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

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 availa

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

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

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

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

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

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

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

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 22nd 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

points for the door-to-door move whose mean and standard deviation of transit time would match the output of the model In addition, the MILP modeling approach provides the ability to quickly conduct sensitivity analysis by testing a variety of scenarios

Managers can then evaluate the sensitivity of the optimal transportation solution to

changes in freight rates and the total logistics cost penalty for using a sub-optimal mode

Although the MILP presented in this chapter is demonstrated at the strategic level,

it can be applied at the operational and tactical levels as well For example, it can be used daily or weekly for operational decisions such as selecting the best carrier available to the firm for allocating individual shipments At the tactical level, the model can be applied

to facilitate the carrier bid selection or contract renewal process and for allocating

shipments among a pool of carriers with varying speed and reliability service attributes This research would be of particular benefit to big companies with large transportation operations

A review of the relevant literature is presented in the next section This is

followed by a discussion of the research setting and model Finally, the research results, managerial implications, and conclusions along with limitations and directions for future research are presented

Literature Review

Shippers typically strive to select a transportation option that will provide the best overall speed, reliability, and cost (Evers, Harper, and Needham 1996; Dobie 2005, Shawdon 2006) The five most important factors to be considered when selecting a

carrier are cost (freight rate), speed, transit-time reliability, product characteristics, and service levels (Cullinane and Toy 2000) There is a wide variety of models that attempt

to consider some or all of the variables when selecting the best transportation option

Cunningham (1982), McGinnis (1989), Min and Zhou (2002), and De Jong, Gunn, and Walker (2004) chronicle the development of transportation mode selection models Although each breaks down the freight transportation models in a different manner, the inventory theoretic approach is commonly identified as a viable approach by all four papers These taxonomies seek to categorize, critique, and offer future directions for research De Jong, Gunn, and Walker (2004) state that the inventory theoretic

approach (which they refer to as the ―disaggregate freight transport model‖) represents one of the most promising freight mode evaluation models This is a result of the

method’s accuracy and flexibility in capturing a wide range of cost variables in addition

to the uncertainty of demand and speed

The inventory theoretic approach is well established in the literature as a

methodology for handling the trade-off between inventory and transportation to minimize total logistics cost while maintaining the necessary level of customer service under conditions of uncertainty for both demand and lead time (Tyworth 1991) Baumol and Vinod (1970) are credited with writing the seminal paper that introduced the inventory theoretic approach These two scholars merged an abstract transportation construct with inventory theory The abstract transportation construct views the carrier as a bundle of attributes shipping cost per unit, mean transit time, and carrying cost per unit time while the product is being transported The second abstract construct considers the

variation in demand By examining carriers and products as a bundle of attributes, Baumol and Vinod’s (1970) model enables researchers to determine the impact of a change in the value of an attribute, which gives their model a great deal of flexibility They found that the optimal choice of transportation requires a trade-off among the cost

of transportation and the cost of inventory Transportation speed reduces pipeline and safety stock while transportation reliability reduces safety stock

Table 2.1 provides an overview of selected research conducted to date on the inventory theoretic approach The literature review focuses on the analytical methods used by various authors who employed the inventory theoretic approach in selecting the optimal transportation option A review of the literature (see Table 2.1) finds that most authors use either indifference curves or individual experiments when determining the optimal transportation carrier or mode Baumol and Vinod (1970) used derivatives to develop indifference curves Their work was extended by Das (1974) who used a normal distribution to approximate demand during lead time and simplified the determination of the order quantity by assuming that the order quantity and the re-order point are

independent By making this assumption, the economic order quantity (EOQ) formula can be used to find the order quantity Das used individual experiments to determine the optimal transportation mode or carrier option Buffa and Reynolds (1977) extended the model to include stockout costs and freight rate discounts for full truck loads and also used indifference curves to determine optimality Constable and Whybark (1978), in one

of the few articles that does not use indifference curves or individual experiments,

developed a heuristic procedure that determines the reorder point, order quantity, and

transport option They also included backorder cost and tested their model on data gathered from a firm (Constable and Whybark 1978)

Authors Year Analytical approach to

Buffa & Reynolds

Constable & Whybark

Tyworth & Zeng

Swan & Tyworth

Vernimmen & Witlox

Zeng & Rossetti

Enumeration of individual experiments

Individual experiments used to develop matrices

Individual experiments Individual experiments Individual experiments Individual experiment

Individual experiments used to develop sensitivity matrix

Individual experiments Individual experiments Individual experiments used to develop cost matrix

Individual experiments Individual experiments

- Use of normal distribution to approximate lead time and used EOQ to simplify procedure

- Extend model to include stock out costs

- Developed heuristic to determine reorder point, order quantity, and transport option

Use of cost functions to more accurately model freight rates

Development of matrix decision tool

Considers point of origin inventory and variable ordering costs

Develops computer modal Shipsmart to evaluate up to

4 transit options with up to 4 segments in each option Critical review of Inventory Theoretic literature and future research recommendations

Develops standard procedures using inventory theoretic approach with uncertain lead time and uncertain demand Allows for non-normal distributions of lead time and demand during lead time Also, relaxes the assumption

of linear transportation costs and treats transit time as a segment of lead time

Impact of transit time on profitability in the railroad industry

Case study/literature review Develops 5 step framework for determining ETLC

Analysis of transportation policy effectiveness using TLC

Impact of service level specification on safety stock

†Estimated Total Logistics Cost

Table 2.1: A Survey of the Inventory Theoretic Approach

Sheffi, Eskandari and Koutsopoulos (1988) developed a computer model called

―Shipsmart‖ that determined the optimal order quantity for up to four different modes of transportation and allowed for four different segments per transportation leg Tyworth and Zeng (1998) conducted individual experiments that are used in the development of a sensitivity matrix that showed how total logistics costs react when transit time parameters

are changed They extended the literature stream by allowing for non-normal

distributions of lead time and demand during lead time and by relaxing the assumption of linear transportation costs Swan and Tyworth (2001) applied the inventory theoretic approach to railroad shipping to show that improving the transit time and increasing reliability is central to the profitability of both the shipper and customer Once again, numerical analysis is accomplished by individual experiments Finally, Zeng and

Rossetti (2003) developed a five-step process to analyze total logistics costs and present a case study of a US aircraft parts manufacturer and its Chinese supplier Through

individual experiments, they determine the cost for five different transportation modes

The inventory theoretic transportation selection model is very effective in trading off transportation cost against inventory cost to find the optimal transportation option that minimizes the long-run total logistics cost (Tyworth, 1991; Tyworth and Zeng 1998) The wide choice of modes and carriers within each mode for international shipments offers a large number of speed and reliability options to shippers The number of

experiments quickly multiplies as the number of product profiles and origins-destinations expand This task is further complicated by the current dynamic business environment,

as can be seen most recently in the uncertainty surrounding the future of fuel costs What

is missing in this robust stream of literature is a response to Tyworth’s (1991)

recommendation for a model that can handle both the non-linear and enumerative

requirements of the inventory theoretic approach This gap in the inventory theoretic literature stream needs to be addressed if the usefulness of the inventory theoretic

approach is to be expanded to other literature streams such as the facility location

problem

This paper attempts to contribute to the inventory theoretic literature by

modifying the classic inventory theoretic transportation selection model to consider speed and reliability as decision variables in a MILP whose objective is to minimize the total logistics cost This optimization model uses a piecewise linear approximation to model the non-linear safety stock function The review of the literature finds that none of the articles as of yet have used the mixed integer linear programming approach to find the optimal transportation option Powers (1989) points out the advantages of using

optimization models include the handling of all kinds of costs (fixed, variable, and

nonlinear) In addition, they efficiently handle a wide variety of variables, constraints are easily added or changed, and they guarantee the optimal answer given valid assumptions and accurate data Hence, additional constraints and other considerations can be added to the MILP formulation This research demonstrates the model’s use in a door-to-door, inter-continental supply chain setting based on secondary data found in the literature as described in the research setting

Research Setting

The shipments examined in this paper encompass a door-to-door move in an international supply chain from the factory of origin in one continent to a destination regional distribution center in another continent To model realistic conditions of door-to-door speed and reliability, all possible combinations of door-to-door transit times and reliabilities that would be encountered in a typical supply chain between Asia and the U.S were considered The representative door-to-door transit times and reliabilities for the typical transportation options are listed in Figure 2.1 These transportation options range from 2 to 50 days and standard deviations range from 0.5 to 5.5 days These ranges were selected after consulting the literature, schedules of carriers offering international transportation service options and shippers who use these services from Asia to the U.S

Each transportation option represents a combination of transportation modes and carriers Freight rates for the transportation options are generally inversely related to the mean and standard deviation of door-to-door transit times Integrated air and ocean guaranteed moves are integrated door-to-door with a single entity managing the

intermodal hand-offs UPS and Federal Express are examples of integrated air freight transportation providers These ―integrators‖ own all assets, often including air cargo terminals, involved in the door-to-door movement of freight by air (Forster and Regan 2001) Hence, they typically have greater control over the entire process and their next-day priority air freight services exhibit the highest speed and greatest reliability Kuehne

& Nagel, APL Logistics, and the Hub Group are examples of third-party logistics

providers offering services for the integrated ocean transportation option (O’Reilly 2008) Ocean guaranteed is a time-definite service offered collaboratively by an ocean carrier and a third-party logistics company to reduce the time and uncertainty during intermodal hand-offs APL Logistics and ConWay Freight have advertised an ocean guarantee less-than-container-load (LCL) service from Hong Kong to Chicago offering eighteen days transit with a standard deviation of half a day (Clancy and Hoppin 2007; Tirschwell 2007) APL Logistics also offers a Day-Definite full-container-load (FCL) service from China to the Mid-West (www.apl.com)

Other door-to-door moves by air freight, passenger belly air freight, and ocean are typically performed by a disconnected group of carriers from multiple modes and

managed by the shipper Dedicated air freight services are slower and less reliable than the services offered by the integrators because of the additional intermodal hand-offs,

2001; Clancy and Hoppin 2007) Direct ocean freight is shipped on a vessel directly from the port of departure in the export country to the port of entry in the import country Indirect ocean services are different from direct ocean as the vessel makes intermediate stops between the port of departure and port of entry Ocean carrier transit time

parameters presented by Saldanha, Russell, and Tyworth (2006) and Leachman (2008) and parameters for port dwell times and inland modes provided by Leachman (2008) were used to set the range of means (22-50 days) and standard deviations (0.5-5.5 days)

of total door-to-door transit times for direct and indirect ocean The myriad of carriers along with their corresponding modes of transportation and implications for inventory make this a complex decision for the logistics manager

The model in this paper assumes a continuous review inventory system

Replenishment triggers are assumed to be set at a 98% probability of no stockout (PNS) per order cycle PNS is one of the most common measures of single item inventory availability (Zinn, Mentzer, and Croxton, 2002) As international shipping is a year-round operation, another assumption is that product can be shipped 365 days per year

Model Framework

The Model

The goal is to minimize the estimated total logistics cost which includes ordering cost, inventory cost (cycle, safety stock, and in-transit), and freight cost The standard deviation of door-to-door transit time demand or, in more general terms, lead time

demand X needs to be calculated in order to determine safety stock levels The equation used is (Fetter and Dalleck 1961, p 61):

Where L and L are the parameters of the normally distributed random variable for

lead time L and D and D are the parameters of the normally distributed random

variable for product demand D Eppen and Martin (1988) point out that the normal

assumption can be problematic; however, the debate on the use of the assumption

continues (Tyworth and O’Neill 1997; Chopra, Reinhardt, and Dada 2004; Bradley and Robinson 2005) The assumption can still be found in just about every operations,

logistics, and inventory text book (Tyworth and O’Neill 1997) Equation (2.1) assumes

that D and L are independent This allows X to be expressed as a function ofL for a given value of L Each potential value of L is represented by a mean lead time

function, examples of which are shown in Figure 2.2 By fixingD,D and by

varyingX ,L, we use equation (2.1) to plotL

Figure 2.2: Mean Lead Time Function

Each of these non-linear functions (L from Figure 2.2) can be approximated with one that is piecewise linear and then the piecewise linear function can be fully

characterized by its segments (Croxton, Gendron and Magnanti 2003) Figure 2.3

illustrates the notation For each segment s of the function, a slope, m s , an intercept, b s,

and upper and lower bounds S s-1 and S s can be defined For each door-to-door transit time from 2 to 50 days, the mean lead time function is approximated using a piecewise linear function with ten segments Each segment of L is 0.5 days in length and covers a range from 0.5 days to 5.5 days, which represents a wide spectrum of reliability in transit Using this notation, the piecewise linear approximation can be expressed

Figure 2.3: Piecewise Linear Notation

The rest of the notation and formulation is as follows:

h 1 = holding cost percentage for cycle and safety stock (% / $ /yr)

h 2 = holding cost percentage for in-transit stock (% / $ /yr)

k = safety factor

F is = freight cost associated with segment s of mean lead time function i ($/lb)

L i = lead time associated with mean lead time function i (days)

Formulation for the total logistics costs (TLC):

The objective function (2.2) minimizes the total logistics cost, which as

mentioned includes terms for the ordering cost, the cycle stock cost, the safety stock cost, the in-transit inventory cost, and the freight cost As is apparent from equation (2.2),

formulation As cycle stock is not considered in the objective function, the order quantity

(Q) can be determined independent of the transportation option selected For example,

the robust EOQ model could be used to determine Q

The piecewise linear function is used to approximate the amount of safety stock The advantage of using the piecewise linear approximation is that it turns a non-linear function into a linear function, which then allows the minimum value of the function to

be found using linear programming Safety stock is represented in the objective function using the common k x (Brown 1967) Constraint (2.3) assures that only one segment

of one mean lead time function is selected Constraint (2.4) assures that Lis falls

between the upper and lower bounds for the corresponding segment, for the segment that

is selected, and Lis=0 for all other segments

Experimental levels

To demonstrate the usefulness of the MILP, experiments were conducted across multiple values of three important product attributes: product weight, coefficient of variation of demand, and product value This illustrates how the model selects the

optimal speed and reliability option across multiple product profiles This enables an analysis of the results from which conclusions can be drawn on how different product profiles affect transportation selection Frontline Systems’ solver engine add-in for Excel, Premium Solver Platform Version 8.0, was used for solving the MILP The

experimental levels used are provided in Table 2.2

Annual Demand, R (lbs/yr)

Table 2.2: Experimental Levels for Product Attributes

To check the validity of each experimental solution, a macro was used to calculate the total logistics cost using the model output optimal speed and reliability values The difference between the optimal total logistics cost using the piecewise linear

approximation to calculate safety cost and the manual calculation using the non-linear function was less than 0.05% This suggests that the error introduced by the piecewise linear approximation is negligible

Real freight rate data are proprietary information and hence not publicly available Freight rates were modeled for all combinations of the forty-nine levels of Land the ten

L

 segments by extrapolating the freight rate data provided in Clancy and Hoppin (2006)

The exponential function (3.0e-0.1*L)*e-0.1*L was found to be the closest approximation

of the freight rates for the modes in Clancy and Hoppin (2006) Freight rate data from a shipper were used to further validate the use of this model A different freight rate was used to approximate each of the ten L segments For the three representative segments shown in Figure 2.4 (s = 1, 5, and 10), a single freight rate was used for all values of Lis

within each segment

Figure 2.4: Door-to-Door Freight Rates as a Function of Mean and Standard

Deviation of Lead Time

The use of exponential functions to represent freight rates is well-established in the

literature (Buffa 1987; Swenseth and Godfrey 1996; Thomas and Tyworth 2007)

Freight Rate ($/lb)