three extensions to the inventory theoretic approach- a transportation selection model, a discrete event simulation of the inventory theoretic approach, postponement from an inventory theoretic perspective

Three Extensions to the Inventory Theoretic Approach:
A Transportation Selection Model
A Discrete Event Simulation of the Inventory Theoretic Approach
Postponement from an Inventory Theoretic Perspective

Dissertation



Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University


By

Doral Edward Sandlin


Graduate Program in Business Administration


The Ohio State University
2010





Dissertation Committee:

Professor Martha C. Cooper, Adviser

Professor Keely L. Croxton,

Professor Alan Johnson

Professor John P. Saldanha

Professor Walter Zinn










Copyright by
Doral E. Sandlin

2010

The views expressed in this article are those of the author and do not
necessarily reflect the official policy or position of the Air Force, the
Department of Defense, or the U.S. Government

ii





Abstract

The objective of this research is to provide three extensions to the inventory
theoretic approach which was developed to explain carrier/mode selection. One of the
strengths of the approach is that it accounts for both demand and lead time uncertainty
when calculating total logistics costs. As the world’s economies become more and more
interconnected, supply chains are growing in length and complexity resulting in increased
lead time uncertainty. To manage costs effectively, supply chain managers need to
account for lead time uncertainty. This research attempts to extend the inventory
theoretic approach in three stand-alone papers that examine issues such as product value,
variation in demand of lead time, equipment shortages, overbooking, and currency
fluctuations across multiple methodologies. The first chapter introduces the inventory
theoretic approach and gives a brief overview of the remaining chapters.
Chapter two develops an optimization model based on the inventory theoretic
approach in an effort to aide managers in selecting the best carrier/mode for their product.
Findings suggest that total logistics costs are minimized by selecting a faster mode of
transportation as the value of the product and the coefficient of variation in demand
increase. The model extends the existing state of the art in the inventory theoretic
transportation selection literature by precluding the need for conducting multiple
experiments among all available transportation options. Converting the inventory

iii
theoretic approach into an optimization problem provides a first step towards extending
the inventory theoretic approach into the facility location literature stream.
Chapter three uses the inventory theoretic approach in a discrete event simulation
in an effort to investigate the accuracy of the numerical approach in estimating total
logistics costs and rank-ordering the best to worst carriers. The inventory theoretic
literature stream is replete with numerical examples and individual case studies, but has
few examples of research that uses simulation. Empirical data for this study are gathered
from a company. The case company uses a portfolio of carriers to ship product world-

wide. Findings suggest that the numerical approach used in the inventory theoretic
approach is robust for selecting the best carriers. In addition, carrier schedules were
found to have an impact on which carrier provides the lowest total logistics cost. Finally,
delays such as equipment shortages, ordering errors, and carrier overbooking were
quantified. The results suggest that delays should be tracked by shippers, because an
excessive number of delays by a carrier can impact the rank-ordering of carriers.
Chapter four, the final chapter, extends the inventory theoretic approach to the
postponement literature stream. A review of the postponement literature found that
transportation uncertainty is largely ignored, lacks examples of an (s, Q) inventory
model, and generally ignores the cost of in-transit stock, which is considered here. The
fourth chapter also explores the concept of postponement as it relates to product life
cycles. The literature supports the notion that postponement is more applicable to
products with short product life cycles due to the risk of obsolescence. The second
concept supported by the literature is the idea that products in the introduction/growth
stage of a product life cycle should use a speculation strategy, while products in the

iv
mature/decline stages should use postponement. Empirical data for chapter four were
gathered from a Global 500 Company. Results from this essay suggest that ignoring
transportation uncertainty can underestimate the cost of using postponement and lead to
the selection of a supply chain strategy that is more expensive. Other findings suggest
that postponement strategies can be used for products with long product life cycles to
reduce the total cost of a product. This is occurs for both products in the
introduction/growth stage of the product life cycle as well as products at the
mature/decline stage. Finally, this research suggests that fluctuations in currency
exchange rates can be mitigated by use of an assemble-to-order strategy which is a form
of manufacturing postponement.

v

Dedication


Soli Deo Gloria

and

in loving memory of my Dad, Doral R. Sandlin







vi





Acknowledgments

A special thanks to my five committee members for their patience, wisdom and
encouraging support. Completing this project was definitely a team effort that could not
have been accomplished without their help. My dissertation chair, Dr. Martha Cooper,

for guiding me through the dissertation process. Not only is Dr. Cooper a gifted scholar,
she spends countless hours mentoring and guiding students in their individual endeavors.
She is truly dedicated to helping people out. I have truly enjoyed working with Dr.
Cooper throughout this process.
The impetus for this research began in early 2007 during my search for
dissertation research topics. When I first met with Dr. John Saldanha, we discovered that
we had a mutual interest in transportation-related research due to our common
backgrounds; he as a former First Officer on ocean carriers and myself as an Air Force
pilot. This commonality in backgrounds eventually led to the selection of a
transportation related research topic and also a friendship between our families. His
insight and guidance on my research has been invaluable and I thank him for the time he
has invested in my studies.
The three other members of my committee also played pivotal roles to any degree
of success that I have achieved in this program. Dr. Keely Croxton was my academic
advisor during my course work at The Ohio State University and her knowledge of piece-
wise linear optimization was a key part of the research done during the first article. Dr.
Alan Johnson was my research advisor and my simulation professor at the Air Force

vii
Institute of Technology. I appreciate his insightful feedback during my research. Finally,
Dr. Walter Zinn was instrumental in ensuring that my knowledge of inventory theory was
sound and offering excellent advice on establishing validity for my simulations. The
contributions made by all of my committee members were greatly appreciated and I
thank them for all of the time and effort that they invested in guiding my research efforts.
Two unnamed individuals from the case companies in Chapter three and Chapter
four deserve special recognition. Without their assistance, which was a significant
investment in time, I would not have been able to collect the data nor would I have had a
proper understanding of their company’s supply chains.
A special thanks to my fellow PhD students, past and present, to include Ping,
Francois, Matias, Rudi, Tim and Chris. I appreciate your friendship and advice. You

seven were a pleasure to work with and will make outstanding scholars.
However, the most important contribution to this work came from my family for
their unconditional support during my long, long hours researching, studying, and
writing. Georgi, Maddie, and Chase you three are my pride and my joy. I look forward
to seeing what life has in store for you. Thank you for your prayers, hugs, words of
encouragement, and constant entertainment. Any tough day at the office was overcome
by spending time with you three.
Finally, to the person I owe the biggest debt of gratitude in supporting all of my
academic endeavors is my beautiful wife. Shannon, thank you for patiently putting up
with my schedule and carrying more than your fair share during my doctoral studies. I
never would have made it through this program without you, nor would I have wanted to
do so. I cherish your love, support, and friendship. You are a special gift from God.

viii




Vita

1992 Bachelor of Science, Civil Engineering
The United States Air Force Academy, Colorado
Springs, Colorado

2004 Masters of Business Administration
Rutgers University, Camden, New Jersey

2006 Masters of Logistics Management
Air Force Institute of Technology, Dayton, Ohio

2009 Masters of Arts in Logistics
The Ohio State University, Columbus, Ohio


Publications

Bird, Donald M., Gregory E. Seely, Carolyn L. Miller, Doral E. Sandlin, Matthew R.
Yakely, and Anthony C. Gomillion, and Peter J. Holland (1993), ―Harnessing the
Resources of Space in the Recovery of Potable Water from Wastewater by Lyophilization
(Freeze-Drying),‖ Proceedings of the 23
rd
International Conference on Environmental
Systems, July 12-15 1993, Colorado Springs, CO.

Holland, Peter J., Carolyn L. Miller, Donald. M. Bird, Jenny E. Yung, and Doral E.
Sandlin (1992), ―Recovering Potable Water from Wastewater in Space Platforms by
Lyophilization,‖ Proceedings of the 22
nd
International Conference on Environmental
Systems, July 13-16 1992, Seattle, WA.


Fields of Study

Major Field: Business Administration

Area of Specialization: Logistics

Minor Field: Operations Management

ix





Table of Contents

page

Abstract ii
Dedication v
Acknowledgments vi
Vita viii
Table of Contents ix
List of Tables xii
List of Figures xiv
Chapter 1: Introduction 1
References 6
Chapter 2: Optimizing Transportation Using a Total Logistics Cost Approach 8
Introduction 8
Literature Review 10
Research Setting 16
Model Framework 18
The Model 18
Experimental levels 23
Results 25
Sensitivity Analyses: Selecting a Sub-Optimal Transportation Option 26
Sensitivity Analyses: Freight Rates 30

x
Managerial Implications 32
Limitations and Future Research 34
Conclusions 35
References 37
Chapter 3: A Discrete Event Simulation of the Inventory Theoretic Approach 41
Introduction 41
Literature review 44
Demand During Lead Time 44
Inventory Theoretic Simulations 48
Scheduling Effects 50
Quantifying the Cost of Delays 51
Research Design 53
Research Setting 54
Calculating Estimated Total Logistics Costs Using the Analytical Approach 56
Calculating Estimated Total Logistics Costs Using a Discrete Event Simulation 59
Model Parameters 63
Assumptions 68
Findings 69
Scenario #1: Low Value/High Volume 69
Scenario #1: High Value/Low Volume 73
Scenario #2: Scheduling Impact 74
Scenario #3: Order Delays 75
Limitations 77

xi
Implications and Conclusions 78
References 79
Chapter 4: The Impact of Product Life Cycle and Transportation Uncertainty upon

Speculation and Postponement 83
Introduction 83
Literature Review 86
Cost Models 87
Postponement and Product Life Cycle 93
Research Design 100
Supply Chain Strategies 102
Total Cost Model 107
Research Setting 110
Findings 119
Total Cost Results 119
Lead Time Uncertainty 122
Sensitivity Analysis 125
Limitations 131
Implications and Conclusions 131
References 133
Bibliography 139
Appendix A 150




xii





List of Tables

Table 2.1: A Survey of the Inventory Theoretic Approach 13

Table 2.2: Experimental Levels for Product Attributes 23

Table 2.3: Optimal Speed & Reliability for Different Product Profiles and Coefficient
Variations of Demand 26

Table 2.4: The Relative Change in Optimal Logistics Costs for a One Day Difference in
Speed 27

Table 2.5: The Relative Change in Optimal Logistics Costs for a Half Day Difference in
Reliability 28

Table 2.6: The Relative Change in Optimal Logistics Costs for a One-Day Difference in
Speed and a Half-Day Difference in Reliability 29

Table 2.7: The Affect of Changing Freight Rates on Optimal Speed & Reliability 30

Table 3.1: Transportation Selection Mode and Carrier Research Methodologies 50

Table 3.2: Transit-time Country A & Country B Destination is Country C (Days) 64

Table 3.3: Simulation Parameters 65

Table 3.4: Scenario #1 Experimental Levels – Door-to-Port Transit Times 66

Table 3.5: Rail and Ocean Carrier Weekly Cutoff Dates 66

Table 3.6: Scenario #2 Experimental Levels–Scheduling plus Transit Times 67

Table 3.7: Carrier Delays 68

Table 3.8: Estimated Total Logistics Costs of Product Family #1 Using Analytical
Approach by Value, Volume, and Customer Service Level 69

Table 3.9: Estimated Total Logistics Costs of Product Family #1 Using Discrete Event
Simulation Approach by Value, Volume, and Customer Service Level 71

Table 3.10: Percent Difference between the Estimated Total Logistics Costs Using the
Numerical Approach and the Simulation Approach 72

xiii
Table 3.11: Actual Level of Customer Service Provided Product Family #1 72

Table 3.12: Estimated Total Logistics Costs of Product Family #2 Using Numerical
Analysis by Value, Volume, and Customer Service Level 73

Table 3.13: Estimated Total Logistics Costs of Product Family #2 Using Simulation by
Value, Volume, and Customer Service Level 74

Table 3.14: Estimated Total Logistics Costs of Product Family #1 w/ Carrier Schedules
Using Simulation by Value, Volume, and Customer Service Level 75

Table 3.15: Estimated Total Logistics Costs of Product Family #1 w/ Carrier Schedules
& Delays Using Discrete Event Simulation by Value, Volume, and Customer
Service Level 76

Table 3.16: Summary Chart of Carrier Selection 77

Table 4.1: Survey of Postponement Literature 93

Table 4.2: Product Part Commonality Matrix 112

Table 4.3: Traditional System Category ―A‖ Component Lead Times 113

Table 4.4: New System Category ―A‖ Component Lead Times 115

Table 4.5: Customer, Customs, Inventory and Distribution Parameters 117

Table 4.6: Experimental Levels 118

Table 4.7: Traditional System Total Cost per Unit 120

Table 4.8: New System Total Cost per Unit 121

Table 4.9: The Cost of Uncertainty 123

Table A.1: 95% Confidence Intervals for Table 3.9 151

Table A.2: 95% Confidence Intervals for Table 3.14 153

Table A.3: 95% Confidence Intervals for Table 3.15 154

xiv





List of Figures

Figure 2.1: Speed and Reliability Profiles of International Door-to-Door Transportation
Options 16

Figure 2.2: Mean Lead Time Function 20

Figure 2.3: Piecewise Linear Notation 21

Figure 2.4: Door-to-Door Freight Rates as a Function of Mean and Standard Deviation
of Lead Time 24

Figure 3.1: Determining Safety Stock 47

Figure 3.2: Research Steps 54

Figure 3.3: The Case Company’s Distribution Channel Studied 56

Figure 3.4: Steps in a Simulation Study 60

Figure 4.1: The Postponement and Speculation Matrix 95

Figure 4.2: Product Life Cycle During Limited Time Offers 97

Figure 4.3: Research Steps 101

Figure 4.4: Full Speculation – Make-to-stock 103

Figure 4.5: Manufacturing Postponement – Assemble-to-Order 104

Figure 4.6: Logistics Postponement – Ship-to-Order 105

Figure 4.7: Full Postponement – Make-to-Order 106

Figure 4.8: Total Landed cost vs Changes in Transportation Costs 126

Figure 4.9: Total Landed Cost vs Changes in Holding Cost 127

Figure 4.10: Total Landed Cost vs Change in MachineCo’s Host Nation Currency
Relative to the Dollar 129

xv
Figure 4.11: Total Landed Cost vs Change in MachineCo’s Level of Customer Service
130

1




Chapter 1: Introduction
The goal of this research is to provide three extensions to the inventory theoretic
literature stream, which will be divided accordingly into three separate papers. Before
discussing the extensions to the inventory theoretic approach, a brief introduction of the
proposed research needs to begin with addressing the following questions: what is the
inventory theoretic approach and why use it? The inventory theoretic approach considers
the trade-off between inventory and transportation in an effort to minimize total logistics
cost, while maintaining the necessary level of customer service under conditions of
demand and lead time uncertainty (Tyworth 1991). This approach defines total logistics
cost as the sum of ordering costs, inventory costs (cycle stock, safety stock, and pipeline
stock), and transportation costs (Tyworth 1991). Accounting for lead time and demand

uncertainty, one of the strengths of the inventory theoretic approach, makes mode and
carrier selection models more difficult (Tyworth 1991); however, the approach is
decidedly more realistic than non-stochastic models (Speh and Wagenheim 1978; Bagchi,
Hayya, and Chu 1986). Baumol and Vinod (1970) are credited with writing the seminal
paper that introduced the inventory theoretic approach. These two scholars merged two
abstract constructs of transportation and product with inventory theory. The first
transportation construct is defined by freight rate, speed, and reliability, while the product
construct is defined by shipping costs, inventory holding costs, ordering costs, and
shortage costs (Tyworth 1991). By examining carriers and products as a bundle of

2
attributes, Baumol and Vinod’s model enables logistics managers to compare modes and
carriers to minimize logistics costs. This approach is well suited to handle the dynamic
nature of today’s business environment (Beamon 1998; Manuj and Mentzer 2008) and
remains a topic of key interest to both scholars (Kutanoglu and Lohiya 2008; Meixell and
Norbis 2008) and practitioners (Page 2008). The usefulness of the inventory theoretic
approach has been detailed in several literature reviews including Cunningham (1982),
McGinnis (1989), Min and Zhou (2002), De Jong, Gunn, and Walker (2004), and Meixell
and Norbis (2008). De Jong, Gunn, and Walker (2004) conclude that the inventory
theoretic approach is one of the most promising mode evaluation models. This research
seeks to extend the inventory theoretic approach in a series of three essays that
contributes to extant theory while also benefitting the practitioner.
Chapter two, the first paper, contributes to the logistics literature by converting
the inventory theoretic equation into a mixed-integer linear program (MILP) that
minimizes the total logistics cost by selecting the optimum mix of speed and reliability
for a given level of customer service. The vast majority of inventory theoretic models
utilize either a matrix table (enumeration of the total costs of every transportation option)
or a set of exchange curves created by taking the derivatives of an inventory theoretic
closed form expression. While the matrix approach is useful for small problems, it is
more challenging for more complex supply chains. Large companies often use a

portfolio of carriers and suppliers that ship via a combination of modes. The enumeration
of every feasible transportation option combined with minimum shipping volume
requirements, carrier quantity discounts, supplier quantity discounts, capacitated shippers
and suppliers, and SKU proliferation to name just a few constraints, makes enumeration

3
of available options problematic (the matrix approach). Conversely, optimization models
can handle a wide variety of variables, easily accommodate additional constraints, and
guarantee the optimal answer given valid assumptions and accurate data. In contrast to
the matrix approach, which explicitly enumerates through the options, a MILP uses
implicit enumeration. Powers (1989) points out that some of the advantages of using
optimization models include the handling of all kinds of costs (fixed, variable, and
nonlinear). The inventory theoretic model developed in chapter two as a MILP will
provide logistics managers or 3PLs with a tool to select the best carriers and modes for
their products, as well as a tool for conducting what-if analyses.
Chapter three, which is the second paper, provides an estimate of the total
logistics cost using a simulation as opposed to numerical analysis which dominates the
inventory theoretic literature stream. In providing this estimate, the simulation tests the
robustness of the normality assumption of demand during lead time when used in the
inventory theoretic approach. A simulation is particularly useful for examining existing
supply chains with a fixed number of routing options. Discrete event simulations have
several advantages over numerical analysis methods. Simulations can easily test different
demand during lead time distributions, capture multiple sources of supply chain
uncertainty, track the passage of time (carrier schedules), and can more realistically
model supply chain complexity. The end result provides a different perspective for
estimating total logistics cost, which is a useful benefit to both scholars and practitioners.
Simulation has been recognized by both scholars and practitioners as one of the most
frequently-used methodologies of classical Operations Research (Hollocks 2006). A
review of the literature finds that simulation research is not only under-represented in the

4
inventory theoretic research stream, but is also notably under-represented in the mode
selection literature stream (Meixell and Norbis 2008). Furthermore, Meixell and Norbis
(2008) state that transportation and carrier selection model research in international
settings are ―lightly represented.‖ In chapter three, we use real data collected from a
company that ships products internationally by multiple modes and carriers. In this
essay, we demonstrate the robustness of the normality assumption in the carrier selection
process. We also show the effects of scheduling and ordering delays by quantifying their
effects in terms of total logistics costs.
Chapter four, which is the third and final paper, is an application of the inventory
theoretic approach to the supply chain strategy of postponement. Alderson’s (1950) and
Bucklin’s (1965) original conceptualization of postponement use a total cost model
approach to determine whether or not it is appropriate to use postponement. Since the
writing of these two seminal articles, numerous total cost models have been developed to
capture the benefits of postponement. A review of these total cost models finds that there
is only one total cost model that accounts for transportation uncertainty. The net result of
neglecting lead time uncertainty is a less accurate estimate of total costs for both
postponement and speculation. Van Hoek (2001) and Boone, Craighead, and Hanna
(2007) both call for further study on the topic of postponement that involves
transportation issues. In this essay we quantify the cost of ignoring transportation
uncertainty for four different supply chain strategies. Chapter four also addresses the
impact that product life cycle has upon postponement. There are two general concepts
that authors often either discuss or assume to be true regarding the influence that product
life cycle has upon the decision to use a postponement strategy. These two concepts will

5
be explored further in chapter four. Van Hoek (2001), Boone, Craighead, and Hanna
(2007), and García-Dastugue and Lambert (2007) all call for research regarding the
influence that product life cycles has upon effectiveness of postponement. Specifically,
these three articles find that there has been little empirical research that explores Pagh

and Cooper’s (1998) postulation on the influence that product life cycle has upon
postponement.

6
References
Alderson, Wroe (1950), ―Marketing Efficiency and the Principle of Postponement,‖ Cost
and Profit Outlook, Vol. 3, pp. 1-3.

Bagchi, Uttarayn, Jack C. Hayya, and J. Keith Ord (1984), ―Concepts, Theory, and
Techniques: Modeling Demand During Lead Time,‖ Decision Sciences, Vol. 16, No. 7,
pp. 413-421.

Baumol, W. J. and H. D. Vinod (1970), ―An Inventory Theoretic Model of Freight
Transport Demand,‖ Management Science, Vol. 16, No. 7, pp. 413-421.
Beamon, Benita M. (1998), ―Supply Chain Design and Analysis: Models and Methods,‖
International Journal of Production Economics, Vol. 55, No. 3, pp. 281-294.
Boone, Christopher A., Christopher W. Craighead and Joe B. Hanna (2007),
"Postponement: an Evolving Supply Chain Concept," International Journal of Physical
Distribution & Logistics Management, Vol. 37, No. 8, pp. 594-611.
Bucklin, Louis P. (1965), ―Postponement, Speculation, and Structure of the Distribution
Channels,‖ Journal of Marketing Research, Vol. 2, No. 1, pp. 26-31.

Cunningham, Wayne H. J. (1982), ―Freight Modal Choice and Competition in
Transportation: a Critique and Categorization of Analysis Techniques,‖ Transportation
Journal, Vol. 21, No. 4, pp. 66-75.

De Jong, Gerard, Hugh Gunn, and Warren Walker (2004), ―National and International
Freight Transport Models: An Overview and Ideas for Future Development,‖ Transport
Reviews, Vol. 24, No.1, pp. 103-124.
García-Dastugue, Sebastián J. and Douglas M. Lambert (2007), "Interorganizational

Time-Based Postponement in the Supply Chain," Journal of Business Logistics, Vol. 28,
No. 1, pp. 57-81.

Hollocks, Brian W. (2006), ―Forty Years of Discrete-Event Simulation—a Personal
Reflection,‖ Vol. 57, No. 12, pp. 1383-1399.

Kutanoglu, Erhan and Divi Lohiya (2008), ―Integrated Inventory and Transportation
Mode Selection: A Service Parts Logistics System,‖ Transportation Research: Part E,
Vol. 44, No. 5, pp. 665-683.

Manuj, Ila and John T. Mentzer (2008), ―Global Supply Chain Risk Management
Strategies,‖ International Journal of Physical Distribution & Logistics Management, Vol.
38, No. 3, pp. 192-223.


7
McGinnis, Michael A. (1989), ―A Comparative Evaluation of Freight Choice Models,‖
Transportation Journal, Vol. 29, No. 2, pp.36-46.

Meixell, Mary J. and Mario Norbis (2008), ―A Review of the Transportation Mode
Choice and Carrier Selection Literature,‖ The International Journal of Logistics
Management, Vol. 19, No. 2, pp.183-211.

Min, Hokey and Gengui Zhou (2002), ―Supply Chain Modeling: Past, Present, and
Future,‖ Computers and Industrial Engineering, Vol. 43, pp. 231-249.

Page, Paul (2008), ―Jet Fumes,‖ Traffic World, July 7, pp 4.

Pagh, Janus D. and Martha C. Cooper (1998), ―Supply Chain Postponement and
Speculation Strategies: How to Choose the Right Strategy,‖ Journal of Business

Logistics, Vol. 19, No. 2, pp.13-33.

Powers, Richard F. (1989), ―Optimization Models for Logistics Decisions,‖ Journal of
Business Logistics, Vol. 10, No. 1, pp.106-121.

Speh, Thomas W. and George D. Wagenheim (1978), ―Demand and Lead-time
Uncertainty: The Impacts on Physical Distribution Performance and Management,‖
Journal of Business Logistics, Vol. 1, No. 1, pp. 95-113.

Tyworth, John E. (1991), ―The Inventory Theoretic Approach in Transportation Selection
Models: A Critical Review,‖ The Logistics and Transportation Review, Vol. 27, No. 4,
pp. 299-318.
van Hoek, Remko I. (2001), "The Rediscovery of Postponement a Literature Review and
Directions for Research," Journal of Operations Management, Vol. 19, No. 2, pp. 161-
184.

8



Chapter 2: Optimizing Transportation Using a Total Logistics Cost Approach


Introduction
As the world’s economies become more interconnected and supply chains expand
globally, interest in transportation mode selection for freight is gaining the attention of
scholars and practitioners (Kutanoglu and Lohiya 2008; Page 2008). Increasingly,
logistics managers are required to manage products in longer supply chains that pass
through congested port terminals. These terminals are the site of complex intermodal
hand-offs that are hampered by security concerns. All these factors affect the speed and

reliability of door-to-door transportation (Norek and Isbell 2005). Fluctuating fuel prices
further complicate transportation selection as logistics managers look to cut
transportation costs as a way of controlling their logistics costs. The unfavorable
economic conditions compressing already thin margins increase the pressure managers
feel to reduce transportation costs. If transportation costs are reduced at the expense of
selecting a slower, less reliable transportation option, this would increase inventory costs,
assuming constant customer service goals. This is due to the speed and reliability of
transportation influencing the level of inventory in the supply chain. Transportation and
inventory costs constitute the largest proportion of the total logistics cost (Ballou 2004,
pg. 14). Therefore, the challenge is to find the right balance of inventory and
transportation costs that achieve customer service goals at the minimum total logistics

9
cost. Transportation carrier and mode selection is critical to achieving this balance. This
paper presents a model that balances transportation and relevant inventory costs to select
the optimum speed and reliability of a door-to-door transportation move. Speed and
reliability are modeled by the mean and standard deviation of door-to-door transit time
for all available transportation options, and each speed and reliability combination has a
corresponding freight rate. This model is grounded in the work of Baumol and Vinod
(1970) and builds on Tyworth’s (1991, 1992) exposition of inventory theoretic
transportation selection models. These models trade off inventory and transportation
costs at a fixed customer service level, to select the optimum transportation for a single
product on a single lane.
This research extends the classic inventory theoretic transportation selection
model to a global supply chain setting. To do this, a new approach for modeling the non-
linear safety stock function as a piecewise linear approximation was developed. This
approximation can then be used in a mixed integer linear program (MILP) to select the
optimum mix of speed and reliability that minimizes total logistics costs at a fixed level
of customer service. The piecewise-linear approximation used in a MILP is well
equipped to handle the non-linear requirements of the inventory theoretic approach.

Transportation managers can use the model’s solution to inform their selection of the best
door-to-door transportation strategy. This extension would be especially useful to a 3PL
(third party logistics provider) who has access to freight pricing for a large number of
carriers that offer a wide range of speed, and reliability options. A 3PL could use this
MILP to tailor the intermodal transportation mode choice to the needs of their customers.
This strategy dictates selecting the right combination of carriers and intermodal hand-off