivery is not reducing the overall

carbon footprint.

Number of trucks, T Nodes, N Customers, n

T = 1 truck N = 30.55 n ≈ 30 customers

T = 2 trucks N = 36.28 n ≈ 35 customers




Table 5.3: Break-even Points for CO2 Emissions

In order to test the feasibility of the break-even points for number of customers, we need

to address the average time a delivery truck spends at each stop and average vehicle speed. Both

of these attributes are addressed in (5-10), which gives the distance a vehicle can travel given an

average vehicle speed (S), hours available for delivery (H), and an average time (a) spent at each

stop.

601max

aNTHSD (5-10)

where

Dmax = Distance in miles.

S = Average vehicle speed in miles per hour (MPH).

T = Number of trucks being used for delivery.

H = Number of hours available for delivery per truck.

N = Number of nodes (customers are n = N – 1).

a = Average minutes spent at each stop or customer location.

87

Using (4-8) and (4-9), the service level (C), which determines the percentage of time that

the delivery route(s) will be completed within the available delivery hours, is given by (5-11).

)|,(

)|,()( max1

TRNSD

TRNMDC

(5-11)

where

C = The service level or confidence level percentage.

)(1 C = The z-score that is returned from C.

Introducing (5-10), (4-8), and (4-9) into (5-11) gives (5-12).

RNcc

RNbba

NTHS

CTT

TT

)ln(

601

)(21

21

1

(5-12)

Solving (5-12) for R yields (5-13), the radius of the delivery region.

NbbNccC

aNTHS

RTTTT 2121

1 )ln()(

601

(5-13)

To evaluate the maximum delivery radius (R) for a given number of trucks (T) at their

corresponding break-even point for number of customers, we need to parameterize S, H, and a.

Using S = 27.68 MPH from our empirical findings, H = 6 available delivery hours per the

Walmart same-day delivery beta testing, and a = 2.5 minutes. The value used for the average

minutes spent at each stop, a = 2.5, was estimated from data collected on the average daily

mileage, planned hours, and numbers of deliveries and pick-ups from 33 UPS drivers (UPS

88

2006). Applying these values returns a maximum region radius with a 95% service level as

follows.

For T = 1, n = 30, S = 27.68, H = 6, a = 2.5: R = 10.83 miles

For T = 2, n = 35, S = 27.68, H = 6, a = 2.5: R = 18.35 miles

For T = 3, n = 40, S = 27.68, H = 6, a = 2.5: R = 24.47 miles

For T = 4, n = 43, S = 27.68, H = 6, a = 2.5: R = 29.29 miles

For T = 5, n = 50, S = 27.68, H = 6, a = 2.5: R = 31.29 miles

The above values of R, which represent the maximum serviceable delivery radius at the

break-even point for number of customers, are reasonable since they exceed the empirically

established R = 6.4 miles. Exceeding the empirically established baseline of R = 6.4 miles

insures that it is possible to service more customers than the break-even point number of

customers. Failure to exceed R = 6.4 miles would have meant that last mile delivery could not

have serviced the break-even number of customers and thus would produce more carbon

emissions than customer pick up. This baseline radius of R = 6.4 miles, which was established

from our empirical data is compatible with the research of Holmes (2005).

Using (5-12), the number of customers that can be serviced in a radius of R = 6.4 miles at

a service level of C = 95% are given as follows.

For T = 1, R = 6.4, S = 27.68, H = 6, a = 2.5: N = 55.90; n ≈ 55 customers





89

In order to assure that the delivering store is reducing the overall carbon footprint while

maintaining its 95% service level, the number of customers requiring delivery needs to be

between the break-even point and the maximum number of serviceable customers. For example,

when using one truck, daily customers need to be between the break-even point of 30 and the

maximum number of serviceable customers, 55.

Continuing the example, in Figure 5.6 a comparison of carbon emissions from last mile

delivery and customer pick up is illustrated. The illustration in Figure 5.6 follows directly from

(5-7) where N – 1 is replaced with n and N with n + 1. The two notches in the last mile delivery

line indicate the customer level at which the number of trucks increased by one. While P was

found to be 0.6368 from the data, the other two levels of P represent the upper and lower limit of

P from a 90% confidence interval (0.5397, 0.7338) on the data.

Figure 5.6: Example CO2 Emissions of Customer Pick Up versus Last Mile Delivery

90

A general form for quantifying the difference in the kilos of CO2 emissions produced by

the alternative delivery strategies of last mile delivery and customer pick up is defined by (5-14).

When SC > 0, last mile delivery produced lower CO2 emissions than customer pick up; SC < 0,

customer pick up produced lower CO2 emissions than last mile delivery.

D

TTD

G

GS

f

Rnbbc

f

nPRcC

1

3

16 21

(5-14)

Figure 5.7 illustrates the tradeoff defined by (5-14) for the previously defined parameters

in which P = 0.6368, R = 6.4 miles, and the minimum number of trucks that can service n

customers are used at a service level of 95%. Again, the three levels of P represent the mean and

the upper and lower limit of P from a 90% confidence interval (0.5397, 0.7338) on the data. The

break-even point of 30 customers moves to 23 using the upper limit of P and 41 using the lower

limit of P.

91

Figure 5.7: Example CO2 Emissions Saved Through Last Mile Delivery

5.5. Carbon Emissions of Last Mile Delivery Versus Customer Pick Up Summary

In this chapter we compared the carbon emissions resulting from the delivery of products

to customers under conventional shopping involving customer pick up and e-commence based

online retailing involving last mile delivery. We integrated customer demand based measures of

carbon emissions into the decision making process for delivery of products to consumers and

provided a decision making framework that can be used to assist organizations in making

decisions involving the choice of delivery options under a policy where sustainable logistical

performance is evaluated. In addition, we integrated carbon emissions that are generated by

customer demand for the delivery of products into the logistical decision process thereby

offering a more comprehensive modeling environment for evaluating logistical performance.

92

Using break-even analysis, we provided a decision framework that can be used by an

organization to identify whether last mile delivery or customer pick up has the least harmful

impact to the environment in terms of carbon emissions. Providing delivery to fewer customers

than the break-even number of customer results in higher carbon emissions than if the customers

had picked up their purchases themselves (conventional shopping). Lastly, we provided a

method to quantify the difference in CO2 emissions resulting from customer pick up versus last

mile delivery as demonstrated in the numerical example and illustrated in Figures 5.6 and 5.7.

93

CHAPTER 6: CONCLUSIONS AND FUTURE RESEARCH

6.1. Summary of Research Contributions

In this dissertation, carbon emissions were integrated into cost-based freight

transportation models that can be used to assist operations and supply chain managers in solving

the “last mile problem”. The models presented herein serve to provide the decision maker with

choices on which strategy to implement depending on the strength of the management’s desire to

reduce carbon emissions. By comparing the optimal solutions that result from using different

delivery strategies, this research provides a basis for evaluating an appropriate trade-off between

transportation cost and carbon emissions.

This dissertation contributed to academia and the literature in several ways. The discrete

supply chain models provide a method for decision makers to analyze and compare the lowest

cost delivery option with the lowest carbon footprint option. The stochastic last mile framework

that was introduced provides a method for researchers and practitioners to measure expected

carbon footprint and compare probabilistic costs, carbon emissions, delivery mileage, and

delivery times in order to make decisions regarding the most appropriate delivery strategy. This

framework was then applied to two different problem settings. The first involved optimizing a

delivery fleet to produce the lowest total cost with carbon emissions integrated into the total cost

equation. The second compared the carbon footprint resulting from last mile delivery

(ecommerce retailing involving a central store delivering to end customers) to customer pick up

(conventional shopping at a brick-and-mortar retail location). The break-even number of

94

customers for carbon emissions equivalence provides a basis for companies to determine the



The fixed charge multiplier transshipment models from Chapter 3 introduced a carbon

penalty factor into a fixed charge transshipment model and compared results from a numerical

example with differing objective functions. The model presented shows how companies can

incorporate a carbon penalty factor into freight transportation planning in order to achieve a

desired reduction in carbon footprint or to minimize costs given the potential for a new

government tax on carbon emissions.

In the last mile delivery fleet model covered in Chapter 4, a mathematical model which

can be used to determine the optimal number of trucks and optimal number of delivery days per

week for delivering a single product to the end customers in a supply chain was presented. The

characteristics of this model were applied in the environment of the LMP. The framework

presented extends distance based models found in the literature by adopting a modeling structure

that uniquely addresses the set of distant demand points found in the delivery region. The model

also incorporates the cost of CO2 emission into the model formulation.

In Chapter 5, a comparison of the carbon emissions resulting from the delivery of

products to customers under conventional shopping involving customer pick up were compared

to e-commence based online retailing involving last mile delivery. Customer demand based

measures of carbon emissions were integrated into the decision making process for delivery of

products to consumers and provided a decision making framework that can be used to assist

organizations in making decisions involving the choice of delivery options under a policy where

95

sustainable logistical performance is evaluated. In addition, carbon emissions that are generated

by customer demand for the delivery of products were integrated into the logistical decision

process thereby offering a more comprehensive modeling environment for evaluating logistical

performance. Using break-even analysis, a decision framework was provided that can be used

by an organization to identify whether last mile delivery or customer pick up has the least

harmful impact to the environment in terms of carbon emissions. Providing delivery to fewer

customers than the break-even number of customer results in higher carbon emissions than if the

customers had picked up their purchases themselves (conventional shopping). Lastly, a method

was provided to quantify the difference in CO2 emissions resulting from customer pick up versus

last mile delivery as demonstrated in the numerical example and illustrated in Figures 5.6 and

5.7.

6.2. Summary of Limitations and Future Research

While the fixed charge multiplier transshipment models from Chapter 3 incorporate

different truck capacities into the model, a limitation is that only one truck capacity is available

per route. This could be addressed by allowing multiple truck types along each route and leaving

the decision on which type of trucks to use to be decided by the optimization. In addition, the

presented problem uses deterministic supply and demand. Utilizing stochastic variables could be

an option for further enhancement. Finally, the model could be expanded to an n-stage supply

chain.

96

Using a set of cost-based models, this research has shown that minimizing total cost is

not always going to jointly satisfy objectives related to green initiatives and sustainability. When

deciding on trucking routes and inventory movements, managers can try to strike a balance

between lowest total cost and reducing carbon emissions. Other strategies such as maximizing

freight trailer capacities and avoiding LTL (less than truck load) shipments are other avenues for

managers to meet these new objectives while still keeping an eye on the bottom line.

From Chapter 4 involving the development of the stochastic last mile delivery framework

and the last mile delivery fleet optimization model, there are several aspects that can be

extended. Firstly, expected optimal tours, which were found to be Gaussian at each individual

demand level N, could be aggregated by into a mixture distribution. This would allow for a more

precise measure on the likelihood of overtime and the resulting cost. Secondly, the model could

be adapted such that carbon emission is constrained subject to a carbon trading/credit scheme.

Thirdly, the model could be expanded to include multiple depots within each region or sub

region.

From Chapter 5 involving the extension of the last mile problem into a comparison of the

carbon emissions resulting from the delivery of products to customers under conventional

shopping involving customer pick up versus e-commence based online retailing involving last

mile delivery, there are several aspects that could be extended. Since the marginal distance

applied to the delivering store impacts the break-even number of customers, additional research

on customer trip chaining could be conducted. In addition, alternative delivery scenarios not

originating from the central depot could be explored. For example, if delivery is farmed out to a

third party that is not located at the central depot, the break-even point would change based on

97

how the expected tour distances change and what proportion of these distances should be applied

to the delivering store due to delivery carrier trip chaining. Lastly, the break-even methodology

employed herein could be extended to include stochastic input parameters.

98

APPENDICES

Appendix 1: Model Formulation of the Example Using LINGO

MODEL:

! A green hybrid fixed cost multiplier transshipment problem;

SETS:

CITIES / BOS CLE ORL COL IND/: F;

ROUTES(CITIES,CITIES): C, K, X, Y, T, G;

ENDSETS

! THE OBJECTIVE;

MIN = @SUM(ROUTES(i,j): C(i,j)*X(i,j) + K(i,j)*Y(i,j) + P*G(i,j)*Y(i,j));

! THE CONSTRAINTS;

! received - shipped = flow constraint;

@FOR(CITIES(j): @SUM(CITIES(i): X(i,j) - X(j,i)) = F(j));

! fixed cost multiplier constraints (if all the same, T(i,j) could be 1 number);

@FOR(ROUTES(i,j): Y(i,j) >= X(i,j)/T(i,j));

@FOR(ROUTES(i,j): @GIN(Y(i,j)));

! calculate total carbon footprint;

@SUM(ROUTES(i,j): G(i,j)*Y(i,j)) = KILOS;

! total cost;

@SUM(ROUTES(i,j): C(i,j)*X(i,j) + K(i,j)*Y(i,j)) = COST;

DATA:

! Penalty Factor, chosen by decision maker;

P = 1.6;

! Flow: received - shipped;

F = -500 -400 -350 500 750;

! Fixed Cost of any size shipment from i to j;

K = 0 200 350 225 290

200 0 325 50 75

350 325 0 325 350

225 50 325 0 55

290 75 350 55 0;

! Per Unit Cost of a shipment from i to j;

C = 0 6 12 8 9

6 0 18 1 6

12 18 0 16 15

8 1 16 0 8

9 6 15 8 0;

! Fixed Cost Factor from i to j (point where additional fixed costs are applied);

T = 1 500 500 300 400

500 1 500 400 300

500 500 1 500 300

300 400 500 1 300

400 300 300 300 1;

! Kilos CO2 from i to j (per truck);

G = 0 1042 2098 1244 1526

1042 0 1692 231 515

2098 1692 0 1549 1584

1244 231 1549 0 285

1526 515 1584 285 0;

ENDDATA

99

Appendix 2: Demand Generation for Stochastic Last Mile Delivery

In order to achieve uniformly distributed points with a single central depot located at the

center of the circular demand region the following procedures were performed.

Let:

R = radius of the demand region

h = a distance (or new radius) from origin used in generating a node, 0 < h < R

Rand() = a generator that gives a uniform random number between 0 and 1

RADIANS() = converts a number within the parentheses from 0 to 360 into radians

A = area of demand region = π*R2

angle = angle (out of 360) that the generated node is from the depot

i = the number of nodes

Xi = the x coordinate of the ith

node

Yi = the y coordinate of the ith

node

N = number of nodes

Demand point (X, Y) generation:

Set (X1, Y1) = (0, 0) for the central depot

h = [Rand()*(A / π)]1/2 = [Rand()*R

2]1/2 = Rand()

1/2*R

angle = RADIANS(Rand()*360)

For all i from 2 to N, Xi = COS(angle)*h

For all i from 2 to N, Yi = SIN(angle)*h

For example, if the areas of the regions chosen are all equal to 10,000, then the radius is

equal to approximately 56.42. However, the resulting optimal tours based on these sizes are

easily transferrable to different sized regions.

When changing the size of a circular region, the expected optimal tour length changes by

the same factor as the change in the radius of the region. So the optimal tour of the same

distribution of points (coordinates change) in a region with a radius of 20 miles is 2 times longer

than this same representation in a region with a radius of 10 miles. In addition to the mean

doubling, the standard deviation will also double in this scenario.

100

Appendix 3: Traveling Salesman Solution Algorithms Employed

TwoOpt or 2-opt (Croes, 1958) is a tour improvement heuristic that works by taking a

complete tour and removing two edges currently in the tour and replacing them with two edges

that reconnect the tour and decrease its length. When all edges around the tour are broken and

no improvement is found, the heuristic is done.

OrOpt (Or, 1976) is very similar to TwoOpt and works by removing substrings of one,

two, or three nodes and reinserting elsewhere (perhaps in reversed order).

OrZweig (Zweig, 1995) is actually a modification of the OrOpt procedure that uses

neighbor lists based on the Delaunay triangulation in order to try and improve the insertion

effectiveness.

CCA stands for convex hull, cheapest insertion, angle selection and is a tour construction

algorithm (Golden and Stewart, 1985). CCA works by constructing the convex hull, which can

be thought of as stretching a rubber band around the nodes as though they were thumbtacks on a

bulletin board. From there, the algorithm determines where each point not touching the rubber

band should be inserted to increase the tour length the least. Among all those possibilities, the

node making the largest angle is inserted and the process repeats.

Using the minimum of these four allows for results closer to the true global minimum

compared to using any one heuristic or algorithm alone, especially as the problem size increases.

There are more heuristics that could be employed, even built-in algorithms in Mathematica like

IntegerLinearProgramming, but computation time becomes unmanageable at high node levels.

101

Appendix 4: Sample Mathematica Code for Finding the Minimum Tour

Sample code generated for Mathematica with associated output using the random node

generating method described in a previous appendix.

For a given trial where T = 1, N = 10, A = 10000 (therefore R = 56.42):

In[1]:= FindShortestTour[{{0,0},{6.601,-19.567},{8.25,40.652},{43.122,43.755},{-

11.085,47.991},{51.792,22.197},{-8.359,-4.464},{-27.494,-8.565},{-7.954,-32.486},{5.068,-

21.792}},DistanceFunction->ManhattanDistance,Method->"OrOpt"]

FindShortestTour[{{0,0},{6.601,-19.567},{8.25,40.652},{43.122,43.755},{-

11.085,47.991},{51.792,22.197},{-8.359,-4.464},{-27.494,-8.565},{-7.954,-32.486},{5.068,-

21.792}},DistanceFunction->ManhattanDistance,Method->"CCA"]


11.085,47.991},{51.792,22.197},{-8.359,-4.464},{-27.494,-8.565},{-7.954,-32.486},{5.068,-

21.792}},DistanceFunction->ManhattanDistance,Method->"TwoOpt"]


11.085,47.991},{51.792,22.197},{-8.359,-4.464},{-27.494,-8.565},{-7.954,-32.486},{5.068,-

21.792}},DistanceFunction->ManhattanDistance,Method->"OrZweig"]

Out[1]= {344.386,{1,6,4,3,5,7,8,9,10,2}} (OrOpt Algorithm)

Out[2]= {347.902,{1,7,8,9,10,2,6,4,3,5}} (CCA Algorithm)

Out[3]= {347.902,{1,7,8,9,10,2,6,4,3,5}} (TwoOpt Algorithm)

Out[4]= {344.386,{1,6,4,3,5,7,8,9,10,2}} (OrZweig Algorithm)

Minimum tour distance for this trial = 344.386 (Tie between OrOpt and OrZweig)

102

Appendix 5: Distribution of Optimal Tours for T=1 with Varying Node Levels

All distances in Appendices 4-8 are with a radius of 56.42 (area = 10,000).

Distributions Nodes=10 Minimum

Normal(353.124,50.8873)

Quantiles

100.0% maximum 464.544 99.5% 464.544 97.5% 450.65 90.0% 420.394 75.0% quartile 388.597 50.0% median 355.078 25.0% quartile 324.026 10.0% 284.776 2.5% 236.346 0.5% 184.972 0.0% minimum 184.972

Moments

Mean 353.12408 Std Dev 50.887309 Std Err Mean 4.6453545 Upper 95% Mean 362.32235 Lower 95% Mean 343.92582 N 120

Fitted Normal Parameter Estimates Type Parameter Estimate Lower 95% Upper 95%

Location μ 353.12408 343.92582 362.32235 Dispersion σ 50.887309 45.161996 58.288156 -2log(Likelihood) = 1282.65250327218

Goodness-of-Fit Test Shapiro-Wilk W Test

W Prob<W

0.990391 0.5697 Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.

103


Normal(485.443,44.3609)

Quantiles


Moments





W Prob<W


104


Normal(577.616,39.0584)

Quantiles


Moments





W Prob<W


105


Normal(674.009,44.7344)

Quantiles


Moments





W Prob<W


106


Normal(751.229,39.932)

Quantiles


Moments





W Prob<W


107


Normal(820.393,36.5354)

Quantiles


Moments





W Prob<W


108


Normal(883.471,42.513)

Quantiles


Moments





W Prob<W


109


Normal(942.879,37.8472)

Quantiles


Moments





W Prob<W


110


Normal(998.27,42.5457)

Quantiles


Moments





W Prob<W


111


Normal(1056.27,39.5665)

Quantiles


Moments





W Prob<W


112


Normal(1108.06,39.0624)

Quantiles


Moments





W Prob<W


113

Minimum, N=160

Normal(1325.61,39.0852)

Quantiles


Moments





W Prob<W


114

Appendix 6: Distribution of Optimal Tours for T=2 at Selected Node Levels

Distributions Nodes=10 Total

Normal(416.773,68.4636)

Quantiles


Moments





W Prob<W


115


Normal(547.51,53.1148)

Quantiles


Moments





W Prob<W


116


Normal(725.28,44.9999)

Quantiles


Moments





W Prob<W

0.971718 0.0124* Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.

117


Normal(863.317,39.9175)

Quantiles


Moments





W Prob<W


118


Normal(1139.79,42.7312)

Quantiles


Moments





W Prob<W


119



Normal(458.5,78.7282)

Quantiles


Moments





W Prob<W


120


Normal(619.107,59.4712)

Quantiles


Moments





W Prob<W


121


Normal(789.732,50.1866)

Quantiles


Moments





W Prob<W


122


Normal(929.854,46.0987)

Quantiles


Moments





W Prob<W


123


Normal(1200.49,45.6623)

Quantiles


Moments





W Prob<W


124



Normal(498.281,92.2506)

Quantiles


Moments





W Prob<W


125


Normal(657.088,62.7635)

Quantiles


Moments





W Prob<W


126


Normal(822.656,51.9562)

Quantiles


Moments





W Prob<W


127


Normal(954.717,40.9587)

Quantiles


Moments





W Prob<W


128


Normal(1214.73,43.2781)

Quantiles


Moments





W Prob<W


129



Normal(541.05,107.135)

Quantiles


Moments





W Prob<W


130


Normal(748.211,77.6399)

Quantiles


Moments





W Prob<W


131


Normal(930.367,64.9812)

Quantiles


Moments





W Prob<W


132


Normal(1047.98,52.7842)

Quantiles


Moments





W Prob<W


133


Normal(1306.74,48.0154)

Quantiles


Moments





W Prob<W


134

REFERENCES

Abdallah, T., Farhat, A., Diabat, A., & Kennedy S. (2012), Green supply chains with carbon

trading and environmental sourcing: formulation and life cycle assessment. Applied

Mathematical Modeling, 36(9), 4271-4285.

Anciaux, D. & Yuan, K. (2007), Green supply chain: intermodal transportation modeling with

environmental impacts, Association of European Transport and Contributors, Metz, France, 1-

11.

Anderson, E., Coltman, T., Devinney, T., & Keating, B. (2011). What drives the choice of a third

party logistics provider? Journal of Supply Chain Management, 47(2), 97-115.

Balcik, B., Beamon, B. M., & Smilowitz, K. (2008). Last mile distribution in humanitarian relief.

Journal of Intelligent Transportation Systems, 12(2), 51-63.

Banjo, S (2012), Walmart delivery service says to Amazon: “bring it”, Wall Street Journal, 10

October, p. B1.

Beamon, B. M. (1998). Supply chain design and analysis: models and methods. International

Journal of Production Economics, 55(3), 281-294.

Beardwood, J., Halton, J. H., & Hammersley, J. M. (1959). The shortest path through many

points. Mathematical Proceedings of the Cambridge Philosophical Society, 55, 299-327.

Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential

data and sources of collinearity. New York: John Wiley.

Bowersox, D. J., Closs, D. J. & M. B. Cooper (2010), Supply Chain Logistics, 3rd Edition,

Management, McGraw-Hill/Irwin, Boston.

Boyer, K. K., Prud’homme, A. M. & Chung, W. (2009). The last mile challenge: evaluating the

effects of customer density and delivery window patterns. Journal of Business Logistics, 30(1),

185-201.

Bromage, N. (2001). Keep the customer satisfied. Supply Management, 6(10), 34-36.

Brown, J. R & Guiffrida, A. L. (2012). Stochastic modeling of the last mile problem.

Proceedings of the Tenth Annual International Symposium on Supply Chain Management in

Toronto, Canada, September 30-October 2, 2012.

Carter, C. R. & D. S. Rogers (2008). A framework of sustainable supply chain management:

moving toward new theory. International Journal of Physical Distribution and Logistics

Management, 38(5), 360-387.

135

Chiou, C.-C. (2008). Supply Chain, Chapter 21: Transshipment problems in supply chain

systems: review and extensions, Vedran Kordic (Ed.), InTech, 427-448.

Chopra, S. (2003). Designing the distribution network in a supply chain. Transportation

Research, 39(2), 123-140.

Clarke, G. & Wright, J. W. (1964). Scheduling of vehicles from a central depot to a number of

delivery points. Operations Research, 12(4), 568-581.

Cook, R. D. (1977). Detection of influential observations in linear regression. Technometrics,

19(1), 15-18.

Cordeiro, M. (2008), Measuring the invisible, quantifying emissions reductions from transport

solutions: Queretaro case study, World Resources Institute.

Croes, G. A. (1958). A method for solving traveling-salesman problems. Operations Research,

6(6), 791-812.

Daccarett-Garcia, J. Y. (2009). Modeling the Environmental Impact of Demand Variability Upon

Supply Chains in the Beverage Industry, Masters Thesis, Department of Industrial and Systems

Engineering, Rochester Institute of Technology.

Daganzo, C. F. (1984). The distance traveled to visit N points with a maximum of C stops per

vehicle: an analytic model and an application. Transportation Science, 18(4), 331-350.

Daganzo, C. F. (1987). The break-bulk role of terminals in many-to-many logistic networks.

Operations Research, 35(4), 543-555.

Dantzig, G. B. & Thapa, M. N. (2003) Transportation problems and variations. Linear

Programming, 207-229.

De Giovanni, P. & Vinzi, V. E. (2012). Covariance versus component-based estimations of

performance in green supply chain management. International Journal of Production

Economics, 135(2), 907-916.

Edwards, J. B., McKinnon, A. C., & Cullinane, S. L. (2010). Comparative analysis of the carbon

footprints of conventional and online retailing: a “last mile” perspective. International Journal of

Physical Distribution and Logistics Management, 40(1/2), 103-123.

Eilon, S., Watson-Gandy, C.D.T., & Christofides, N. (1971). Distribution Management:

Mathematical Modelling and Practical Analysis, Griffin, London.

El Saadany, A. M. A., Jaber, M. Y., & Bonney, M. (2011). Environmental performance

measures for supply chains. Management Research Review, 34(11), 1202-1221.

136

EPA (U.S. Environmental Protection Agency), The Environmental Protection Agency's White

Paper on Greenhouse Gas Emissions from a Typical Passenger Vehicle, EPA Publication EPA-

420-F-11-041, December 2011.

EPA (U.S. Environmental Protection Agency), The Environmental Protection Agency’s White

Paper on Average Annual Emissions and Fuel Consumption for Gasoline-Fueled Passenger Cars

and Light Trucks, EPA Publication EPA420-F-08-024, October 2008.

Ericsson, E., Larsson, H., & Brundell-Freij, K. (2006). Choice for lowest fuel consumption –

potential effects of a new driver support tool. Transportation Research Part C, 14(6), 369-383.

Ernst, R., Kamrad, B., & Ord, K. (2007). Delivery performance in vendor selection decisions.

European Journal of Operational Research, 176(1), 534-541.

Esper, T. L., Jensen, T. D., & Turnipseed, F. L. (2003). The last mile: an examination of effects

of online retail delivery strategies on consumers. Journal of Business Logistics, 24(2), 177-203.

Evans, J. R., Anderson, D. R., Sweeney, D. J., & Williams, T. A. (1990). Applied Production

and Operations Management, 3rd

edition, West Publishing Company, St. Paul.

Forslund, H., Jonsson, P., & Mattsson, S. (2009). Order-to-delivery performance in delivery

scheduling environments. International Journal of Productivity and Performance Management,

58(1), 41-53.

Gendreau, M., Hertz, A., & Laporte, G. (1994). A tabu search heuristic for the vehicle routing

problem. Management Science, 40(10), 1276-1290.

Gevaers, R., Van de Voorde, E., & Vanelslander, T. (2011). Characteristics and typology of last-

mile logistics from an innovative perspective in an urban context, presented at the Transportation

Research Board Annual Meeting, Washington, DC, Jan. 25, 2011.

Golden, B. L. & Stewart Jr., W. R. (1985). Empirical analysis of heuristics in the traveling

salesman problem. A guided tour of combinatorial optimization (pp. 207-249), Chichester, UK:

John Wiley.

Golicic, S. L., Boerstler, C. N. & Ellram, L. M. (2010). Greening transportation in the supply

chain. Sloan Management Review, 51(2), 47-55.

Golini, R. & Kalchschmidt, M. (2010), Global Supply Chain Management and Delivery

Performance: A Contingent Perspective, in Rapid Modelling and Quick Response (pp. 231-247).

G. Reiner (ed.), London Limited: Springer-Verlag.

Goodman, R. W. (2005). Whatever you call it, just don’t think of last-mile logistics, last. Global

Logistics & Supply Chain Strategies, 9(12), 46-51.

137

Green, K. W., Zelbest, P. J., Meacham, J., & Bhadauria, V. S. (2012). Green supply chain

management practices: impact on performance. Supply Chain Management: An International

Journal, 17(3), 290-305.

Gunasekaran, A., Patel, C., & McGaughey (2004). A framework for supply chain performance

measurement. International Journal of Production Economics, 87(3), 333-347.

Gunasekaran, A., Patel, C. & Tirtiroglu, E. (2001). Performance measures and metrics in a

supply chain environment. International Journal of Operations and Production Management,

21(1/2), 71-97.

Harris, I., Naim, M., Palmer, A., Potter, A., & Mumford, C. (2011). Assessing the impact of cost

optimization based on infrastructure modeling on CO2 emissions. International Journal of

Production Economics, 131(1), 313-321.

Hervani, A. A., Helms, M. M. & Sarkis, J. (2005). Performance measurement for green supply

chain management. Benchmarking: An International Journal, 12(4), 330-353.

Hirsch, W. M. & Dantzig, G. B. (1954). The fixed charge problem, Rand Corporation Santa

Monica, CA.

Hitchcock, F.L. (1941). The distribution of a product from several sources to numerous

localities. Journal of Mathematics and Physics, 20, 224-230.

Holmes, T. J. (2005). The diffusion of Walmart and the economies of density, working paper,

University of Minnesota, Federal Reserve Bank of Minneapolis and National Bureau of

Economic Research, November.

Huang, M., Smilowitz, K., & Balcik, B. (2011). Models for relief routing: Equity, efficiency and

efficacy. Transportation Research Part E: Logistics and Transportation Review, 48(1), 2-18.

Jaillet, P. (1988). A priori solution of a traveling salesman problem in which a random subset of

the customers are visited. Operations Research, 36(6), 929-936.

Kenny, T. & Gray, N. F. (2009). Comparative performance of six carbon footprint models for

use in Ireland. Environmental Impact Assessment Review, 29(1), 1-6.

Kleindorfer, P. R., Singhal, K., & Van Wassenhove, L. N. (2005). Sustainable operations

management. Decision Sciences, 14(4), 482-492.

Kodjak, D. (2004). Policy discussion – heavy-duty truck fuel economy. National Commission on

Energy Policy. 10th

Diesel Engine Emissions Reduction (DEER) Conference, August 29 –

September 2, 2004, Coronado, California, available at:

http://www1.eere.energy.gov/vehiclesandfuels/pdfs/deer_2004/session6/2004_deer_kodjak.pdf

(accessed 30 October 2012).

138

Kull, T. J., Boyer, K., & Calantone, R. (2007). Last-mile supply chain efficiency: an analysis of

learning curves in online ordering. International Journal of Operations and Production

Management, 27(4), 409-434.

Lane, R. & Szwejczewski, M. (2000). The relative importance of planning and control systems

in achieving good delivery performance. Production Planning and Control, 11(5), 423-433.

Langevin, A., Mbaraga, P., & Campbell, J.F. (1996). Continuous approximation models in

freight distribution: an overview. Transportation Research, 30(3), 163-188.

Laporte, G., Mercure, H., & Nobert, Y. (1986). An exact algorithm for the asymmetrical

capacitated vehicle routing problem. Networks, 16(1), 33-46.

Laporte, G. (1992). The vehicle routing problem: an overview of exact and approximate

algorithms. European Journal of Operational Research, 59(3), 345-358.

Larson, R. C. & Odoni, A. R. (1981). Urban Operations Research, Prentice-Hall, Englewood

Cliffs, New Jersey.

Lee, H. L. & Whang, S. (2001). Winning the last mile of e-commerce. MIT Sloan Management

Review, 42(4), 54-62.

Lee, K-H. (2011). Integrating carbon footprint into supply chain management: the case of

Hyundai Motor Company (HMC) in the automobile industry, Journal of Cleaner Production,

19(11) 1216-1223.

Linton, J. D., Klassen, R., & Jayaraman, V. (2007). Sustainable supply chains: an introduction.

Journal of Operations Management, 25(6), 1075-1082.

McIntyre, K., Smith, H. A., Henham, A., & Pretlove, J. (1998). Logistical performance

measurement and greening supply chains: diverging mindsets. The International Journal of

Logistics Management, 9(1), 57-68.

Moran, A. (2010). Government warning to a carbon tax. The Institute of Public Affairs Review:

A Quarterly Review of Politics and Public Affairs, 62(4), 39-41.

Newell , G. F. (1973). Scheduling, location, transportation, and continuum mechanics: some

simple approximations to optimization problems. SIAM Journal on Applied Mathematics, 25(3),

346-360.

Or, I. (1976). Travelling salesman-type combinatorial problems and their relation to the logistics

of regional blood banking. Ph.D. Dissertation, Northwestern University, Evanston, IL.

Orden, A. (1956). The transshipment problem. Management Science, 2(3), 276-285.

139

Paksoy, T., Ozceylan, E. & G.-W. Weber (2010). A multi objective model for optimization of a

green supply chain network, Proceedings of PCO 2010, 3rd

Global Conference on Power

Control and Optimization, February 2-4, 2010, Gold Coast, Queensland, Australia.

Panneerselvam, R. (2006). Operations Research, PHI Learning Pvt. Ltd, 106-117.

Porter, M. (1980). Competitive Strategy. New York: The Free Press.

Punakivi, P., Yrjölä, H., & Holmström, J. (2001). Solving the last mile issue: reception box or

delivery box? International Journal of Physical Distribution & Logistics Management, 31(6),

427-439.

Ramudhin, A., Chaabane, A., & Paquet, M. (2010). Carbon market sensitive sustainable supply

chain network design. International Journal of Management Science and Engineering

Management, 5(1), 30-38.

Rao, C. M., Rao, K. P., & Muniswamy, V. V. (2011). Delivery performance measurement in an

integrated supply chain management: case study in batteries manufacturing firm. Serbian

Journal of Management, 6(2), 205-220.

Rao, P. & Holt, D. (2005). Do green supply chains lead to competitiveness and economic

performance. International Journal of Operations and Production Management, 25(9), 898-916.

Reed, B. D., Smas, M. J., Rzepka, R. A., Guiffrida, A. L. (2010). Introducing green

transportation costs in supply chain modeling, Proceedings of the First Annual Kent State

International Symposium on Green Supply Chains, July 29-30, 2010, Canton, Ohio, 189-197.

Sandrock, K. (1988). A simple algorithm for solving small, fixed-charge transportation

problems, The Journal of Operations Research, 39(5), 467-475.

Sarkis, J. (2003). A strategic decision making framework for green supply chain management,

Journal of Cleaner Production, 11(4), 397-409.

Sarkis, J. (2012). A boundaries and flows perspective of green supply chain management. Supply

Chain Management: An International Journal, 17(2), 202-216.

Sarkis, J., Zhu, Q., & Lai, K-H. (2011). An organizational theoretic review of green supply chain

management literature. International Journal of Production Economics, 130(1), 1-15.

Schipper, L., Anh, T. L. & Orn, H. (2008). Measuring the invisible, quantifying emissions

reductions from transport solutions: Hanoi case study, World Resources Institute.

Seuring, S. (2013). A review of modeling approaches for sustainable supply chain management.

Decision Support Systems, 54(4), 1513-1520.

140

Seuring, S. & Müller, M. (2008). From a literature review to a conceputal framework for

sustainable supply chain management. Journal of Cleaner Production, 16(15), 1699-1710.

Shin, H., Benton, W. C., Jun, M. (2009). Quantifying suppliers’ product quality and delivery

performance: a sourcing policy decision model. Computers and Operations Research, 36(8),

2462-2471.

Siikavirta, H., Punakivi, M., Karkkainen, M., & Linnanen, L. (2003). Effects of e-commerce on

greenhouse gas emissions. Journal of Industral Ecology, 6(2), 83-97.

Srivastava, S. K. (2007). Green supply-chain management: a state-of-the-art literature review.

International Journal of Management Reviews, 9 (1), 53-80.

Stalk, G. (1988). Time – the next source of competitive advantage. Harvard Business Review,

July-August, 55-59.

Stank, T. P., Goldsby, T. J., Vickery, S. K., & Savitskie, K. (2003). Logistical service

performance: estimating its influence on market share. Journal of Business Logistics, 24(1), 27-

55.

Stapleton, O., Pedraza Martinez, A., & Van Wassenhove, L. N. (2009). Last mile vehicle supply

chain in the international federation of red cross and red crescent societies, working paper,

INSEAD, Fontainebleau, France, 23 October.

Stein, D. M. (1978). An asymptotic, probabilistic analysis of a routing problem. Mathematics of

Operations Research, 3(2), 89-101.

Stone, R. E. (1991). Technical note – some average distance results. Transportation Science,

25(1), 83-90.

Sundarakani, B., de Souza, R., Goh, M., Wagner, S. M., & Manikandan, S. (2010). Modeling

carbon footprints across the supply chain. International Journal of Production Economics,

128(1), 43-50.

Supply Chain and Logistics (2009). “Green” supply chain movement hits a speed bump,

www.industryweek.com.

Tan, K. C., Lyman, S. B., & Wisner, J. D. (2002). Supply chain management: a strategic

perspective. International Journal of Operations and Production Management, 22(6), 614-631.

Tang, C. S. & Zhou, S. (2012). Research advances in environmentally and socially sustainable

operations. European Journal of Operational Research, 223(3), 585-594.

Ubeda, S., Arcelus, F. J., & Faulin, J. (2011). Green logistics at Eroski: a case study.

International Journal of Production Economics, 131(1), 44-51.

141

Ülkü, M. A. (2012). Dare to care: shipment consolidation reduces not only cost, but also

environmental damage. International Journal of Production Economics, 139(2), 438-446.

UPS, Anonymous Driver. (2006). Average stops per day delivery and pickups, available at

http://www.browncafe.com/forum/f6/average-stops-per-day-delivery-pickups-35610/ (accessed

30 October 2012).

Vachon, S. & Klassen, R. D. (2006). Extending green practices across the supply chain: the

impact of upstream and downstream integration. International Journal of Operations and

Production Management, 26(7), 795-821.

Van Woensel, T., Creten, R., & Vandaele, N. (2001). Managing the environmental externalities

of traffic logistics: the issue of emissions. Production and Operations Management, 10(2), 207-

223.

Vaughan, R. (1984). Approximate formulas for average distances associated with zones.

Transportation Science, 18(3), 231-244.

Wahab, M. I. M., Mamun, S. M. H., & Ongkunaruk, P. (2011). EOQ models for a coordinated

two-level international supply chain considering imperfect items and environmental impact.

International Journal of Production Economics, 134(1), 151-158.

Wang, F., Lai, X., & Shi, N. (2011). A Multi-objective optimization for green supply chain

network design. Decision Support Systems, 51(2), 262-269.

Weisstein, E. W. Disk Point Picking. From MathWorld--A Wolfram Web Resource, available at:

http://mathworld.wolfram.com/DiskPointPicking.html (accessed 11 April, 2013).

Zweig, G. (1995). An effective tour construction and improvement procedure for the traveling

salesman problem. Operations Research, 43(6), 1049-1057.

142

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