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Essays on Supply Chain Coordination

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Title:
Essays on Supply Chain Coordination
Creator:
Wang, Ruoxuan
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (11 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Business Administration
Information Systems and Operations Management
Committee Chair:
CARRILLO,JANICE ELLEN
Committee Co-Chair:
VAKHARIA,ASOO J
Committee Members:
PAUL,ANAND ABRAHAM
GEUNES,JOSEPH PATRICK
Graduation Date:
8/9/2014

Subjects

Subjects / Keywords:
Compliance costs ( jstor )
Contract theory ( jstor )
Customers ( jstor )
Fees ( jstor )
Guideline adherence ( jstor )
Market prices ( jstor )
Options contracts ( jstor )
Prices ( jstor )
Retail stores ( jstor )
Supply chain management ( jstor )
Information Systems and Operations Management -- Dissertations, Academic -- UF
capacity -- contract -- coordination -- disruptions -- dual-channel -- option -- resource -- service-planning
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Business Administration thesis, Ph.D.

Notes

Abstract:
Supply chain coordination is an ultimate goal for firms in the supply chain. This dissertation investigates the use of dual-channel strategies and contracts to coordinate the supply chain. In the first essay, we formulate a dual channel model for a retailer who has access to both online and traditional market outlets to analyze the impact of customer environmental sensitivity on its supply. We analyze stocking decisions for each channel incorporating price dependent demand, customer utility for online channels, and channel related costs. We compare and contrast the findings for disparate industries, such electronics, books and groceries. In the second essay, we model different types of contracts between a manufacturer and a supplier in the event of disruption utilizing options contracts and game theory methodologies. We develop theoretical results which show the specific mechanisms of different types of contracts which can effectively coordinate the supply chain. In particular, we create a policy for which the buyer asks for a specified level of capacity in the event of a disruption. The supplier has flexibility in determining the optimal capacity but must pay a penalty for a potential shortage. Finally, numerical results show that the benefits of these types of contracts include (a) increased profit for the buyer, (b) increased flexibility for the supplier, and (c) increased risk mitigation for the buyer in the event of a power disruption. Due to the high frequency of supply chain disruptions from power outages, demand is increasing for the temporary power equipment market. We investigate the capacity allocation plan for the supplier providing power rental service to multiple buyers for both planned services (i.e. a large planned event) and unplanned emergency services (i.e. a large disruptive event) in the third essay. We analyze how the resource sharing strategy in capacity planning impacts the profit of supplier and the decision for the buyers in choosing a contracted service or emergency response. Furthermore, the lack of a contract offer from the supplier serves as an indirect signal concerning the availability for capacity of supplier. Finally, we analyze the capacity allocation decision and service planning in terms of profitability. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: CARRILLO,JANICE ELLEN.
Local:
Co-adviser: VAKHARIA,ASOO J.
Statement of Responsibility:
by Ruoxuan Wang.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
LD1780 2014 ( lcc )

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1 ESSAYS ON SUPPLY CHAIN COORDINATION By RUOXUAN WANG A DISSERTATION PRESENTED TO GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 201 4

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2 201 4 Ruoxuan Wang

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3 To my parents: Pu Wang and Ru Fang for a lifetime of love and support

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4 ACKNOWLEDGMENTS I would like to express my sincerest gratitude to my advisor Dr. Janice Carrillo for guiding me through the exploration process and encouraging me all along. Without her support this dissertation would not have been possible. My thanks also go to my committee members Dr. Asoo Vakharia, Dr. Anand Paul and Dr. Joseph Geunes for freely sharing their time and providing insightful comments and other academic support. I also thank Dr. Ira Horowitz, Dr. Tharanga Rajapakshe, Dr Amy Pan and other faculty members for their kindness help in my career pursuit and providing the resources for me to achieve my goal. I would like to extend my thanks to all my colleagues in the Ph.D. program for t heir support and friendship through my years in Gainesville, esp ecially Ms. Patricia Brawner, Ms. Tiffany Hatch Ms. Jennifer DeHart and Ms. Shawn Lee Thanks also go to my friends who have been patient, understand ing and encouraging. Finally I want to th ank my mom Ru Fang, my dad Pu Wang, and my husband Tong Wang, who ar e always there for me, for their endless love and support

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 12 Environmental Issues for Online Retailing ................................ .............................. 12 Supply Chain Coordination ................................ ................................ ..................... 13 The S tructure of the D issertation ................................ ................................ ............ 14 2 ENVIRONMENTAL IMPLICATIONS FOR ONLINE RETAILING ............................ 15 Motivation ................................ ................................ ................................ ............... 15 Literature Review ................................ ................................ ................................ .... 17 E Commerce and the Environment ................................ ................................ .. 17 Industry Related Literature ................................ ................................ ............... 18 E Commerce/Dual Channel Literature ................................ ............................. 20 Operations/Demand Related Literature ................................ ............................ 22 Contribution to the Literature ................................ ................................ ............ 23 Modeling Framework ................................ ................................ .............................. 24 Preliminaries ................................ ................................ ................................ ..... 24 Deterministic Demand ................................ ................................ ...................... 27 Stochastic Demand ................................ ................................ .......................... 32 Single Channel Setting ................................ ................................ .............. 32 Both C hannels ................................ ................................ ........................... 34 Sensitivity Analysis for the Stochastic Model ................................ ............. 37 Numerical Analysis ................................ ................................ ................................ 38 Policy Issues ................................ ................................ ................................ ........... 44 Concluding Remarks ................................ ................................ ............................... 47 3 OUTSOURC ING FOR POWER DISRUPTION ................................ ....................... 52 Motivation ................................ ................................ ................................ ............... 52 Literature Review ................................ ................................ ................................ .... 55 Disruptions ................................ ................................ ................................ ....... 55 Contracts ................................ ................................ ................................ .......... 56 Model and Types of Contract ................................ ................................ .................. 59

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6 Background ................................ ................................ ................................ ...... 59 Contract I Buyer Specified Contract ( ) ................................ ....................... 64 Contract I: walk in service ................................ ................................ .......... 66 Contract I: forced compliance ................................ ................................ .... 67 Traditional policy under forced compliance: ............................ 69 Integrated disruption policy under forced compliance: ............. 70 Contract I: v oluntary compliance ................................ ................................ 71 Traditional policy under voluntary compliance: ....................... 71 Integrated disruption policy under voluntary compliance ......... 74 Comparison of alternate buyer controlled contracts ................................ ... 76 Contract II Supplier Specified Contract ( ) ................................ .................. 77 Contract II: walk in service ................................ ................................ ......... 78 Contract II: forced compliance ................................ ................................ ... 79 Traditional policy under forced compliance: ........................... 79 Integrated disruption policy under forced compliance ............ 79 Contract II: Voluntary Compliance ................................ ............................. 80 Traditional policy under voluntary compliance: ...................... 80 Integrated disruption policy under voluntary compliance: ....... 81 Comparison of alternate supplier controlled contracts ............................... 82 Summary of Analytic Results ................................ ................................ ............ 83 Numerical Experiment and Sensitive Analysis ................................ ........................ 84 Impact of changes in ( ) on capacity and profit ................................ ......... 86 Impact of changes in ( ) on feasible region for contract type II ................. 88 Concluding Remarks ................................ ................................ ............................... 89 4 RESOURCE SHARING IN POWER RENTAL SERVICE ................................ ....... 93 Literature Review ................................ ................................ ................................ .... 95 Capacity Allocation and Newsvendor Model ................................ .................... 95 Options Contracts ................................ ................................ ............................. 9 6 Contribution to the Literature ................................ ................................ ............ 98 Models in Centralized Supply Chain ................................ ................................ ....... 98 Dedicated Capacity ................................ ................................ ........................ 100 Resource sharing ................................ ................................ ........................... 101 Models in Decentralized Supply Chain ................................ ................................ 105 Case ................................ ................................ ................................ ............ 108 Case ................................ ................................ ................................ ........... 112 Case ................................ ................................ ................................ ............ 114 Numerical Experiments ................................ ................................ ......................... 117 Conclu ding Remarks ................................ ................................ ............................. 122 APPENDIX A PROOFS OF THEOREMS AND ANALYTICAL RESULTS IN CHAPTER 2 ......... 125 Proof of the Optimal Pricing for the Dual Channel (DC) Strategy ......................... 125 Proof of Theorem 1 in Chapter 2 ................................ ................................ .......... 126

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7 Proof of Corollary 1 and 2 in Chapter 2 ................................ ................................ 128 B PROOFS OF THEOREMS AND COROLLARIES IN CHAPTER 3 ....................... 130 Proof of Corollary 1 in Chapter 3 ................................ ................................ .......... 130 Proof of Theorem 1 in Chapter 3 ................................ ................................ .......... 130 Proof of Theorem 4 in Chapter 3 ................................ ................................ .......... 132 Proof of Theorem 6 in Chapter 3 ................................ ................................ .......... 133 Proof of Theorem 7 in Chapter 3 ................................ ................................ .......... 134 C PROOFS OF THEOREMS IN CHAPTER 4 ................................ .......................... 135 Proof of Theorem 1 in Chapter 4 ................................ ................................ .......... 135 LIST OF REFERENCES ................................ ................................ ............................. 139 BIOGRAPH ICAL SKETCH ................................ ................................ .......................... 144

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8 LIST OF TABLES Table page 2 1 Notation used in Chapter 2 ................................ ................................ ................. 25 2 2 Prices, quantities, and firm profits for each strategy ................................ ........... 28 2 3 Numerical results for sensitivity to salvage value and demand uncertainty ........ 40 2 4 Numerical results for sensitivity to environmental cost differential effects .......... 42 3 1 Notation of parameters in Chapter 3 ................................ ................................ ... 61 3 2 Comparison of buyer controlled contracts ................................ .......................... 75 3 3 Comparison of profit levels for buyer controlled contracts ................................ .. 75 3 4 Comparison of supplier controlled contracts ................................ ....................... 83 3 5 Comparison of profit levels for supplier controlled contracts .............................. 83 3 6 Numerical results from contract type I under base case ................................ ..... 85 3 7 Numerical results from contract type II under base case ................................ .... 85 4 1 The notation for the decentraliz ed supply chain ................................ ............... 107

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9 LIST OF FIGURES Figure page 2 1 Comparison of firm profits as a function of consumer propensity for environmental costs ................................ ................................ .................. 39 2 2 Comparison of firm profits as a function of consumer propensity for environmental costs ................................ ................................ ............. 43 2 3 Comparison of firm profits as a function of consumer propensity for environmental costs ................................ ................................ ............. 44 3 1 The timeline for buyer controlled contracts ................................ ......................... 64 3 2 The timeline for supplier controlled contracts ................................ ..................... 77 3 3 Capacities change along the probability of disruption ................................ ...... 87 3 4 under different situations ................................ ................................ ................................ ............ 87 3 5 The feasible region of each policy given the value of ............................. 88 4 1 How the servicizing model aligns incentives for different firms ........................... 94 4 2 The ranges of cases and ................................ ................................ ........ 106 4 3 The profit comparison in centralized supply chain ................................ ............ 118 4 4 The profit comparison in case ................................ ................................ ....... 119 4 5 The profit comparison in case ................................ ................................ ....... 120 4 6 The profit comparison in case ................................ ................................ ........ 121 4 7 .................. 122

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10 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ESSAYS ON SUPPLY CHAIN COORDINATION By Ruoxuan Wang August 2014 Chair: Janice E Carrillo Major: Business Administration Supply chain coordination is an ultimate goal for firms in the supply chain. This dissertation investigate s the use of dual ch annel strategies and contracts to coordinate the supply chain. In the first essay, we formulate a dual channel model for a retailer who has access to both online and traditional market out lets to analyze the impact of customer environmental sensitivity on its supply. We analyze stocking decisions for each channel incorporating price dependent demand, customer utility for online channels, and channel related costs. We compare and contrast th e findings for disparate industries, such electronics, books and groceries. In the second essay, we model different types of contracts between a manufacturer and a supplier in the event of disruption utilizing options contracts and game theory methodologie s. We develop theoretical results which show the specific mechanisms of different types of contracts which can effectively coordinate the supply chain. In particular, we create a policy for which the buyer asks for a specified level of capacity in the even t of a disruption. The supplier has flexibility in determining the optimal capacity but must pay a penalty for a potential shortage. Finally, numerical results show that the benefits of these types of contracts include (a) increased profit for the buyer, ( b) increased flexibility for the

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11 supplier, and (c) increased risk mitigation for the buyer in the event of a power disruption. Due to the high frequency of supply chain disruptions from power outages, demand is increasing for the temporary power equipment market. We investigate the capacity allocation plan for the supplier providing power rental service to multiple buyers for both planned services (i.e. a large planned event) and unplanned emergency services (i.e. a large disruptive event) in the third essa y. We analyze how the resource decision in choosing a contracted service or emergency response. Furthermore, the lack of a contract offer from the supplier serves as an ind irect signal concerning the Finally, we analyze the capacity allocation decision and service planning in terms of profitability.

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12 CHAPTER 1 INTRODUCTION Environmental Issues for Online Retailing Recent press has highlighted the environmental benefits associated with online shopping, such as emissions savings from individual drivers, economies of scale in package delivery, and decreased inventories. Weber et al. (2008) performed a case study for buy.com comparing the environm ental impact of e commerce vs. traditional retailer for the purchase and delivery of a flash drive. A key finding of this study is that the total energy usage for a traditional retailer is higher than that typically associated with e commerce delivery. Mor eover, consumer awareness concerning the environmental impact associated with particular product choices is growing. Internet companies are undertaking initiatives to highlight the environmental choices to consumers when they purchase goods via the interne t. Fichter (2002) emphasizes that there are three main categories of environmental effects caused by e commerce. The first order effects are those associated with the information and communication technologies (such as PCs, mobile phones, servers, routers, etc.) Typically, the environmental impact of these technologies includes energy usage, hazardous substances, and electronic waste. The second order effects are those associated with the production and delivery of goods via manufacturing and logistics proc esses. The third order effects identified by Fichter (2002) are those associated with changes in consumption patterns which indirectly influence the growth rate of cons umption outweighs the efficiency improvements. Another problem that Fichter highlights is a lack of formalized metrics for companies to utilize in

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13 measuring and managing their environmental impact. Fichter links these metrics to consumer behavior by noting that in addition to traditional competitive measures such become a decision criterion, at least with regard to certain IT products and ecommerce fore, environmental factors associated with e commerce may influence consumer choice in the future. Supply Chain Coordination actions are not always in the best interest of a ll the members in the supply chain, since the supply chain members are primarily concerned with optimizing their own profit, and such self interest focus often lead s to a poor performance. However contracting a set of transfer payments can coordinate each supply chain membe rs (Cachon 2003). The n ewsvendor model is used to exam the important research questions under the framework of a single supplier and a single buyer with stochastic demand. Under such setting, t no reorder opportunity. The c ontract between the supplier and the buyer determines how much the buyer chooses to order. The first important research question is to determine the typ es of contracts that coordinate the supply chain. A contract is designed to coordinate the supply chain if the set of optimal actions is a Nash equilibrium for all firms. In the newsvendor model the in some case s, also the contract s ha ve any flexibility by adjusting the parameters to allow for any division of

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14 allocate the profit arbitrarily, then there always exist s a contract the Pareto dominates any non coordinated contract. In that case, at least one firm is strictly better off with the coordinated contract. The third important research question is finding a contract worth adopting. In reality, the contract designer may prefer to offer a simple contract even if that contract does not coordinate desirable. The contract efficien cy is the ratio of realized supply chain profit with contract Over the last decade the supply chain contracting research has bee n established. The key findings are as follows. (1) I ncentive conflicts arise in a wide range of operational cases which lead to coordination failure. Those conflicts can be managed through contract s (2) There are multiple kinds of contracts that achieve the supply chain coordination and arbitrarily divide profit in certain situation. The s election of proper contract depends on criteria or objectives, like relative bargaining power or the ease of implementation. (3) Pareto improvements can be achieved by managing incentive conflicts, which is often stated as a The S tructure of the D issertation The rest of the dissertation is arranged as follows. Chapter 2 emphasizes the environmental implications for online retailing. The coordination of dual channel for a single firm is analyzed Chapter 3 proposes the coord inating outsourcing contract for power disruption, and provides the o ptimal contract terms on the relative bargaining power levels Finally, C hapter 4 presents the resource sharing strategies for po wer rental industry, discusses the capacity allocation pla ns and the optimal service planning

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15 CHAPTER 2 ENVIRONMENTAL IMPLICATIONS FOR ONLINE RETAILING Motivation The environmental benefits associated with online shopping, such as emissions savings from individual drivers, economies of scale in package deliver y, and decreased inventories, are well documented. Weber et al. (2008) performed a case study for buy.com comparing the environmental impact of e commerce vs. traditional retailer for the purchase and delivery of a flash drive. A key finding of this study is that the total energy usage for a traditional retailer is higher than that typically associated with e commerce delivery. The main factors driving this result are the distance that the customer has to drive to buy the item via a traditional retailer (on average they drive 14 miles for a round trip), and the consumer fuel economy (assumed to be 22 miles/gallon from the US EPA). The authors also note the limitations of these results. For instance, if express air shipping is chosen as the delivery method by the customer, then the carbon emissions for both modes (i.e. e commerce and traditional retailer) are roughly comparable. Moreover, consumer awareness concerning the environmental impact associated with particular product choices is growing. A recent article appearing in the Wall Street Journal summarizes the results of a poll which finds that 17% of U.S. consumers and 23% of European consumers are willing to pay more for environmentally friendly significantly over the past year. Consequently, major retailers such as Wal Mart are undertaking initiatives to include environmental information on labels along with pricing information. To start the process of gathering more environmental information fr om suppliers, Wal Mart will

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16 require its suppliers to answer questions concerning energy costs and emissions, material efficiency, natural resources, and ethical workforce concerns (Bustillo, 2009). percentage of advertise ments in major magazines making green claims has also grown. However, many vendors have overstated the environmental properties of their goods (a practice commonly referred to as nst these claims Internet companies are undertaking initiatives to highlight the environmental choices to consumers when they purchase goods via the internet. For example, transactio between different shipping methods, and to specifically market this service to consumers who are willing to pay more for delivery methods which have a lower environmental impact. cost more, and entail a longer wait for a package, but presumably Amazon sees a use of hybrid vehicles, minimization of packaging materials, and efficient truck utilization techniques. Many retail firms are grappling with the issue of how to best manage dual distribution channels for their goods as demand via internet channel grows. To illustrate, the U.K. r etailer Tesco established a home delivery service in 2000 and advertised their other retailers may fear that there is a conflict between these two important channels,

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17 Tesco embraced the complementarities between the new and old channels while concurrently continuing to expand its traditional bricks and mortar stores. In contrast, Webvan tried to establish a single online channel to deliver groceries by investing in large ware houses and inventory management systems (Spurgeon, 2001). Unfortunately, they went bankrupt due to a lack of customers willing to pay a higher premium for their service. Therefore, primary concerns of dual channel distribution include supply chain costs, c ustomer service, and pricing. In this essay we introduce a single firm model focusing on supply chain and marketing choices for a dual channel strategy. We explicitly address the environmental implications of each channel to determine appropriate pricing and stocking decisions. Through our analysis, we address the following key research questions: 1. If a firm has both traditional and online sales channels, how should they manage the split between these? 2. Are there circumstances under which a retailer should f ocus only on online and/or traditional channels? 3. How will consumer behavior evolve in response to these environmental channel concerns? 4. Which factors associated with e commerce have the most significant impact on the environment? 5. How will policy issues Literature Review E Commerce and the Environment Several conceptual papers have been written which identify and categorize environmental effects associated with e commerce, including technology drive rs, paperless transactions, transportation, production, and changes in consumption. Sui

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18 and Rejeski (2002) discuss the benefits of ecommerce to the environment. They utilize complexity theory to describe some of the more complicated potential problems asso ciated with e nature of technological innovations, we want to caution the scientific community and particular, they presage that the accessibility of goods via the internet may someday lead to excessive consumer consumption. Furthermore, an increasing number of consumers expecting overnight deliveries will contribute to excessive emissions from air frei ght delivery. Industry Related Literature Several notable case based and empirical studies have been published which analyze the environmental effects of e commerce for specific industries, including electronics, groceries and books. As previously mentione d, Weber et al. (2008) utilize monte carlo simulation techniques to analyze key factors involved in the delivery of a flash drive for buy.com. A key finding of this study is that the total energy usage for retailer is higher than that typically associated with e commerce delivery. Similar results are also shown in Sivaraman et al. (2007) who apply life cycle analysis (LCA) techniques to analyze the delivery of a DVD via traditional (i.e. Blockbuster) and e commerce channels (i.e. Netflix). The grocery indus try has had mixed results with e commerce in the past. Fernie et al. (2000) offer an excellent overview of past trends in the grocery supply chain in the UK, including supplier control, centralization and just in time. They also surveyed senior executives currently working in grocery supply chain companies and conclude that some of the top issues that these executives are concerned about for the future

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19 included both e commerce and environmental factors. In particular, the most important factors identified w ere traffic congestion, transport taxation levels, 24 hour trading, and home shopping/home delivery initiatives. These authors also note that grocery supply chain members are preparing for an increase in home ordering and home delivery by investing in auto mated sortation systems to enable the picking and packing of smaller case quantities. Siikavirta et al. (2002) employ simulation methodologies to analyze greenhouse gas emissions associated with home delivery grocery services. They identify scenarios under which the home delivery service can cut green house gases by up to 87%. Cullinane et al. (2008) performed a study of online grocery shopping behavior where they surveyed students in a town in Scotland. They found that factors influencing online food shoppi ng behavior include nationality, car ownership and residential location relative to the supermarkets. One unique factor that these authors identify is the large potential for environmental benefits if the students pooled their online grocery purchases. The starting point to understanding these interactions. Several authors have analyzed the impact of online vs. tradition al sales channels for the book industry. Matthews et al. (2001) perform a study of the online book industry to directly analyze the environmental impact of online vs. traditional book retailers. They find that, when there are no returns, both modes have a comparable environmental impact. However, when the remainder rates are significant (they are typically 35% for best selling books that are not sold at the end of the selling season from the retailer), the environmental impact of the traditional retailer is much worse, as they must stock

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20 higher inventories. Matthews et al. (2002) has a similar conclusion, but analyzes U.S. online book sales in addition to those in the Japan. In this study, they find that e commerce delivery of books in the United States is c heaper than those for a bookstore, but that environmental impact is roughly comparable for both modes. In the Japanese case study, they found that traditional book retail mode can actually be more energy efficient in highly populated areas due to additiona l packaging and fuel for delivering individual packages. E Commerce/Dual Channel Literature In his seminal paper, Bakos (2001) offers an overview of the impact of e commerce on the retailing landscape and summarizes several key issues associated with e com merce. Factors relevant in our context include increased price competition and the changing role of different supply chain members (i.e. intermediaries) for goods ordered online. Brynjolffson and Smith (2000) explore the impact of internet commerce on pric e by analyzing data from book and CD industries for both traditional and e commerce channels. These authors find that prices on the internet are significantly lower than those in a traditional retailer even when accounting for taxes, shipping, shopping and transportation costs. Balasubramanian (1998) investigates the impact of a direct channel (such as catalog or internet) on conventional retailers by analyzing a game theoretic model based on a circular spatial market. He concludes that the presence of a di rect competitor changes the nature of conventional competition such located traditional retailers. Specifically, traditional retailers compete directly against the direct channel instead of their neighboring retailers. Bryjolffson et al. (2009) further characterize the nature of competition between traditional bricks and mortar stores and

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21 an internet retailer. Their empirical study shows that the competition between these t wo channels is strongest when the goods are mainstream products that are typically associated with lower search costs. A body of literature within the operations management area addresses supply chain issues typically associated with dual channel models of distribution. For an overview of these models, see Cattani et al. (2006). In particular, many of these analytic channel (i.e. online sales) and sales via a traditional e stablished retailer (i.e. bricks and mortar). The key decision variables in these models classically include both the wholesale/transfer price between the manufacturer and the retailer and the price offered to customers in both of the channels, (Chiang et al. 2003, Tsay and Agrawal 2004 and Cattani et al. 2006.) These game theoretic models directly address the problem of double marginalization and characterize the circumstances under which the traditional retailer may actually benefit from the second online channel. In addition, Tsay and Agrawal (2004) explicitly consider investments in sales activities, while Chen et al. (2008a) consider investments in activities which improve product availability (for the traditional retailer) or leadtime (for the online c hannel). Cattani et al. (2006) and Chen et retailer vs. an online retailer via channel cost differentials. Boyaci (2005) addresses stocking decisions for both channels and explicitly models substitution effects for the situation where there is a stockout in one of the channels. Netessine and Rudi (2006) also address stocking decisions for a retailer with the possibility of drop shipping directly from the wholesaler to th e customer. Finally, Tsay and Agrawal (2000) consider

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22 competition between two retailers via price and service mechanisms when selling a single product procured from a single manufacturer. Operations/Demand Related Literature Several papers utilize price de pendent demand models to analyze various stocking and pricing decisions for a duopoly where there are two substitute products in the marketplace. Singh and Vives (1984) derive linear demand functions with substitution from quadratic utility functions. Spec ifically, they characterize demand for of competition and concludes that Bertrand compe tition where each firm sets its prices which in turn determine the quantity demanded is more efficient than Cournot competition. Lus and Muriel (2009) also consider two different forms of price linear demand functions and conclude that this form of the fun (2000) utilize a price quantity linear demand structure when developing optimal wholesaler and retailer pricing policies for two competing r etailers selling the same product. Under a different context, Chen et al. (2008b) also use price quantity linear product which combines products currently selling in d ifferent markets into a single product. Stochastic demand and pricing models typically utilize a newsvendor approach to determine optimal stocking policies. For a complete review of these models, see Qin et al. (2011). Two papers are of particular relevanc e for this model. Petruzzi and Dada (1999) analyze pricing decisions for different variations of the newsvendor model for a

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23 single product. One case that they consider utilizes a price linear additive function of demand which is similar in nature to those shown in the deterministic demand literature. These authors derive mathematical conditions under which an optimal solution for both price and quantity can be determined for the situation when there is demand uncertainty. Specifically, they show that when t he probability distribution function which characterizes demand uncertainty has certain properties, then the optimal solution within a pre specified range is unique. Van Ryzin and Mahajan (1999) also utilize a newsvendor framework to analyze a store assort ment problem. These authors combine a multinomial logit (MNL) model which determines demand for each product variant with the newsvendor model to determine the optimal stocking quantities. Similar to our model, these authors utilize a multiple product/chan nel newsvendor framework. Contribution to the Literature While several authors have addressed the environmental impact of e commerce via case based and empirical methodologies, we contribute to this literature by developing a math model which offers manage rial guidance concerning this important area of inquiry. Our model links the empirical literature on environmental issues in e commerce with classic marketing and operations models. Specifically, we formulate a dual channel model of a retailer which has ac cess to both online and traditional market outlets to analyze the impact of environmental factors on its supply. We also analyze stocking decisions for each channel incorporating price linear demand, customer preference for online shopping, and channel rel ated costs. We develop analytic solutions for both deterministic and stochastic versions of the dual channel models, and utilize numerical examples to illustrate the implications of industry specific factors on these decisions. Note that this model is part icularly relevant to an individual retail firm

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24 deciding whether or not to complement its traditional sales with an online sales channel, in industries, such as electronics, books and groceries. Modeling Framework Preliminaries In this section, we outline the key parameters and variables utilized in our model. A summary of the model notation is included in Table 2 1. Our stylized modeling product. The three choices for the firm we investigate are to offer its product through: (a) = 1; or (b) the online channel or OC indexed as = 2; and (c) both the RC and OC or a DC (dual c hannel) and indexed as = 3. The RC represents the established configuration where the firm stocks its product and customers are required to travel to the location to purchase the product. These types of structures are well established in practice and th e cost per unit to process a product through this channel is assumed to be channel or as an additional channel for serving the market demand and in this setting the firm inc urs a per unit cost for processing the product through this channel. In order to investigate the impact of environmental aspects, we assume that the co st differential between the RC and the OC is where the parameter represents the envi ronmental cost /savings of the OC as compared to the RC, and represents cost differences between channels due to other factors. We allow to be either positive or negative, and note that the differential in these costs is partially driven by environme ntal issues associated with channel costs.

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25 Table 2 1 Notation used in C hapter 2 Sy m bol Description Index for channel structures for RC; for OC; and for DC Unit cost for channel ( ) Environmental unit cost savings/premium for OC channel Unit cost savings/premium for OC channel Demand for channel ( ) Unit price for channel ( ) Unit Price for channels ( ) for channel structure DC Quantity offered through channel ( ) Quantity offered through channels ( ) for channel structure DC Maximum market size for channel ( ) Total market sizze Propensity of customers for OC Price elasticity of demand for channel ( ) Symmetric price substitution parameter Random variable associated with uncertain demand Probability density function for Cumulative density function for Minimum and maximum values for Salvage value for an unsold unit Firm profit associated with channel structure ( )

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26 To illustrate, implies that the OC provides environmental economies as compared to the RC while the reverse is true when For example, when considering the OC for non perishable products (e.g., books), it is highly likely that there would be a reduction of total inventories due to pooling effects. This would be reflected in environmental savings associated with using less pap er since fewer books would need to be printed for the OC (i.e. ). On the other hand, for perishable (or short shelf life) grocery items, an OC would require the use of a ssociated with the OC and hence, would result in a negative value of On the demand side, we assume that for the market demand ( ) is linear in price ( ). We let and represent the maximum potential market for the RC and OC respec tively. Similarly, represents the price elasticity of demand for channel For the case where the firm has the possibility of operating in both channels simultaneously, we also incorporate a symmetric price based substitution effects parameter N ote that Tsay and Agrawal (2000) choose similar demand forms for a situation where two independent retailers are selling the same product procured from a single manufacturer. When analyzing the channel choice decision under demand uncertainty, we also use a random term is a continuous random variable with probability density function and distribution function defined in the interval We also define the following additional notation. Let represent the quantity stocked by channel under demand certainty (uncertainty) when the firm chooses either single channel strategy RC or OC ; represent the quantity

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27 stocked by channel under demand certainty (uncertainty) when the firm chooses the DC strategy and hence, offers the product through both channels simultaneously; represent the market price for channel under demand certainty (uncertainty) when the firm chooses either sing le channel strategy RC or OC ; represent the market price for channel under demand certainty (uncertainty) when the firm chooses the Dual Channel (SC) strategy; and represent the firm profits for channel under dem and certainty (uncertainty) for The primary focus of our analysis is on analyzing the channel selection decision for the firm in the presence of the environmental related savings/costs on the supply side and consumer preferences on the demand s ide. We start by focusing on the case where the firm demand is deterministic and follow this up with analyzing the stochastic demand scenario. Deterministic Demand Under this setting, the optimal stocking quantity for the firm for each channel setting is a nalogous to the market demand satisfied. Hence, the demand functions for each strategy choice are: For channel strategy RC: For channel strategy OC: ; and For channel strategy DC: and Under each strategy choice, the firm solves the following profit maximization problems: For strategy choice RC

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28 ( 2 1) For strategy choice OC ( 2 2 ) For strategy choice DC ( 2 3) For each setting, it is easy to show that the profit functions are strictly concave in the decision variables 1 Based on this, the optimal prices, quantities and firm profits under each strategy choice are shown below in Table 2 2 (with all proofs shown in Appendix A ). Table 2 2 Prices, quantities, and firm profits for each s trategy Strategy Prices Quantity Profits RC OC DC In T able 2 2 and To fu rther delineate the impact of demand on our optimal solution, we utilize a change of variables. Specifically, we replace the variables and which reflect the 1 In case of strategy DC, the profit fu nction is strictly and jointly concave in the decision variables provided and

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29 maximum market size for the RC and the OC with two alternate variables. We let represent the maximum total market size such that We also integrate a propensity of customers for the OC by a parameter which represents the proportion of the total number of customer who would prefer the online channel ( For the variab le substitution, we let represent the maximum demand for channel OC and represent the maximum demand for channel RC. Hence, a higher value of is associated with a high total potential market for the OC and vice versa. In examining Ta ble 2 2 strategies is parameter dependent. However, as stated in Theorem 1 below, these can be structurally characterized based on the parameter. First, we define the following additional notation. For the lowest value breakpoint: For the highest value breakpoint: ; and For the difference in the breakpoints: Theorem 1 : Assuming that all three strategies are feasible, the optimal strategy choice for the firm is as follows: 1. If the firm should choose strategy RC (i.e., only offer the product through the retail bricks and mortar channel); 2. If the firm should choose strategy DC (i.e., offer th e product through dual channels); and 3. If the online channel). Proof : See Appendix A

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30 From Theorem 1, it is clear that (which reflects the channel choice propensity) is a key factors s optimal channel strategy choice. Recall that can also be interpreted as a proxy for customer utility for goods sold through a particular channel, and is influenced by factors such as convenience, distance to the traditional store, the type of product (i.e. mainstream or niche), and customer service. A second key result concerns the impact of the environmental costs/savings. As would be expected, as the value of the increases the region of dominance of the RC st rategy grows (i.e. increases). Similarly, the region of dominance for the OC strategy shrinks (i.e. increases), and the region of dominance for the differential for the two channels shrinks (i.e. decreases). In particular, if the unit cost for the traditional channel increases, or if the unit cost for the online likely that the bricks and mortar channel strategy will be optimal. Suppose the cost of stocking online is lower due to risk pooling, then the firm shou ld use an online or dual channel strategy. To illustrate, consider online book stores such as Amazon which sell solely through an online channel and reap the benefits of lower costs due to inventory centralization, (see Matthews et al. 2001). In contrast, in the grocery industry, the environmental costs for the online channel may come at a premium due to the investment in trucks refrigerator capabilities. optimal strategy. The i individual channels is significant in driving a single channel strategy. When the price elasticity of demand ( ) for channel decreases, then (1) a single channel solution for channel is m ore likely to be optimal, (2) the optimal price decreases for the single

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31 channel, and (3) the optimal quantity increases for the single channel. Conversely, if there is an increase in the total market for the product as represented by the variable ( ) or if there is an increase in the demand substitution parameter ( that a dual channel solution will be optimal. Indeed, the grocery/retail firm Tesco has introduced an online channel in addition to their traditional channel to reap t he benefits from this unique channel A comparison of optimal channel prices in the DC setting is also of interest. Given the optimal market prices shown in Table 1 for the setting where the firm oper ates both channels, we note that the optimal market prices between channels will not be equal provided that: ( 2 4) Where and Note that the left had side is the difference function of the consumer propensity ) while the right hand side reflects the cost by the relative differential of channel demand elasticity parameters (i.e., , and ). Based on this relationship, the following results hold: The retail channel price will always be greater than the online channel price (i.e., ), if either : (a) and ; or (b) and hold; The retail channel price will always be lower than the online channel price (i.e., ), if and This result essentially indicates that only under very restrictive conditions will the online channel price be higher than that of the retail channel. This finding is in line with

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32 that of Brynjolffson and Smith (2000) who find that online channel prices are significantly lower than that of the retail likely that the environmental savings result in lower costs for the online channel as compared to the retail channel and this compensat es for lower levels of consumer propensity for the online channel. It is only when the consumer propensity for the online channel is high and the cost differential between channels is not significant, that the optimal price for the online channel is higher than that of the retail channel. Stochastic Demand Similar to the previous section on deterministic demand, we start this section by analysis of the case where the firm chooses to operate both channels simultaneously. Single Channel Setting For each single channel setting, the process of obtaining an optimal solution to general p rocedure which applies to each channel setting (recall that the index = 1 is = 2 is for the online channel). Considering either channel individually, it is assumed that the market demand is ch aracterized by the following linear demand function: ( 2 5) Where is a random variable with probability density function and distribution function and defined in the interval such that and is the mean for In this setting, we allow for the possibility that the firm could have leftover inventory (if ) and we assume that this is sold at a markdown price per

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33 unit 2 Hence, the firm makes the market pricing and stock ing quantity decision using a newsvendor framework. Based on this, to maximize expected end of season firm profits, the firm solves the following problem: ( 2 6) where (similar transformations were proposed by Ernst(1970) and Thowsen (1975)). The first order conditions for this problem are: ( 2 7) ( 2 8) and the second order conditions are: ( 2 9) ( 2 1 0 ) ( 2 11) For strict concavity of Equation ( 2 6) to hold, it is necessary to assume that Other technical conditions for the 2 assume that the markdown price is not channel specific.

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34 uniqueness of the solution to the problem stated in Equation ( 2 6) have been specified by Petruzzi and Dada (1999). Regardless of whether either of these conditions are met, it is relatively straight forward to note that for a given Equation ( 2 10) indicates that Equation ( 2 6) is strictly concave in Hence, for a given value of the opti mal obtained from the first order condition in Equation ( 2 8) is: ( 2 12) Based on this, the following search algorithm can be used to identify the optimal market price, the optimal stocking quantity, and the corresponding optimal profit for the firm. 1. Set ; ; ; and 2. If goto 5. 3. Compute using Equation ( 2 12). Set 4. Compute using Equation ( 2 6). If goto 2, else set ; ; and goto 2. 5. The optimal market price is the optimal stocking quantit y is and associated optimal profit is maximization problem in a multiple channel setting. Both Channels In this setting, the ma rket demand functions for each channel are assumed to be characterized by the following linear demand functions: ( 2 13) ( 2 14)

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35 where as defined earlier and are random variables defined in the interval and with means and respectively. In order to maximize end of season profits, the firm solves the following problem: Maximize : ( 2 15) where and The first order conditions for this problem are: ( 2 16) ( 2 17) ( 2 18) ( 2 19) and the second order conditions are: for ( 2 20) for ( 2 21)

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36 ( 2 22) ( 2 23) ( 2 24) ( 2 25) ( 2 26) As in the single channel setting, we can see that for specific value of and Equation ( 2 19) is strictly and jointly concave in and 3 Thus, for given values of and the optimal prices can be determined by solving the following simultaneous equations (obtained by setting the first order condition in Equation ( 2 18) and ( 2 19) equal to 0): ( 2 27) ( 2 28) The solution to this set of equations is: ( 2 29) ( 2 30) where and Based on this, the following search algorithm can be used to identify the optimal market prices, t he optimal stocking quantities, and the corresponding optimal profit for the firm. 3 This is the result of the fact that Equation (21) and (26) indicate that and since it was assumed that for

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37 1. Set ; ; ; ; and 2. If goto 6. 3. If goto 2. 4. Compute using Equation ( 2 29) and using Equation (2 30). Set and 5. Compute using Equation ( 2 15). If goto 3, else set ; ; ; ; and goto 3. 6. The optimal market prices are: and ; the optimal stocking quantities are: and and associated optimal profit is Sensitivity Analysis for the Stochastic Model While we do not have explicit expressions for the optimal values for the stochastic models, the separable nature of the price functions as shown Equation ( 2 29) and Equation ( 2 30) facilitates sensitivity analysis on key parameters. Corollary 1 : Assuming that a dual channel (DC) strategy is optimal, then the optimal price for RC ( ) will increase in response to the following: 1. An increase in the maximum market size ; 2. A decrease in the propensity of customers for the OC channel ; 3. A decrease in the price sensitivity to demand for the RC channel ; 4. A decrease in the price sensitivity to demand for the OC channel ; 5. An incre ase in the symmetric price based substitution effects parameter ; 6. An increase in the unit cost for the RC channel ; Proof : See Appendix A Corollary 2 : Assuming that a dual channel (DC) strategy is optimal, then the optimal price for OC ( ) wil l increase in response to the following: 1. An increase in the maximum market size ; 2. An increase in the propensity of customers for the OC channel ; 3. A decrease in the price sensitivity to demand for the RC channel ;

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38 4. A decrease in the price sensitivity to demand for the OC channel ; 5. An increase in the symmetric price based substitution effects parameter ; 6. An increase in the environmental cost premium for the OC channel ; 7. An increase in the unit cost premium for the OC channel ; Proof : See Appen dix A Results from Corollaries 1 and 2 show that the optimal prices for the dual channel in the stochastic environment behave similarly to those derived for the deterministic environment with regards to changes in demand related parameters. One key result here is that when a dual strategy is optimal (DC), the cost premium for the online channel ( ) does not influence the price for the traditional channel and vice versa. Although, the cost differentials are likely to impact the region of dual channel optim ality for which these prices are valid, as shown in Theorem 1. Numerical Analysis In this section, we outline the results of numerical examples intended to complement the analysis for the stochastic demand case shown in the previous section. Because we can not derive explicit solutions for the optimal values of the quantity and price variables for the stochastic dual channel model, we turn to numerical examples to illustrate the impact of key factors on these variables and the overall firm profit. The numeri cal examples were written in the JAVA programming language, and utilize the search algorithms outlined in the previous section. The specific parameter values used in the numerical base case example are as follows: (a) the unit cost for the RC ( ) is set to $ 20. In order to focus on the impact of environmental costs/savings for the OC, we set the value of Hence, the unit cost for the online channel is ; and (b) the maximum market size ( ) is set equal

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39 to 2500. Both channels are as sumed to have an equal price elasticity (i.e., ) and this value is set equal to 30. The symmetric price substitution parameter ( ) which applies only to channel structure DC is set at 10. The minimum and maximum values of are equal across both channel structures and is assumed to be uniformly distributed. Finally, we vary the value of between [0, 1] by increments of 0.01 and calculate the optimal prices, quantities and profits for both single channel and the dual channel solutions and t his is used to identify the range of values over which single and/or dual channel solutions are optimal. Figure 2 1. Comparison of firm profits as a function of consumer p ropensity for environmental costs Consider a base case example where = $10, = 10, and e = 0. For values of the firm optimally sells only via the traditional channel and makes a fairly low profit. For values of between 0.24 and 0.75, the firm optimally sells via both channels and reaps the benefits of higher profit. For values of the firm optimally sells via the online channel only and earns a fairly low profit. A graph of the profit for this case as a function of is shown in Figure 2 1. Note that the profit values are symmetric around

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40 the value =0.5, because the base case demand and cost parameters are similar for both channels. When is extremely high or low and a single channel solution is optimal, then the dual channel solution is infeasible and the total profit in these tails is fairly low. When a dual channel solution is feasible and optimal (i.e. in the center of the graph), the profit is much higher due to the synergy between the two channels in terms of the demand substitution parameter. Therefore, the firm should plan for single channel distr ibution if environmental and/or consumer related factors drive the demand to be extremely high for one of the single channels. In addition to the base case scenario, we also investigated the impact of the salvage value ( ) and demand variability ( ) on the optimal channel choice. Table 3 summarizes the results of these examples for salvage values ( ) of 10 and 20, and also for demand variability (i.e. and ) values of 10, 375, 675 and 1250. These levels of demand variability correspond to 0. 4% 15%, 25% and 50% of the total demand ( ) for the product amongst both channels. We also set the demand variability for both channels to be equivalent for each example (i.e. ). Finally, note that the previously discussed base case scenari o is shown in the upper left hand corner of Table 2 3 with values of and Table 2 3 Numerical results for sensitivity to salvage value and demand u ncertainty Strategy None RC DC OC None RC DC OC

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41 The results shown in Table 2 3 illustrate that increasing levels of demand uncertainty for both channels decreases the range under which a dual channel solution is optimal. For example, focusing on the top row of the results where and comparing the values where and we see that the range of customer preference ( ) where the dual channel strategy is optimal shrinks from between [0.24,0.75] to between [0.32, 0.68]. For these situations, increasing demand uncertainty inc reases the risk of stocking both channels. However, when the demand uncertainty is extremely high, a dual channel solution is no longer optimal. Focusing on the right most column of Table 2 3, we find that for values of the region where a dual cha nnel solution is optimal (and feasible) disappears. Instead, it is optimal for the firm to operate with a single channel only if demand for that channel is extremely high. When the customer preference is somewhat indifferent between the two channels (i.e. is between 0.19 and 0.81), then it is actually optimal for the firm to stay out of the market in this situation. We denote this situation as No Channel or NC. Apparently, the demand uncertainty is too high such that stocking for these intermediate scena rios is excessively costly. Additional numerical experiments show that when is greater than approximately 685, then the dual channel optimal solution disappears. Next, we focus on the impact of the salvage value on the optimal channel strategy. When a dual channel strategy is optimal, increasing the salvage value also increases the range of optimality for a dual channel strategy. To illustrate, focusing on the left most column of Table 2 3, we see that the range of customer preference ( ) where the du al channel strategy is optimal grows from between [0.24, 0.75] for a

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42 salvage value of to [0.23, 0.77] for a salvage value of Recall that a higher salvage value corresponds to an increased value for the leftover inventory. Therefore, the firm can absorb more risk in stocking two individual channels when the salvage value is higher. To illustrate, consider the book industry. While stocking is risky at the traditional retailer, the salvage value for books is relatively high due to well developed sec ondary wholesale markets for remainder books. In contrast, in the grocery industry, salvage values are very low due to the perishability of the fresh products. Consequently, the range for which a dual channel solution exists may be smaller. However, when t he dual channel strategy is not optimal, an increase in the salvage value increases the range for which the single channel strategy is optimal. This result concurs with those typically reported for a traditional single channel newsvendor problem, where the quantity stocked increases in response to an increased salvage value. Table 2 4. Numerical results for sensitivity to environmental cost differential e ffects Strategy RC DC OC We also investigate the impact of the environmental cost differential effects on the optimal strategy for the firm. For these examples, we set the salvage value and the demand uncertainty The results for these examples (summarized in Table 2 4) show that when the online channel is less costly and/or the environmental impact is lower, then the optimal range for the dual channel strategy (DC) and the online channel strategy (OC) are more vi able. Similarly, Figure 2 2 and Figure 2 3 also

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43 illustrate the impact of environmental costs/savings on channel cho ice. For example, in Figure 2 2 we see that when (i.e, the OC provides environmental savings as compared to the RC), the break point decreases and the difference increases. In Figure 2 3 we see that when (i.e., the OC is more costly than the RC due to environmental effects), the break point increases and the difference decreases. To summarize, if one channel has h igher costs, then the optimal range for that channel shrinks. Figure 2 2. Comparison of firm profits as a function of consumer p ropensity for environmental costs

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44 Figure 2 3. Comparison of firm profits as a function of consumer p ropensity for e nvironmental costs Policy Issues as driven by factors including customer preferences, demand uncertainty, and cost differentials. In this section, we investigate the i mpact of several policy issues on this important decision. First, firms should consider the rising costs associated with carbon emissions in the delivery of their goods. To illustrate, many countries have levied energy related taxes based on the carbon con tent of the goods. In July 2011, Australia implemented a carbon tax whereby firms are charged 23 Australian dollars per ton, and this tax will eventually be replaced with a carbon trading scheme (Curran 2011). While many countries currently have not undert aken such taxation measures, many companies are voluntarily purchasing carbon credits to justify the emissions of carbon dioxide in their company. One such company is Dell, who purchases renewable energy certificates which reflect investments in wind power energy projects to offset the carbon emissions from its facilities (Ball, 2008).

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45 In terms of our model, the net effect of these schemes is to amplify the cost differential associated with environmental factors as captured in the variable Recent studie s have shown that the total energy usage for a traditional retailer is higher than that typically associated with e commerce delivery in the delivery of certain electronic goods (Weber, 2008). For such industries, and the impact of a carbon tax or vol untary carbon credit program is to amplify the magnitude of the value of such that the differential between the costs for the two channel choices is even greater. From Table 2, a firm using an OC only strategy should price the goods lower and to increa se the total quantity sold via the more environmentally efficient online sales channel. For a DC company in an industry where the firm should lower the price for the online channel, raise the quantity of goods sold via the online channel, and lower the quantity of goods sold via the traditional channel. Note also that the region of optimality for the DC and OC grow, whereas the region of optimality for the RC shrinks in this situation. Conversely, for an industry where (such as groceries), the following occurs when the environmental differential increases: (1) the RC and DC regions grow, (2) the OC region shrinks, (3) the p rice of the online channel for a DC increases, (4) the quantity of goods sold via the online channel for a DC decreases, and (5) the quantity of goods sold via the traditional channel for a DC increases. A key issue associated with carbon tax schemes is ho w to apply it to different industry sectors. From our analysis, the outcome of such a tax can yield quite different results depending on the industry under consideration. With regards to the carbon tax, another complicating factor concerns the logistics/de livery arrangements for the firm. Consider again the book industry where

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46 and customers typically pay an additional charge for the delivery of their goods. Suppose the firm is currently utilizing a dual strategy arrangement. Then the firm will pay prop ortionately more for the traditional retail center where more carbon taxes are incurred for delivering the goods to the store. Consequently, the prices will increase for the book via the traditional channel. Suppose also that the delivery of the goods for the customer pays an additional charge for the delivery. In this scenario, the third party logistics provider will incur a large portion of the carbon tax, presumab ly which will be passed on to the customer. The firm will likely favor the internet channel in this situation, as it is penalized proportionately more for its traditional channel. Consider also the company Amazon, which is an OC firm that sales books via a n online channel only. Amazon has invested heavily in logistics assets such as warehouses and utilizes a practice of postal injection to deliver products to the mail carrier associated with the customer an additional fee for the transportation portion of the item. Presumably, these fees will increase if a carbon tax is implemented. As previously mentioned, Amazon has recently allow them to distinguish different delivery options based on the carbon usage. If such a carbon tax occurs, then customers will be able to choose whether they want a high carbon delivery option with additional taxes (such as air delivery) o r a low carbon option without additional taxes. However, further research is necessary to verify the specific impact of the carbon tax on the different parties (i.e. retailer, 3PL, and consumer) in this situation.

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47 Concluding Remarks In Chapter 2 we formul ate a dual channel model of a retailer which has access to both online and traditional market outlets to answer several key research questions regarding the environmental impact of the dual channel strategy for retail. The first a firm has both traditional and online sales channels, how strategies for the firm: the traditional retail channel only (RC), the online channel only (OC), and the dual channel which combines both (DC). Utilizing the results from Theorem 1 concerning the optimal channel choice for the case with deterministic demand, we find that all three of these strategies can be optimal depending on the ) to b uy from the online channel. This propensity is driven partially by customer awareness concerning the environmental impact of their product their traditional retail chann propensity is of medium strength, then the firm should focus on the dual channel strategy (DC) and can reap the b enefits of higher profits due to synergy between the two channels. Furthermore, the break points which determine the optimal strategy choice are driven by the following factors: the unit costs for each channel, the environmental cost savings/premium for th e online channel, the price elasticity of demand for each channel, the maximum market size, and the price substitution effects. retailer should focus only on online and/or traditiona previous paragraph, analysis in Theorem 1 from the deterministic model shows that the

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48 ) is a crucial factor in this decision. In particular, if this parameter is extre mely high or extremely low, then a single channel strategy is optimal. The numerical examples shown in Section 4 also highlight the impact of stochastic elements on this important decision. In particular, we find that a single channel strategy is more like ly to be optimal when the salvage value ( ) of the item sold is relatively low. In this situation, there is an increased risk associated with leftover items and consequently the region of optimality associated with the single channel strategy is slightly g reater. Interestingly, we also show via the numerical results that when demand uncertainty is extremely high, then the region where a dual channel solution is optimal actually disappears. Under extreme demand uncertainty, the firm should focus on a single channel strategy or stay out of the market altogether. consumer behavior chiefly through the variable wh ich represents the customers propensity to buy from the online channel. As listed in Sections 1 and 2 of our paper, evidence exists which links the consumers channel choice with environmental concerns. As firms start to promote the environmental impact of this alternative and as consumers consumer propensity will increase over time. Consequently, some firms which had previously focused only on a traditional retail outlet (RC) will need to plan for a dual channel (DC) strategy. There are some notable exceptions, however, based on factors such as the population of the particular region where the traditional retailer is located and also the service levels associated with the potential online retailer (OC) channel.

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49 For example, Matthews et al. (2002) show that in Japan, a traditional book retailer can be more energy efficient due to the highly concentrated population. ors associated with e deterministic analysis, two main factors relevant to our model influence the environmental impact of e commerce, including the customer propensity to buy online ( ) and the cost differential associated with each channel ( ). From the numerical section, the analysis of the cost differential ( ) shows that environmental cost differences can significantly shift the ranges of optimality such that the dual channel (D C) option is more prevalent. In addition, if the online channel has a smaller environmental impact such that ( ), then the firm should prepare for a dual channel (DC) or strictly online sales (OC) in the future. From the Numerical analysis, we also show that the salvage value and demand uncertainty are significant determinants of the Industry specific characteristics are also important when answering the question concerning which factors have the most significant impact on the environmen t. Three e commerce industries which have been studied in the past include groceries, electronics, and books. For the grocery industry, the environmental cost differential between the two channels could actually be positive ( ) due to the refrigeration capabilities necessary for delivery. Also, the high perishability of these items is such that the salvage value ( ) is fairly low. For the electronics industry, consider the study by Weber et al. (2008) which shows that the environmental impact of e commer ce is lower such that Obsolescence rates are also high in this industry due to the decrease in the

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50 price of these items and the shorter product life cycles (i.e. low ). For the book industry, the existence of secondary markets is such that the salva ge value is fairly high ( ). In addition, the costs of dealing with returns or remainders may actually drive the environmental differential costs ( ) to favor the online channel. However, further empirical analysis is needed in each of these industries to verify the relative magnitude of these environmental factors on the channel choice. an d voluntary carbon credit schemes will have the effect of amplifying the environmental differences between the two different retail channels. The industry specific characteristic relevant in this context is the environmental cost differential. as reflected via the variable Therefore, policy makers need consider the disparate impact on different industries for carbon tax schemes. Future topics of inquiry on e commerce and the associated environmental impact are numerous. Our model focuses on a specific firm level decision, in particular trading off the environmental impact of online vs. traditional retail sales. While the focus of this model is on single firm decision making, there is an opportunity to consider social policy issues in the future. For example, a holistic objective which incorporates both consumer utility and firm profit could yield insights concerning the implication s of these firm decisions on broader societal goals. To illustrate, both Sui and Rejeski (2002) and Fichter (2002) discuss the possibility that sales via the internet may lead to excessive consumer consumption, thereby negating some of the environmental im provements offered by this channel. Second, the model here takes into account customers who will

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51 mpact of competition on this decision has the potential to make an important contribution to this field.

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52 CHAPTER 3 OUTSOURCING FOR POWER DISRUPTION Motivation type of supply chain disruption concerns power outages due to weather related events (such as hurricanes, earthquakes, or snow storms) and problems with the local power supply (such as blackouts). Examples of such events include the recent earthquake and tsunami in Japa n in March, 2011. As a consequence of this large scale disruption, several companies had to re evaluate their contingency plans to better address these supply chain disruption events. According to Murphy (2011), companies such as Jabil Circuits Inc. and Ilumina Inc. decided to add backup redundancies in the form of alternate suppliers as a result of the earthquake. More recently, Hurricane Issac caused large scale power disruptions throughout the southeast region of the United States. According to Sweet (2012), the storm knocked out power to approximately 342,000 customers in South Florida and 27,000 customers in Louisiana. The key business challenge is the rise of supply chain risk. In a survey conducted by the Business Continuity Institute, 85% of co mpanies surveyed said they have experienced at least one supply chain disruption in the 2011 (Brady, 2012). A study by CFO research revealed the magnitude of problems caused natural disasters, as 45% of senior finance executives participating in the resear ch said their company had been somewhat or substantially affected by a natural disaster from 2006 2011. (Rogers, 2009) Participants also indicated their operations had been shut down by tornadoes, deliveries to customers disrupted by floods and factories i dled by hurricanes.

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53 In their seminal article on supply chain disruptions, Kleindorfer and Saad (2005) classify different types of supply chain risks and advocate that firms undertake specific strategies to mitigate such risks. In their article, they devel op 10 simple principles to back up systems, contingency plans, and maintain reasonable slack, can increase the such back up systems can be practice for a manufacturer is to diversify their supply base in terms of the number and location of suppliers. Another practice is simply to cr eate a redundancy or back up for production somewhere in the supply chain. For a complete review of the literature on supply chain disruptions, see V akharia and Yenipazarli (2008). As an alternative to creating redundant capacity, the manufacturer may consider the possibility of outsourcing for certain activities during a supply disruption. Essentially, they would utilize a specific supplier only in the event of such a supply disruption. While the policy of outsourcing has been investigated quite exte nsively for normal supply chain operations, the notion of outsourcing during a disruption has not been thoroughly explored. As an example, we consider the possibility of a manufacturer or supply chain member outsourcing specifically in the event of a powe r disruption. Such contracts can also be used to outsource other portions of the supply chain pa rticularly during a disruption. Aggreko is an example of one such company that rents temporary power generation solutions including generators, air conditioner s and heaters (www. us.aggreko.com). A portion of their business concerns contracting power solutions for

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54 planned events such as the Super Bowl or the Cricket World Cup. A key segment of their business, however, is to supply generators for businesses in the event of a power outage. To illustrate, an OEM for a major automobile manufacturer suffered a power outage during an ice storm. Aggreko was able to provide them with generators and the accompanying equipment so that the disruption to their manufactu ring was minimal. This was an example of their walk in type service, but Aggreko also offers monthly contracts to buyers whereby Aggreko agrees to make their generators available in the event of a power disruption. In Chapter 3 we consider three differe nt variations of contracts that a manufacturer may utilize to buffer against power disruptions. The first and most proactive type is when the buyer contracts in advance for the possibility of a disruption. For this type of contract, the power supplier mu st comply with the capacity request for the contract by making the capacity available in the event of disruption (i.e. forced compliance). The second type of contract is when the buyer contracts in advance, but the supplier has the option of how much capa city to make available (i.e. voluntary or unforced compliance). The third type of contract is simply when the buyer contacts the supplier after the disruption occurs. If the supplier has excess capacity available at the time, then the buyer can purchase scheme (i.e. walk in service). We also consider two different variations of the forced and voluntary compliance contracts, taking into account the relative bargaining power of the buyer and the supplier. These contracts are typically modeled using options contracts that include both option and exercise prices. In addition, the voluntary compliance contract may be

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55 associated with a penalty in the event that the supplier cannot provide full service during t he disruption. We solve the problem for the situation where (a) the buyer determines the contract parameters and (b) the supplier determines the contract parameters. These two different approaches allow for different negotiating positions in the supply c hain for the most general situation. We compare and contrast these two variations to generate insights concerning the bargaining power of each party. Through our analysis we address the following research questions: 1. What is the best contract when the buy er/manufacturer determines the contract parameters? Are there situations under which the buyer would prefer a particular type of contract? 2. What is the best contract when the supplier determines the contract parameters? Are there situations under which the supplier would prefer a particular type of contract? 3. What is the impact of the probability estimate for the disruption event? 4. What are the limits of pricing for these types of contracts? Literature Review Disruptions The framework of disruption risk m anagement in supply chains is built on the risk management literature and models of supply chain coordination. There are two categories of risk affecting supply chain d esign and management including (1) risks arising from coordination between supply and de mand and (2) risks arising from disruptions to normal activities. Focused on the second category of risks, which may arise from natural disaster, strikes and economic disruptions, and acts of purposeful agents, Kleindorfer and Saad (2005) provide a concept ual framework that reflects the joint activities of risk assessment and risk mitigation. The three tasks as the foundation of disruption risk management are as follows: Specifying sources of risk and

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56 vulnerabilities, assessment and coordination among suppl y chain partners, and mitigation. Based on an empirical assessment from a behavioral view, both the probability supply disruption risk (Ellis et al., 2009). In this power disruption case, the probability of disruption within a certain time range and magnitude is utilized to represent two important dimensions of the disruption. An extensive body of the literature focuses on outsourcing strategies between a single buyer and one/multiple suppliers. Tomlin (2006) considers both the magnitude and response time as two key parameters of volume flexibility specifically in the situation where a disruption is caused by a supplier. He also distinguishes different types of disruptions, such as frequent but short versus rare but long disruptions. Several mitigation and contingency options used by buyers to manage supply disruption risk are listed, including investing in inventory as a hedge, alternative supply sources, rerouting orders t o alternative suppliers etc. He compares the sourcing mitigation and inventory mitigation. And the preferable strategy is given under different disruption conditions and risk orientation of the buyer. Our study focuses on the sourcing mitigation in the eve nt of a disruption. Single supplier providing different types of service which are force compliance with little flexibility on capacity delivered and voluntary compliance with great flexibility compared to multiple supply sources in Tomlin (2006) Contracts The Contract is actually adopted at the end of the negotiation process depends

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57 this concept which is easy to understand but difficult to qualify. The first one is to assume one of the firms has an exogenous reservation profit. The higher the relative bargaining power into the profit split. The higher the proportion of the total profit, adjusting power by changing which firm makes the contract offer. The one makes the contract offer is absolutely stronger in the market, assuming it is offer. Assuming the weaker firm is indifferent with all the contract offers available, the stronger firm chooses his optimal policy with maximization profit. There are several contract types for supply chains with two firms, stochastic demand an d within a short time horizon. Cachon and Lariviere (2001) utilize the options contracts with both a firm commitment option price and also an exercise price as determined by the buyer. Two compliance regimes are considered, including both forced and volun tary. The supplier has little flexibility with respect t o her capacity choice under contract with forced compliance while under voluntary compliance, she maintains substantial flexibility. The contract compliance regime has a significant impact on the anal ysis and outcome of the supply chain contracting game. Since both the supplier and the buyer act independently in the supply chain, voluntary compliance diminishes the power of the buyer to enforce appropriate capacity availability from the supplier. Thes e parties to share equally the burden of future over capacity (Arensman 2000) Supply agreements are important to chip makers because they guarantee that the billions of dollars invested in new production facilities will actually be used

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58 Manufacturers may also prepay suppliers for guaranteed production capacity. Tomlin The author p roves the existence of a class of coordinating price only contracts that arbitrarily allocate the supply chain profit. This paper also enriches the case of voluntary compliance and demonstrates that firm commitment and options contracts can indeed increase supplier capacity. However, they are not necessarily sufficient to achieve supply chain coordination. Erkoc and Wu (2005) propose capacity reservation contracts designed for short life cycle products (such as make to order high tech products) under stocha stic demand. In contrast to Cachon and Lariviere (2001), these authors consider the case where the supplier identifies the optimal contract parameters. They show that the standard options contracts do not lead to channel coordination when the wholesale pri ce is exogenous. Our work differs from the supply chain contracting literature mentioned above al ong three dimensions. First implementation of outsourcing only happens when there is power disruption. The existing literature focuses mostly on the situation where the downstream firm (the buyer) outsources the whole production or certain parts to the upstream firm (the supplier) on a regular basis. We consider the situation in which the buyer satisfies the demand on his own but that the buyer loses that capabi lity during a (power) disruption. The supplier will provide a certain amount of power capacity specified in the contract under a (power) disruption. Second we consider three service types in our model at the same time, which are two compliance regimes and walk in service. Usually quantity flexibility and backup agreements contracts assume forced

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59 compliance while price only contracts often assume voluntary compliance. Third, we compare the different bargaining power between the buyer and the supplier. Previo us work in the supply chain literature has not focused on comparing the contract offers from both sides. In general, these previous models generally assume that the supplier sets the contract offer prices, the contract parameters are exogenous (Erkoc and W u 2005), or the buyer sets all contract parameters (Cacho n and Lariviere 2001, Gurnani and Tang 1999 ). Model and Types of Contract Background In this section, we introduce the key parameters for our models which are summarized in Table 3 1 First, we assume that the demand for the buyer within a certain single range of time is stochastic. Let be the continuous and differentiable demand distribution, with as its density function and for If there is no disruption, the buyer satisfies demand internally by setting the capacity before demand is realized at a capacity cost of per unit. Under disruption, the buyer loses all of his c apacity and will rely upon the supplier to provide backup capacity to satisfy the demand. In addition, we assume that there is only one supplier available in this region for the buyer to outsource the backup capacity. In the case of a power disruption, sin ce special equipmen t and skilled human resources are required for the service, the supplier must invest capacity at a cost of per unit before demand is realized. The cost here a mixture of depreciation and maintenance costs for the power re ntal equipment. We assume that there is no salvage value associated with the leftover items.

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60 Let represent the probability of disruption. Since the contract length for these types of contracts is typi cally short (i.e. monthly), it is reasonable to assum e that there is only one possible disruption in this short time range. The variable cost per unit for the buyer to meet the demand without disruption is and the variable cost per unit for the supplier to provide the service is under disruption. There are three types of service options that the supplier can potentially provide to the buyers under disruption. The first two are contracted services where the buyer receives a priority service, and the third type is simply a walk in service. In contrac ted service, the first option we consider is the service provided under forced compliance, where the supplier must reserve the exact amount of capacity that the buyer requires. The second option is the service provided under voluntary compliance, where the supplier can consider reserving less capacity than the amount required by the buyer. In this situation, the supplier has the power and flexibility to allocate her own capacity. But the supplier potentially pays for a shortage penalty if the disruption oc curs and demand In the first two options, the buyer pays the supplier an option fee in advance of the season ( =1 for forced compliance, =2 for voluntary compliance). When there is no d isrupt service from the supplier. On the other hand, under disruption when demand is realized, the buyer pays an exercise fee to the supplier for the amount of capacity she provides ( ). In addition, under voluntary complia nce, the supplier pays the buyer a penalty fee for lost sales. The third type of service is a walk in service where there is no contract between the buyer and the supplier in advance.

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61 Table 3 1 Notation of parameters i n Chapter 3 Symbol Descriptions Symbol Descriptions The cost for each option paid to the supplier under forced compliance The cost for exercised option paid to the supplier under forced compliance The cost for each option paid to the supplier under voluntary compliance The cost for exercised option paid to the supplier under voluntary compliance Contract Type I, when buyer designs the contract Contract Type II, when supplier designs the contract The realized demand The revenue that the buyer earns per unit sold capacity capacity in contract (Marginal capacity cost) The cost per unit for the buyer to meet the demand without disruption The per unit cost for supplier to provide the service under disruption in contract Transfer payment from the buyer to the supplier Unit price for the supplier to charge walk in buyer The per unit penalty cost paid from the supplier to the buyer for unmet demand due to lack of capacity Profit for the supplier under force compliance with disruption The density function associated with demand The cumulative probability function associated with demand The probability of supply disruption during the contract The capacity choice for an integrated supply chain The capacity reserved for no disruption productivity in centralized supply chain The capacity reserved for disruption back up in centralized supply chain Expected sales given a capacity level K capacity in walk in service Minimum possible demand The per unit cost for supplier to provide the service under disruption in walk in service

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62 When a disruption occurs, the buyer contacts the supplier for outsourcing and pays an amount for a unit of capacity procured. We assume that full information regarding is known in advance to both the buyer and the supplier. From the in services. Specifically, the capacity reserved for the forced or voluntary contracts can not be used for walk in service. The unit fixed cost per unit of capacity for the walk in service is and the variable cost per unit for the supplier to provide the walk in service is under disruption. Table 3 1 summarizes the not ation of paramet ers used in Chapter 3 First, we analyze the decision for a centralized supply chain whereby a single decision maker optimizes the integrated supply chain decisions with his own backup capacity. In a centralized supply chain, the decision maker chooses th e capacity to maximize the supply chain expected profit. This integrated capacity is composed of two parts and where represents the capacity for normal production activities when there is no disruption and represents the b ackup capacity reserved in this centralized supply chain. The profit for the integrated supply chain is as follows: (3 1 ) where represents the expected sale given the capacity level and demand distribution function The optimal integrated capacity is defined as From the first order conditions of optimality, the optimal values are and which satisfy the following relationships:

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63 and (3 2 ) It is simple to show that is concave in and Thus is the unique optimal solution for Note that these values represent the optimal capacities in a centralized supply chain, when the buyer prepares his own backup capacity for disruption and capacity for production under no disruption. We utilize these values as a benchmark for comparison in our analysis for the decentralized supply chain. Even there is a single decision maker in centralized supply chain, there are two decision variables together determining the optimal capacity. In the previous literatures (Tomlin (2003), Cachon and Lariviere (2001)), their centralized supply chain models only con tain one decision variable Traditional policy is developed to see if this single variable model behaves similar under power disruption settin g. It is adopted both in forced compliance and voluntary compliance. The comparison of two variable centralized supply chain and one variable centralized supply chain is shown in Corollary 1. Corollary 1: In centralized supply chain, the buyer optimizes th profit by setting up the capacity which satisfies The supply and : Proof : See Appendix B

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64 In this single variable centralized supply chain, the buyer decides on the capacity to optimize whole s orollary 1 it always performs worse than two variable centralized supply chain. Contract I Buyer Specified Contract ( ) Figure 3 1 The timeline for bu yer controlled c ontracts When the buyer is in charge of designing the contract, he first determines the values for the option and exerc ise fees under each type of service. In addition, the buyer specifies a planned capacity level ( ). Then the supplier makes a decision concerning which types of contract to choose and how to allocate her own capacity. In the meantime, both the buyer an d the supplier are aware of the price for walk in service which is exogenous. The timeline for Contract is illustrated in Figure 3 1 and the steps are as follows: End of the Contract End of the Contract Supplier reveals the capacity 1 No disruption Under disruption Time 0 Buyer designs the terms of contract Supplier decides which types of service to provide Supplier sets up the capacity Buyer pays for the option fee if needed Buyer satisfies the demand with his own capacity Buyer pays for exercise fee or walk in p rice Supplier satisfies the demand and/or incurs the penalty

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65 1. The buyer decides on the price to offer to the supplier ( ) per option when the supplier accepts the offer and ( ) per option exercised when the supplier delivers the service for forced compliance (voluntary compliance). 2. After reviewing the contract, the supplier determines whether or not to accept the offer. a) Accept means the supplier will provide service under either forced or voluntary compliance. Under forced compliance, the supplier plans for a capacity as required by the buyer. Under voluntary compliance, the supplier has the flexibility to set up the capacity less than the amount required by the buyer. b) Reject denotes the case where the supplier rejects the advanced contract. And the supplier only provides walk in service under disruption. The supplier then allocates capacity 3. If the supp lier accepts the contract, the buyer needs to pay the supplier for each option, where =1 corresponds to forced compliance and =2 corresponds to voluntary compliance. 4. The time length for the contract is fixed. The probability of disruption durin g the range is If a disruption occurs: a) The buyer with a contract under forced compliance will pay for where is the realized demand; or b) The buyer with a contract under voluntary compliance will pay for capacity than the amount buyer requires, the supplier will be responsible for a penalty of per unit for the lost sale amount paid to the buyer; or c) The buyer without a contrac t will pay per unit for walk in service All of the shortages that occur when will be treated as lo st sales for the buyer with no additional loss of goodwill in the market. We assume that there is no salvage value from both buyer and supplier sides. To facilitate our analysis, we adopt a specific notational subscript for the different contract type and state of nature. Let N complian in s

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66 In general, the optimization problem for the buyer under contract type I is: (3 3 ) (3 4 ) satisfies the specific term in different policies (3 5 ) (3 6 ) All in Contract I: w alk in service If the walk in service is requested, it will cost the supplier a greater amount to provide this service than it would its other contracted services. To illustrate, consider the power generator example. If an emergency disruption happens to a buyer who does utilize higher cost methods to transfer and/or re allocate this capacity to the buyer. Thus, we assume that the following relationship holds: The profit for the supplier is: The optimal value for satisfies the following relationship: Therefore, becomes the reservation profit for the supplier when the supplier is considering other alternate contracts from the buyer. in price is too low such that the supplier will not provide the walk in service. Therefore the lower

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67 threshold value for the walk in price is which satisfies with The walk in service can also be treated as an outside op portunity, which is independent of the terms of the contract. For the sake of long term reputation, the buyer may be forced to take the walk in service regardless of the price. Meanwhile, there are limitations on the amount that the supplier can charge in this situation due to government regulations. In particular, regulations which limit price gouging in emergency situations are relevant here. We assume that is within the range of the market price determined by government regulation. We will discuss the relationship of those boundaries on walk in price and its corresponding changes in results in the sensitivity analysis section of the paper. In Section 4 we simply assume that the optimal reservation profit that the supplier can earn in the walk in ca se is equal to zero, (i.e. ). Contract I: forced c ompliance In this section, we calculate the optimal contract and capacity amounts under forced compliance when the buyer is in control. We develop the general conditions of optimality whi ch must be satisfied under the forced compliance contract focusing first on the dominant buyer, and then on the supplier. Then, we compare and contrast two specific alternate policies which both satisfy these general conditions. If there is no disruption the expected profit for the buyer is: where: and

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68 own capac ity. The second term represents the transfer payment between the buyer and the supplier which is the mechanism investigated to achieve supply chain optimal behavior. When there is no disruption, the transfer payment is equivalent to the option fee based on the requested amoun t of capacity. The last term is the investment If there is a disruption, the expected profit for the buyer is: where Under disruption, the transfer payment includes the option fee on requested capacity and the exercise fee on the expected sales which is the exact amount of capacity provided by the supplier. Thus, T he total expected profit for the buyer is: ( 3 7 ) Next we consider the expected profit for the supplier for the case with forced compliance. If there is a disruption, then the expected profit for the supplier is: If there is no disruption, the expected profit for the supplier is: The total expected profit of the supplier is: ( 3 8 )

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69 The buyer/supplier can evaluate the contract in terms of his/her share of the optimal profit achieved (the efficiency of the contract) and supply chain profit. (The contract is attractive to the supplier if its efficiency and her profit share are close to one.) ( 3 9 ) We focus on two feasible types of contracts adopted in the forced compliance regime. The first one is similar to that shown in Cachon and Lariviere (2001), where the ). In this situation, the buyer wants to keep the same level of capacity even under disruption to satisfy the demand. Note that this policy works to enhance the n we analyze it later. The second type of contract focuses on the integrated disruption capacity in integrated supply chain prepared for disruption (i.e. ). This policy emulates the capacity level in the integrated supply chain in order to coordinate different from these two policies. Traditi onal p olicy u nder f orced c om pliance: Utilizing a traditional policy similar to that shown in Cachon and Lariviere (2001) we let as in Equation (3 5 ) in general optimization problem. The buyer offers the contract as in Theorem 1.

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70 Theorem 1: For the forced compliance traditional policy, the buyer determines the capacity as and offers the following prices: satisfies: The total profit of the supply chain u nder forced compliance traditional policy is less than centralized supply chain, Proof : See Appendix B Integrated d isruption p olicy under f orced c ompliance: For this policy, the buyer asks the supplier to provide a capacity level similar to that in the integrated disruption case. Specifically, the forced capacity is as in Equation (3 5 ) in general optimization problem. The buyer offers the contract as stated in Theorem 2. Theorem 2: For the integrated disruption forced compliance policy, the buyer determines the capacity as and offers the following prices: with The supplier accepts that contract and recovers her opportunity cost The buyer earns the integrated profit less the

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71 reservation profit of the supplier Consequently, the policy coordinates the supply chain. This integrated disruption forced compliance policy has several advantages. First, the choice of option and exercise prices forces th e supplier to have only as much as an integrated supply chain wo uld in the case of disruption. Second, the option and exerci se fees are very similar to those of the traditional policy but are adjusted for a lower expected capacity level. Finally, the buyer reservation profit. Contract I: v oluntary compliance For the voluntary compliance policies, the supplier has additional flexibility in setting her capacity less than the amount demanded, but must pay a penalty to the buyer if demand is higher than that capacity level during the disruption. The penalty paid from the supplier to the buyer is per unit. Consequently, the total penalty paid by the supplier to the buyer in this situation is In addition to the general optimization problem, one more constraint should be considered unde r voluntary compliance which is The following shows the specific details f this policy. Traditional p olicy u nd er v oluntary c ompliance: Under the general optimization problem, the constraint (3c) becomes For the buyer, if there is a disruption then the associated profit is The profit equals to the revenue from expected sale

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72 minus transfer payment to the supplier, and investment on his o wn capacity. In addition, The last term in is the penalty paid from the supplier when the shortage occurs and Due to the monotonic increasing of the sales function, the last term will be greater than or equal to zero. Different from Cachon and Lariviere ( 2001 ) in our model the buyer pays the option fee for the amount he would like the supplier to prepare for ( ), while the exercise fee is paid for the amount of capacity that the supplier actually provides for the service. In Tomlin ( 2003 ) it is assumed that the buyer p ays both the option and exercise fee for the exercise capacity. Our assumption represents the option contract case in power gene rator rental industry. The buyer then decides on the value of and such that the corresponding capacity levels are equivalent to the integrated supply chain values. The equivalent policy is outlined in Theorem 3. Theorem 3: For the voluntary co mpliance policy, the buyer determines the capacity as and offers the following prices: The supplier accepts the contract, provides an optimal capacity level of and recovers her rese rvation cost Furthermore, the policy coordinates the supply chain. While the aforementioned policy achieves a coordinated supply chain, the profit of each party depends on the penalty cost The following corollary characterizes the admissible range of values for the penalty function.

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73 Corollary 2: For the voluntary compliance policy outlined in Theorem 3, the supplier will only accept the contract if where When then the supplier earns their reservation profit, and the buyer earns the profit of the This traditional voluntary compliance policy h as the advantage that o ption and ex ercise prices allow the supplier to have less than the amount requested by the buyer. Thus, the supplier is afforded more flexibility in capacity planning. However, the buyer sets the contract such that both the supplier and buyer behave similar to a cen tralized coordinated supply chain. Given this choice for the voluntary compliance policy, the buyer knows that the supplier will optimally stock a level of So, even though the supplier will optimally respond with a particular level of capacity. Moreover, the supplier will not accept the policy when the expected profit is less than that of the reservation value. While we assume that the penalty function is exogenous in natu it exceeds the threshold value specified in Corollary 2 then the supplier will not accept this contract as her expected profit is lower than the target level specified in the res ervation profit. If the penalty value is between zero but less than the threshold value, the suppler earns slightly higher profit than she could from the reservation profit value. If the penalty value is exactly equal to the threshold value, then the sup plier earns the reservation profit, and the buyer earns the maximal profit possible for this contract.

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74 Consequently, if the buyer has control over the value of the penalty cost, then we would set it equal to the threshold value to earn the maximal profit. Integrated d isruption p olicy under v oluntary c ompliance Under the voluntary compliance integrated disruption policy, when the buyer pays the supplier according to integrated policy, it means the buyer will pay the supplier in advance for the amount that maximizes the integral supply chain at the price per unit, and per unit for expected sale when there is a disruption. The constraint represents Equation (3 5 ) in general optimization problem for the buyer. The detail of policy is illustrated in Theorem 4. Theorem 4: Under voluntary compliance integrated policy, the buyer determines the optimal capa city and offers the following prices: with The supplier recovers the reservation profit T he buyer earns the int egrated profit less the reservation profit of the supplier Consequently, the policy coordinates the supply chain. Proof : See Appendix B The Theorem 4 looks like Theorem 2 in terms of optimal capacity and contract terms. However it stands for different bargaining power scenarios between the buyer and the supplier. In Theorem 4, the supplier has the flexibility to set her optim al capacity and it is the same as with the buyer manipulat ing the contract terms to optimize his own profit and further to achieve the supply chain coordination. The supplier pays the

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75 penalty cost due to shortage under this policy. In Theorem 2, the supplier has to set up the capacity as as required by the buyer with no responsibility for capa city shortage. Table 3 2 Comparison of buyer controlled c ontracts Contract type I/Optimal Capacity In terms of Buyer Supplier Forced compliance Traditional: Traditional: Integrated disruption: Integrated disruption: Voluntary compliance Traditional: Traditional: Integrated disruption: Integrated disruption: Walk in Integrated Supply Chain Table 3 3 Comparison of profit levels for buyer controlled c ontracts Contract type I/ Profit Buyer Supplier Forced Traditional Forced Integrated Voluntary Traditional ( ) Voluntary Traditional ( ) Voluntary Integrated Walk in Profit (Reservation) Compare the traditional and integrated policy under voluntary compliance (Theorem 3 and Theorem 4), although the option fee is paid on different amount, they both can achieve the supply chain coordination. The penalty cost is not a constant value to achie ve supply chain coordination. When the penalty cost is exogenous with and the buyer would prefer voluntary compliance integrated disruption policy. Otherwise when and the buyer would prefer walk in service rather than contracted

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76 service. When is endogenous, the buyer could get the maximum profit from voluntary compliance integrated disruption policy. Comparison of a lternate b uyer c ontrolled c ontracts In contract type I ( varies under different contract policies. The power is stronger in voluntary compliance than in forced compliance. As in the analysis before, the forced compliance traditional coordinate the supply chain. The forced compliance integrated policy can achieve the optimization for both firms thus achieving the supply chain coordination. In voluntary The penalty cost plays an importan t role in achieving supply chain coordination. The voluntary compliance across the literature (Cachon 2001, Tomlin 2003) without penalty cost cannot coordinate the supply chain. Table 3 2 and Table 3 3 summarize the contract parameters and profit for all of the buyer controlled contracts discussed in this section.

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77 Contract II Sup plier Specified Contract ( ) Figure 3 2 The timeline f or supplier controlled c ontracts When the supplier is in charge of designing contract, the timeline of the contract is shown in Figure 3 2 and the steps are as follows: 1. The supplier announces the price ( ) per option and ( ) per option exercised for forced (voluntary) compliance, and for walk in service 2. The buyer decides to choose forced compliance, voluntary compliance or walk in option, and informs the supplier his capacity for expected demand. 3. The supplier chooses her fixed capacity level for contracted service or flexible capacity for walk in service. 4. If the buyer accepts the contract, he needs to pay supplier for each option. 5. The time length for the contract is fixed. T he probability of disruption during this range happens is If there is a disruption: a) The buyer with contract u nder forced compliance will pay for expected sale where is the realized demand; or b) The buyer with contract under voluntary compliance will pay for expected sale If there is lost sale due to supplier fle xibility of not matching the End of the Contract End of the Contract Supplier reveals the capacity 1 No disruption Under disruption Time 0 Buyer decides on which type of service to choose Supplier designs the terms of the contracts Supplier sets up the capacity Buyer pays for the option fee if needed Buyer satisfies the demand with his own capacity Buyer pays for exercised fee or walk in price Supplier satisfies the demand and/or incurs the penalty

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78 amount required by the buyer, the supplier will be responsible for penalty as per unit paid to the buyer; or c) The buyer without a contract will pay per unit for walk in service In general, the optimization for the supplier is: (3 10 ) (3 11 ) satisfies the specific term in different policies (3 12 ) (3 13 ) (3 14 ) (3 15 ) All in Contract II: w alk in service Similar to the discussion under contract type I, the walk in price is exogenous and is bounded by the non directly compare the two contract types, we use the same value of as in the contrac t type I for the following analysis which satisfies: with with in case is considered as reservation profit when the buyer decides on whether to take the contract or not. ( 3 16 )

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79 Contract II: forced c ompliance Traditional policy under forced c ompliance: This policy contains the constraint Equation (3 12 ) as in the general optimization problem for the supplier. There are no feasible contract terms existing ), the supplier is in the stronger position, and controls the con tract design. Since this supplier will never consider such a policy. Integrated disruption policy under f orced c ompliance The constraint Equation (3 12 ) is for the optimization problem for the supplier. The supplier offers the contract as illustrated in Theorem 5 Theorem 5 : For the integrated disruption force d compliance policy, the supplier offers the following prices and the buyer determines the capacity as : The buyer accepts this contrac t and recovers his opportunity cost w h il e the supplier earns ( 3 17 ) Consequently Therefore, this policy yields the same supply chain profit as the integrated supply chain.

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80 Unlike in the contract type I ( ), this policy is not always feasible. In particular, ation profit such that Contract II: Voluntary C ompliance Traditional policy under voluntary c ompliance: Replace t he Equation (3 12 ) with for the supplier, t he contract offer is shown in Theorem 6. Theorem 6: For the traditional voluntary compliance policy, the supplier offers the following prices and the buyer determines the capacity as : The buyer accepts this contrac t and recovers his opportunity cost T he supplier earns the integrated profit less the re servation profit of the buyer Consequently t his policy coordinates the supply chain. Proof : See Appendix B Corollary 3 provides the criterion for determining the feasible policy between F.I. an d V.T. Corollary 3: Let Theorem 5 is feasible when while Theorem 6 is valid when Thus for a given either

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81 forced compliance integrated disruption policy (F.I.) or voluntary compliance traditional policy (V.T) is feasible in contract type II ( ). Integrated disruption policy under voluntary compliance: The optimization problem for the supplier is: The Equation (3 12 ) is updated as The corresponding feasible policy is illustrated in Theorem 7. Theorem 7 : For the integrated disruption voluntary compliance policy, the supplier offers the following prices and the buyer determines the capacity as : With The buyer accepts this contrac t and recovers his opportunity cost The supplier earns the integrated profit less the re servation profit of the buyer Consequently t his policy coordinates the supply chain. Proof : See Appendix B Compare Theorem 7 with Theorem 6 when they are both feasible policies under voluntary compliance. If the penalty cost is exogenous, but is not equal to the one shown in Theorem 6, the supplier chooses only to provide voluntary integra ted policy to the buyer when If the penalty cost is decided by the supplier, the supplier will choose to provide the both policies under voluntary compliance with corresponding that coordinates the total supply cha in.

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82 Compare Theorem 7 with Theorem 5 when the supplier will provide forced compliance integrated policy or voluntary compliance integrated policy depends on the relative bargaining power between the buyer and the supplier. Comparison of a lternate supplier controlled c ontracts In our model, we represent the absolutely stronger bargaining power in terms of the ability to design the contract. There are differences between contract policies even in the same contract type regarding the relat ive bargaining power F or example, when the supplier controls the contract, there are still different bargaining levels between different buyers. Thus, the reservation profit could be used to represent different types of buyer s Our model is based on a single buyer and a single supplier framework, but the buyer could be treate d differently depending on his bargaining power. The bargaining power for the buyer is str onger in forced compliance than in voluntary compliance, and it is stronger in traditional policy than in integrated policy. As in the previous discussion, forced compliance traditional policy is infeasible in contract type II ( ) This policy is too strict on the supplier; thus it contradicts with the stronger power of supplier assumed in co ntract type II ( ). Next, the forced compliance integrated policy is feasible on the particular small value o f the policy rgaining power by assuming small reservation profit; thus it is feasible for the supplier to achieve the supply chain coordination. The third one, voluntary compliance traditional policy forces the supplier to pay for the penalty cost with t he capacity expectation set by the buyer. This gives a certain bargaining power to the buye r and puts a constraint on bargaining power. T herefore it is only feasible for a particular penalty cost level. The last one, voluntary compliance integrated

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83 disruption poli cy provides more flexibility to the supplier optimizing her own pr ofit; thus is feasible for the supplier in most cases. Table 3 4 Comparison of supplier c ontrolled c ontracts Contract type II/Optimal Capacity In terms of Buyer Supplier Forced compliance Traditional: N/A Integrated disruption: Traditional: N/A Integrated disruption: Voluntary compliance Traditional: Traditional: Integrated disruption: Integrated disruption: Walk in Integrated Supply Chain Table 3 4 and Table 3 5 summarize the contract parameters and profit for all of the supplier controlled contrac ts discussed in this section. Table 3 5 Comparison of p rofit l evels for supplier c ontrolled c ontracts Contract type II/ Profit Buyer Supplier Forced Integrated ( ) Voluntary Traditional ( ) Voluntary Integrated Walk in Profit (Reservation) Summary of Analytic R esults Firstly, from contract type I ( ) where the buyer is in charge of the contract: 1. Forced compliance traditional policy generates the profit which does not coordinate the supply chain. 2. Forced compliance integrated disruption policy can coordinate the supply chain.

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84 3. Voluntary compliance traditional policy can coordinate the supply chain given If is exogenous and this policy cannot coordinate the supply chain. If is exogenous and there are no feasible contract terms. 4. Volun tary compliance integrated disruption policy can coordinate the supply chain given the feasible range of If is exogenous and beyond that range, the contract terms are infeasible. Secondly, from contract type II ( ) where the supplier is in ch arge of the contract: 1. Forced compliance traditional policy is infeasible. 2. Forced compliance integrated disruption policy can coordination the supply chain only when Otherwise, the contract terms are infeasible. 3. Voluntary compliance traditi onal policy can coordinate the supply chain only when Otherwise, the contract terms are infeasible. 4. Voluntary compliance integrated disruption policy can coordinate the supply chain, when is within the feasible range. If is exoge nous and beyond that range, the contract terms are infeasible. Numerical Experiment and Sensitive Analysis In this section, numerical experiments are performed under the base case setting. Sensitivity analysis shows the influence of the key parameters, su ch as the probability of disruption ( ) and the walk in price ( ). There are five scenarios we need to compare with the centralized supply chain under both contract type I and contract type II including forced compliance (traditional and integrated policy), voluntary compliance (traditional and integrated policy) and the walk in service. Under the base case, the stochastic demand is assumed to be the uniform distribution in the range where The cost parameters are following:

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85 in service) are Recall that these values are different from the for the emergency response. The revenue for each unit sold is and the probabili ty of disruption is Other conditions to be considered are: elimination of the possibility of outsourcing when there are no disruptions ( ), the demand functions are well behaved such that , are between and Table 3 6 Numerical results from contract type I under base case Contract type I Forced Traditional Forced Integrated Voluntary Traditional Voluntary Integrated Walk in Service Total profit Total capacity Option fee Exercise fee Penalty cost --Table 3 6 and Table 3 7 summarize the numerical results from contract type I and contract type II under the base case. Table 3 7 Numerical results from contract type II under base case Contract type II Forced Traditional Forced Integrated Voluntary Traditional Voluntary Integrated Walk in Service Total profit Total capacity Option fee Exercise fee Penalty cost -* the voluntary traditional policy is infeasible.

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86 Impact of changes in ( ) on capacity and profit Sensitivity analysis is performed to see how the results stated above change along with the key parameters. Figure 3 3 demon strates how capacity levels change in response to changes in the probability of disruption from the single variable and the two variable centralized supply chain. Because we assume that demand is uniformly distributed with a lower bound ( a ), the two var iable centralized supply chain model is only feasible when the corresponding capacity level to outsource for disruption is greater than or equal to a For the base case numerical scenario, this corresponds to a probability of disruption Figure 3 4 changes in the probability of disruption under different situations including the following: coordinated contract service, non coordinated contract service, walk in service in contract type I and no back up at all. Note that the profit of the coordinated (i.e. two variable centralized) supply ch ain contracts dominate all other methods for values of disruption that are greater than the lower bound Moreover, counter to our intuition, Figure 3 4 illustrates that the supply chain profit for the two variable centralized supply chain is particularly high when the probability of disruption is low. Recall that from Equation (2), the integrated disruption solution adjusts the relative capacity l evels based on the probability of disruption. In contrast, in the single variable centralized solution which is a non coordinated contract, the amount of capacity that the firm plans for in the case of disruption is the same level as the non disruption ca se. Therefore, the costs of the excess capacity are particularly high when the probability of disruption is low.

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87 When the probability of disruption is greater than the profit under the coordinated contracts (i.e. two variable) is dominant, but the profit under the non coordinated (i.e. single variable) contract choice is actually fairly close. The profit values from walk in service and no back up case drop dramatically along with decreases in However, for values of disruption less than the lowe r bound, the expected profit is greatest if the buyer does not have a back up contract. Figure 3 3 Capacities change along the p robability of d isruption Figure 3 4 under different situations

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88 Impact of changes in ( ) on feasible region for contract type II Recall that in contract type II, is the criterion determining whether the forced compliance integrated disruption policy (F.I.) or the voluntary compliance traditional policy (V.T.) is valid. Figure 3 5 displays the feasible policies in the regions of given the value of the left bottom region, then the forced compliance integrated disruption policy (F.I.) is under certain value of This value falls in the feasible region of V.T., an d the policy (V.I.) is feasible through a much wider range, which is dependent on the values of Figure 3 5 The feasible region of each policy given the value of Impact of changes in ( ) on feasible region for the walk in price The supplier agrees on the walk in price when it is greater than Max{ } while the buyer agrees on the walk in price when it is smaller than Just for economic sake without any government regulation involved, the feasible range of is V.T F.I Reservation Profit

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89 (Max{ }, ). is convexly decreasing in ( Figure 3 6 ). In the base case, when , t he walk in price is equal to the revenue. It means when the probability of d isruption is less than 6.7%, government regulation s are needed to make sure that the buyer keeps the normal production activities during power disruption for the sake of humanitarian consideration. At the same t ime, the regulations prevent price gouging when disruption happens and limit the walk in price within the shaded area if possible. Figure 3 6 illustrates the feasible regions for the walk in price and indicates when the government regulation is needed. Figure 3 6 The feasible region of exogenous Concluding Remarks In Chapter 3 we consider several different types of contracts whereby a firm outsources in the event of a large scale power disruption. Forced compliance and setting her own ca pacity. Under each compliance regime, traditional and integrated policies are investigated to coordinate the supply chain. In the existing literature on Regulations Needed Optimal for Both

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90 contracting to achieve supply chain coordination, these models utilize a traditional approach when the supplier is contracted for regular production. We develop an integrated policy to suit the situation when outsourcing is only for disruptions. We find that the integrated policy performs better than traditional policies when it is feasible. Not only does i t provide superior profit levels than other policies, it also allows the supplier flexibility in determining an appropriate capacity level. Furthermore, it allows the buyer to hedge against the possibility of a disruption in production due to a power outag e. Figure 3 7 gives an overview of the decision process for the power outsourcing contracts considered in the paper. The optimal path is given depending on the relativ e bargaining power between the buyer and the supplier, and other conditions like penalty cost and reservation profit. The optimal contract terms for each policy are derived in previous sections. All of the contracting policies chosen at the end of the flow chart in Figure 3 7 achieve supply chain coordination. In general, the voluntary integrated compliance policy performs the best under the widest range of parameters. If there is no feasible policy available, the buyer (supplier) will not agree to an advance contract and choose the walk in service when there is a disruption. Previous studies find that only forced compliance (as opposed to voluntary) can coordinate th e supply chain. In our modified voluntary compliance, with the introduction of penalty costs and updated option payment schemes, the voluntary compliance achieves the supply chain coordination in both buyer controlled and supplier controlled contracts. The penalty cost plays an essential role in this voluntary compliance to encourage the supplier to stock up to the optimal capacity level for the whole supply chain.

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91 In our model, the capacity prepared for a contracted service has high priority and is not all owed to be shared with other buyers. Considering the case that multiple buyers be enough capacity for all the buyers waiting for the walk in service. Consequently issues such as (a) how the supplier determines the capacity for walk in service and (b) how it allocates the capacity among multiple buyers warrant further investigation in the future. Another key future direction for research concerns the utilization of similar contract methodologies as a backup for regular sourcing. Instead of a single supplier sourcing model, the firm may consider such contracts when there is a regular supplier for outsourcing and a backup supplier for disruption outsourcing.

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92 Figure 3 7 Flow chart of optimal polic ies

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93 CHAPTER 4 RESOURCE SHARING IN POWER RENTAL SERVICE Manufacturers are increasingly vulnerable to supply chain disruptions due to power outages caused by external events such as adverse weather conditions. Empirical evidence shows that manufacturing productivity is typically reduced during periods of weather related events such as heat waves, blizzards, and hurricanes (Cachon et al. 2012). While these events are on the whole unavoidable, companies can guard against the power outages associated with these events by (a) providing an onsite back up power source such as a large scale generator, or (b) sourcing to a company who can provide such generators in the event of such a disruption. Although many companies have considered the benefits of sourcing instead of purchasing equipment which will likely be idle, the notion of outsourcing solely during a disruptio n is fairly novel. business model. They sell the service of the product instead of the production itself, such as a car sharing service. Such strategies focus on not only th e profit for the manufacture but also the sustainable levels of consumption (Toffel, 2008) It aligns the incentives of both the manufacture r and the customers as shown in Figure 4 1 base on Reiskin, et al (2000) It is typical in servicizing models to use pay per use pricing, where consumers only pay for their usage. This may provide consumers with an incentive to curtail their usage and reduce overconsumption, lowering the use impact. Under this setting, the manufacture r may not need to provide each consumer with dedicated product; instead, the manufacture r may maintain a pool of products, which can be used to meet the

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94 r ma intains the ownership of the product and incurs the associated operating costs, it has an incentive to increase the product efficiency, consequently reducing environmental impact. Figure 4 1 How the servicizing model aligns incentives for different firms In the power rental case, suppose there is a monopolist that can choose between selling the power equipment and providing a power rental service under disruption. The supplier sells the product at a fixed price, and the buyer owns the product. Or the supplier sells the use of the equip ment by charging a usage price and incurs an additional transaction cost. There are two different types of servicizing models based on whether resource pooling is feasi ble or not in other words, whether the supplier is in charge of the inventory or not. The se two types of service s are contracted service and walk in service. Under contracted service, the buyer will use the units dedicated to him, but under walk in service the aggregated demand may lead to a shortage for the buyer or reducing available capacity for the supplier. One such company which provides such a service is Aggreko (Aggreko.com) which sources power generator equipment. Aggreko offers many alternative c ontracts depending on the needs of the supplier, including contracts for installation, contracts for temporary but planned events (such as the 2014 FIFA World Cup Brazil ), contracts for

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95 temporary but unplanned events, and finally a walk in service. In thi s walk in service, a company such as a manufacturer contacts Aggreko in the event of a disruption and if Aggreko has generators available, then the buyer can rent out their services. To illustrate this type of walk in service, an auto manufacturer recentl y contacted Aggreko during an ice storm which caused large scale power outages. Aggreko was able to provide generators, transformers, etc. so that the company minimized its disru ption due to the power outage. We incorporate the cost structure to find out the differences in results with resource pooling effect or without it. The expected results show how the differe nces impact on the total profit. Specifically, we address the following research questions: 1. In the presence of scarce capacity, how should the s upplier allocate this capacity amongst multiple buyers? 2. What is an appropriate allocation scheme when both buyers have contracted in advance of the disruption? 3. Are there s ituations under which the supplier should steer a buyer away from an advanced contrac t? Literature Review The model introduced in the following section incorporates elements from both the multi item newsvendor problem and also from the options contracting literature. As such, we briefly review these two bodies of literature and contrast ou r model relative to the established body of literature. Capacity Allocation and Newsvendor Model A body of literature related to our paper addresses the situation where a newsvendor sales multiple products, but has some sort of constraint limiting the tota l number of products that it can serve. Consequently, it must decide how to allocate the

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96 limited capacity amongst multiple buyers. Hadley and Whiten (1963) discuss this and discuss an approximate algorithm to solve the problem. More recently, Erlebacher (2000) formulate an expression which optimally solves the problem when demand is uniformly distributed, and gives a near optimal solution for other continuously distribute d demand functions. Chung et al. (2008) formulate a multi product newsvendor that has two stages which correspond to preseason capacity (with no capacity limits) and also a reactive capacity (with limits). These authors also assume that demand is independe nt for each of the buyers. However, in our model, the contracted units and the walk in units come from the same limited capacity bank. In addition, we utilize options contracts whereby the buyers can contract in advance for capacity in the event that a dis ruption occurs. For a detailed review of the multi product newsvendor problem, see Turken et al. (2012). Options Contracts Options contracts are common in the literature, whereby the buyer offers the supplier a contract with two parts including an options fee to reserve a certain portion of capacity and an exercise fee which is paid when the capacity is actually used. Cachon and Lariviere (2001) analyze such an option scheme where the buyer sets the terms of the contracts and the supplier accepts if a mini mal reservation profit is met. Moreover, they consider the case of uncertainty in demand which could possibly be misrepresented by the buyer. Tomlin (2003) enhances this approach by addressing the notion of partial compliance. He shows that under nonlinear price only contracts, options can induce higher supplier capacity. In contrast, Erkoc and Wu (2005) consider a capacity reservation scheme where the supplier determines the terms of the contract

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97 with a single buyer which also includes a noncompliance pena lty in the case where the supplier canno t meet the needs of the buyer. Several authors also consider the possibility of a spot market to complement th e In this environment, the buyer has the opportunity to contract capacity in advance of demand, or to wait until the period in which demand is real ized to purchase the capacity. Cvsa and Gilbert (2002) consider the case where multiple buyers who compete in the same marketplace are contracting with a single supplie r for a short life cycle good. These authors identify circumstances under which it is optimal for the supplier to provide adequate incentive for the buyers to purchase t he goods in advance of demand. Furthermore, they show that the advance purchase can be advantageous to th e buyers even in the absence of significant leadt imes and capacity constraints. In our paper, we also consider the possibility that the buyers can contract in advance of demand, or actually wait until the period in which demand is revealed to utilize a wal k in service. However, due to the nature of the service offered, we assume that the buyers do not compete in the same market, but that they do compete for limited capacity availability. Wu et al. (2002) consider options contracts in an environment with non scalable capital intensive goods, such as power companies, which also has a well deve loped competitive spot market. They first formulate and solve a model with a single buyer and a single supplier (and eventually generalize to multiple suppliers) and show the circumstances under which it is optimal for the supplier to offer an advanced contract. Spinler and Huchzermeier (2006) focus on the case with a single buyer and single supplier where there is price uncertainty for the goods under consideration. Thes e

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98 demonstrated to be Pareto improving as compared to n contrast to our model, both of these models assume that no demand goes unsatisfied as the r esult of a competitive spot market. We assume that during a single period of disruption, the supplier has a virtual monopoly such that its capacity constraints are relevant. Consequently, the supplier may not have sufficient capacity to meet demand for all of the buyers in the case of a disruption. Contribution to the L iterature Our model is unique in the l iterature for several reasons. First, while our basic model exhibits similar characteristics as the multi product newsvendor problem, there are several c omplicating factors, including the possibility of contracting in advance of demand and also when demand is realized. I n addition, we explicitly consider not only the uncertainty in demand, but the uncertainty concerning the possibility that an actual disru ption will occur and the units are neede d by several different buyers. Second, while several authors have utilized options contract models, they typically assume that the capacity available during the spot buy or reactive period of demand is unlimited. Third, we identify unique properties of these options contracts whereby the allocation between different buyers is independent of the probability of disruption for each buyer due to resource sharin g on the part of the supplier. Finally, we show the conditi ons under which a supplier would optimally steer a buyer towards the walk in service instead of contracting with them in advance of demand. Models in Centralized Supply Chain We introduce the model by focusing first on the necessary notation, formulating t he model, and then analyzing the model in the next section. Let denote the

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99 probability of the single disruption events happened to the buyer Note that represents the probability when both buyer 1 and buyer 2 encountered the power disr uptions at the same time, let Thus, we assume that the two potential buyers are geographically dispersed and that the probability of disruption is independent at each location. Since we consider the buyers are from different types of industry, the revenue is respectively (Let ) ( ) is the revenue generated by retailer if supplied by one unit of power generator. Let where is the revenue per unit product sold by the retailer and is the uni ts of product produced for retailer by each unit of the generator. The variable is the fixed investment cost for power equipment per unit for the supplier, while the variables and are the cost per unit to provide service to the buyer 1 a nd buyer 2 separately. We assume that the buyers only compete for limited capacity from the supplier, buyer is independent and is represented by with stochastic dist ribution functions and . The fixed investment on the power equipment for the supplier is per unit for every buyer which includes depreciation and maintenance fees. And the cost to provide the service from the supplier to each buyer is (operational, personnel, transportation cost). Due to the nature of demand from temporary disrup value of the power equipment.

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100 analyzed first, and will be used as a benchmark for corresponding decisions under a decentralized supply chain. Dedicated Capacity The decision variables represent buyer 1 and 2 which reflect dedicated between buyers. Specifically, the buyer agrees to dedicate this portion of capacity to the supplier to be used by only that supplier in the event of disruption. profit under centralized supply chain, and it is as follows: The optimal solution for decision variables are: (4 1 ) Let and be the optimal solution if the supplier assigns dedicated capacity (4 1 ) indicates that both the probability of disruption and the profit rate will influence the capacity allocation between the buyers from the supplier. The decision variables for the buyers are and which represent the capacities reserved for decision variables are as follows: Buyer 1:

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101 (4 2 ) The optimal solution satisfies: Buyer 2: (4 3 ) The optimal solution satisfies: Let and be the optimal solution that will maximize the profit of buyer 1 and buyer 2 under a dedicated strategy in the centralized supply chain. These calculations are utilized as a benchmark for more realistic decentralized scenarios. Resource sharing We consider the situation where the supplier utilizes a resource sharing strategy and but we assume that this capacity can be shared with other buyers when the allocated buyer is not under disruption. The shared capacity will ensure the buyer get as backup capacity, which is calculated from dedicated capacity. The capacity is shared to ensure that even under capacity shortage the buyer can have approximately the same service level as under the dedicated strategy. When the s resource sharing method, the sales associated with each buyer is equal to expected sale under single disruption. By assumption thu s

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102 allocation under the resource sharing approach is as follows: (4 4 ) in resource sharing with in dedicated capacity planning, the capacity needed in resource sharing is significantly less than that in dedicated capacity plan, given , The total capacity reserved by supplier is less in resource sharing than in dedicated capacity. Thus, The buyer dedicated capacity.

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103 Given that we get and However because the sign of is parameter dependent, and is not always positive. Th us, with shared resources, only when the supplier can achieve much more profit with a lower level of capacity. When the probability of di sruption at both of the buyers is extremely low (i.e. ) or the fixed investment for the capacity ( ) is high, then the difference is positive and the capacity sharing strategy yields higher profit for the supplier. less than the maximum demand, the realized demand is still for buyer under single disruption. Consider the situation when follows: Let and

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104 Thus, Equation (4 4 ) holds for two cases. This indicates that when the capacity can be shared between two buyers under a single disruption, only the profit rate would influence the allocation of priority capacity to each buyer. Given and the sign of is not always positive or negative. Only when could the supplier achieve higher profit with a lower level of capacity. When plan. However the comparison between profits is not straightforward. Compare the Equation (4 4 ) to Equati on (4 1 ) in the dedicated capacity strategy, we can infer that if the two buyers have the same probability of disruption, there are no

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105 differences in allocating the s pecific capacity to each buyer between dedicated and resource sharing methods. In summary, the optimal total capacity needed for resource sharing is always less than that needed in dedicated capacity; however the profit impact is indeterminate. Corollary 1 : In the centralized supply chain, utilizing a resource sharing strategy will reduce the capacity needed for the supplier while there are multiple buyers. However the relationship between total supply chain profits under dedicated capacity and resource sharing allocation models depends on the specific parameter setting. Models in Decentralized Supply C hain capacity to dedicate to multiple buyers as stated above in the central ized supply chain scenario. Thus, the supplier tends to adopt the resource sharing method indicating that the capacity can be shared amongst multiple buyers if there is only one disruption. The supplier decides the amount of capacity allocated to each buye r with priority. When both buyers are under disruption, then the supplier does not have enough capacity available to serve both suppliers. Under the asymmetric information setting, the buyers are not ther provide voluntary contract service or emergency response (i.e. walk in service) based on the amount of total capacity available. There are several scenarios depending on the relationship between the total capacity level and required capacity by each b uyer. Under each scenario, we analyze specific methods of capacity allocation to determine the optimal strategy depending on capacity availability. Utilizing the resource sharing method, we compare and contrast the results between providing contract servic es to both buyers and the mixed strategy with contract service and emergency response.

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106 0 levels. We will analyze them individually and determine the allocation plan and correspo nding price terms. (According to Chapter 3, we adopt the option contract under voluntary compliance integrated policy due to its performance.) The following notations are relevant to the decentralized supply chain model: : the optimal capacity reserv ed for buyer under voluntary compliance with sufficient capacity : the optimal profit for buyer under walk in service with sufficient capacity Let: From the above discussion in the centralized supply chain, Depending upon the relationship between and there are four cases to analyze. Under each case, the supplier will allocate to the buyer to The supplier will also de cide on the option and exercise fee to ensure that the buyer agrees with the advanced contract. capacity for all the buyers For this situation, there i s more than enough capacity to allocate to each buyer such that there are no significant capacity limitations. Consequently, the supplier allocates the capacity according to as the baseline in the centralized supply chain. The ranges of the rema ining cases and are shown in the Figure 4 2 The notations used in this section are shown in Table 4 1 Figure 4 2 The ranges of cases and

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107 Table 4 1 The notation for the decentralized supply chain Symbol Description The optimal capacity reserved for buyer under voluntary compliance with sufficient capacity The optimal profit for buyer under walk in service with sufficient capacity The capacity level that the supplier allocates to the buyer The option fee per unit paid by the buyer in the option contract The exercise fee per unit paid by the buyer in the option contract The penalty cost per unit paid to the buyer in the option contract The walk in price per unit charged by the supplier to the buyer The buyer The buyer disruptions In each case, the optimization problem for the supplier is as follows with the decision variables: option fee, exercise fee and penalty cost in the option contract; walk in price in walk in service; and the capacity allocation plan (capacity r atio) between buyer 1 and buyer 2. (4 5 ) s.t. (4 6 ) (4 7 )

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108 (4 8 ) In general, the steps for solving the optimization model are: 1. plan and Let them equal to zero, thus, obtain the ratio of With the given and distribution functions, the values of and are obtained. 2. As in Equation (4 6 ) and Equation (4 7 ) the equalities hold when the supplier reaches her optimal profit. Thus, let and the expressions of option fee the exercise f ee and the penalty cost or walk in price are obtained. 3. ble between different case and scenarios analytically. Please see Appendix C for an example of this approach to identifying the optimal solutions. Case The key question concerns whether or not the supplier should still provide v oluntary compliance contract to both buyers. As an alternate, the supplier may consider providing a voluntary contract only to buyer 1 while providing a walk in service to buyer 2. Furthermore, the supplier needs to determine the price terms in or der to o ptimize its own profit. Recall that under a voluntary compliance contract, the buyers pay the option fee for

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109 n the supplier provides two service cost, option fee and exercise fee from each buyer. The first term is fixed investment cost; the second and the third terms are t he service cost for each buyer; the fourth and fifth terms are the option fees paid by each buyer; the next two terms are the exercise fees paid by each buyer when there are disruptions; and the last two terms are the penalty fee paid to the buyers if supp lier underestimated the capacity due to her flexibility in capacity planning. Let then disruption to any buyer. Also, the reason for being the option fee paid to the supplier instead of the true amount that allocated to each buyer is that the

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110 resource sharing strategy either. Thus, the buyers estimate the amount to pay the option fee by benchmarking what happened under centralized supply chain asking for dedicated capacity from the supplier. Using this strategy, the buyer will obtain the profit is greater than that from walk in service, the buyer is satisfied wi th the result The procedure to solve the optimization problem is slightly different from the general steps; please see Appendix C providing two option contract s is: (4 9 ) resource sharing strategy to gain the maximum profit from providing two voluntary contracts. The next analysis considers the situation where the supplier provides one buyer with voluntary compliance and the other buyer with walk in service. We consider the case where the supplier forms a contract with buyer 1, but not with buyer 2. Since the buy capacity, when there is only a single disruption which occurs for the buyer 1, the supplier will allocate enough capacity for that buyer. When there are disruptions that occur simultaneously for bot h buyers, the supplier will satisfy buyer 1 first and then allocate the remaining capacity to buyer 2 through walk in service.

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111 However, in this situation, there is a chance that no capacity will be available for buyer 2. The supplier needs to determine the option fee, exercise fee for the buyer 1, the capacity allocated to each buyer during simultaneous disruptions. Let be the capacity that supplier allocate to buyer 1 when there are two disruptions at the same time. When the supplier provides priority contract service to buyer 1 and walk in service to buyer 2, the supplier needs to determine the decision variables Through the steps stated before, the optimal profit for the supplier is: (4 10 ) contract to the buyer 1. The expression of unction. arrangement. Theorem 1 : When not enough to satisfy option contracts to both buyers ( ), the supplier is better off to provide a single contract and a walk in service to the buyers.

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112 Mathematically, when single w alk in service is better than that under two contracts. Consider the managerial implications to each supply chain partner from Theorem contract to the most lucrative buyer rather than offering a second contract to the least profitable buyer. The most lucrative buyer receives the guarantee of capacity availability under disruption via a voluntary contract, whereby the supplier must pay a penalty if there is a shortage. While it appears that the second supplier may lose out of the assurance associated with an advanced contract, they do gain valuable signaling supplier has more tha n enough capacity to meet demand for this buyer, then it is optimal for them to offer a second contract to buyer 2. However, if the supplier has less capacity available, then they forego a contract with the less viable supplier. Therefore, supplier 2 als o received valuable information about capacity availability via the lack of an advanced contract. Case voluntary contract. In this situation, we determine whether to (a) offer a contract to buyer 2 (where we have sufficient capacity), or (b) offer a contract to buyer 1 (the more lucrative buyer), or (c) simply provide walk in service to both buyers. Firstly, when the supplier provides one voluntary contract to buyer 2 and walk in

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113 Through the steps listed where we offer a contract to buyer 2 instead of buyer 1: (4 11 ) parties act optimally. Secondly, if the supplier provides one voluntary contra ct to buyer 1 and walk in service to buyer 2, the optimization for the supplier is similar to the one in case Thus (4 12 ) and : Since we obtain These results are summarized in Theorem 2, which are self explanatory.

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114 Theorem 2 : : When not enough to cover both ), the supplier is better off to provide an option contract to the buyer 1 which is the more lucrative buyer. There is a possibility that the supplier may consider providing walk in servi ce to both buyers when her capacity is greater than the smaller threshold value. The profit for the supplier under this scenario is With optimal capacity allocation ratio: in service to buyers. When the walk in price and are allowed to achieve the levels of and separately, the profit under walk i n service partially dominates the other scenarios for this case. However when there is a government regulation posed on the boundary of walk in prices, the comparison between walk in service and option contracts varies depends on the exogenous walk in pric e. Case compliance if under dedicated capacity. The research question is: should the supplier provide one voluntary compliance contract to buyer 1 and w alk in service to buyer 2 or walk in service to both buyers?

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115 When the supplier provides walk in service to both buyers, the supplier needs to specify the walk in price for both buyers and then determine the allocation of capacity if both buyers ask for walk in service at the same time: imal allocation are: It seems intuitive that the supplier allocates the resource according to the marginal profit regardless of the probability of events. Thus Let Buyer 2 is following the same rule: Thus,

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116 and is solvable with specific di stribution (4 13 ) Secondly, if the supplier provides the option contract to buyer 1 and walk in service to buyer 2, (4 14 ) The first term is negative, and the second term is positive. It means the profit under walk the profit in Equations (4 13 ) and (4 14 ) dominate the profit when the supplier provides option with a contract only to the buyer 2 and walk in service to the buyer 1. This result i mplies that when the supplier does not have sufficient capacity even for the less lucrative buyer, then the supplier is better off without advanced contracts for certain range of capacity. As a consequence, an indirect signal is given to the buyers concer Corollary 2 : Let be the ratio of sales difference and be the ratio of marginal profit. In case when in which the supplier prefers to provide the optional contract to the lucrative buyer. Otherwise, the supplier prefers to provide walk in service to both buyers.

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117 Numerical Experiments I n this section, we perform numerical experiments to show the differences in profit in centralized supply chain and decentralized supply chain cases. Under the parameter setting: ; ; ; ; Demand is uniformly distributed over for each buyer, with ; Thus, Buyer 1 is more lucrative than buyer 2. First, we compare the total profit under centralized supply chain between different capacity allocation plans. When the probabilities of disruptions are given as the profit under dedicated capacity ; or Figure 4 3 shows how this relationship changes along with It confirms the results shown in Corollary 1 that in centralized supply chain, with sufficient capacity to a degree, the profit that under a resource sharing strategy generates is greater than that derived from the dedicated capacity allocation strategy. Und er that case, the resource sharing strategy uses less capacity than that in dedicated strategy. But when the capacity is not enough to cover any only in the range of th e small values of probabilities of disruptions. Otherwise, the dedicated capacity allocation strategy dominates the resource sharing when the probabilities of disruptions increase.

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118 Figure 4 3 The profit comparison in centralized supply chain Secondly, we compare different scenarios under a decentralized supply chain. In case but only one of them, the profit earned from providing an optio n contract to the buyer 1 and walk in service to the buyer 2 dominates the profit associated with providing pure option contracts to both of the buyers. Moreover, there is a large difference between those two profits. Figure 4 4 shows the significant advantage for the supplier to provide the optimal option contract to the more lucrative buyer.

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119 Figure 4 4 The profit comparison in case Recall that in case buyer but can cover the less profitable buyer 2. As expected from Theorem 2, the supplier still benefits more from providing option contract to the lucrative buyer. As s hown in Figure 4 5 the profit of contracting with buyer 1 is greater than the profit of contracting with buyer 2. However the difference between these two is not significant. By knowing that the supplier only provides the option contract to the lucrative buyers, the buyers can signal the capacity shortage, but are not aware of the degree. It means and case

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120 Figure 4 5 The profit comparison in case In case when the supplie cover the option contract for either buyer. The profit for the supplier providing pure walk in service partially dominates the profit providing option contract to buyer 1 when the capacity is greater than 247, and fully dominates the profit providing option contract to buyer 2. As shown in Figure 4 6 the difference between those two is not large. Due the assumption of bound of the demand distribution. Thus, is the starting point for the value of in case

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121 Figure 4 6 The profit comparison in case In conclusion, when we combine the above three cases together, there is a trend Figure 4 7 The solid red and green lines represent the profit under the same strategy, which is the supplier providing the option contract only to buyer 1 and walk in service to buyer 2. They are conti nuous in case and The purple dashed line represents the profit for providing option contract to buyer 2 and walk in service to buyer 1. They are continuous and dominated by the solid lines. The orange dotted line represents the largest profit from p roviding walk in service to both buyers without any regulation. For this numerical experiment, the

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122 walk in only service dominates the solid lines in case and for the most range of However if there is regulation on the upper bound of walk in pri ce, the profit associated with the pure walk in service will decrease. Figure 4 7 Concluding Remarks In this chapter, we analyze the capacity allocation plan between one supplier and multiple buyers. First, we analyze two planning models under centralized planning. In the dedicated capacity model, the supplier reserves capacity to each buyer individually

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123 to access in the case of a disruption. In the capacity sharing model, the supplier effectively pools the capacity needed for the buyers and reserves only enough to serve each buyer individually. In this situation, in the event that there is a disruption for both of the buyers, then the capacity is not sufficient to meet the demand of both of the buyers. Certainly, the capacity sharing model the total capacity level is much lower than that needed for the dedicated capacity model. Moreover, we identify th e circumstances under which the capacity sharing model is more profitable. When the probability of disruption at both of the buyers is extremely low (i.e. ) or the fixed investment for the capacity ( ) is high, then the difference is positive and the capacity sharing strategy yields higher profit for the supplier. In the decentralized supply chain, we analyze three cases based on the values for the centralized supply chain. The results we generate offer insights for the supplier on service planning (i.e. which types of service to provide to each buyer) when offering an option cont supplier should also consider providing walk in service to both buyers for certain range of capacit y. Under each scenario, the option and exercise fee for the option contract or the walk in price for walk in service are generated for optimal results. These results are important because when the buyer is using voluntary contracts, the lack of a contract offer from the supplier to the buyer serves as an indirect signal

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124 her profit by offering a contract only to the most lucrative buyer. Even when the capacity is not s ufficient to cover the single buyer under contract when there is a disruption, this buyer has the assurance of a penalty fee that the supplier must pay to the buyer in the event of a shortage. The buyer who is not under contract maintains the possibility of walk in service, but without a capacity availability guarantee. This buyer When capacity is not sufficient to serve the needs of the most lucrative buyer, then the su pplier may consider providing only walk in service to both buyers. Analytic results are derived for the situation where the supplier can charge a maximal price for the walk in service (i.e. the walk in price for each buyer is equivalent to the revenue ear ned for each buyer). Our numerical results for this situation indicate that the walk in service can be more lucrative than providing an advance contract. However, regulations concerning price go uging may limit this price for the walk in service such that it is optimal for the supplier to offer a single advanced contract. In conclusion, our analysis shows the optimal service planning for the single supplier when facing multiple buyers. The utilization of voluntary contracts with capacity sharing increases t

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125 APPENDIX A PROOFS OF THEOREMS AND ANALYTICAL RESULTS IN CHAPTER 2 Proof of the Optimal Pricing for the Dual Channel (DC) Strategy Claim : For the following profit maximization problem: (A 1) Where and The optimal prices are: (A 2) (A 3) Where ; ; and Proof: The first order conditions (ROCs) for the problem stated in Equation (A 1) are: (A 4) (A 5) And the second order conditions are: (A 6) (A 7) (A 8) These second order conditions indicate that is strictly and jointly concave in and This is based on observing that and since

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126 it was assumed that for Equations (A 4) and (A 5) equal to 0 and determine the optimal prices by solving the following two simultaneous equations: (A 9) (A 10) And the result is: This proves our claim. Proof of Theorem 1 in Chapter 2 Theorem 1 : Assuming that all three strategies are feasible, the optimal strategy choice for the firm is as follows: 1. If the firm should choose strategy RC (i.e., only offer the product through the retail bricks and mortar channel); 2. If the firm should choose strategy DC (i.e., offer the product through dual channels); and 3. If the online channel). Where and Proof: Our proof is based on the assumption that the firm will always choose to adopt at least one of the three strategies: RC, DC, or OC. To start with, we make the following observations:

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127 Observation 1: If both and as defined in Table 2 are positive then Observation 2: If both and as defined in Table 2 are positive then Observation 3: If both and as defined in Table 2 are positive then Observation 4: If both and as defined in Table 2 are positive then Observation 5: Strategy RC is feasible if since this implies that is non negative. Observation 6: Strategy DC is feasible if since this implies that both and are non negative. Observation 7: Strategy OC is feasible if since this implies that is non negative. Case 1: We start by assuming that this is a feasible range (i.e., ). Then, we observe that in this range: (a) strategy DC is infeasible (Observation 6); and ( b) strategy OC is infeasible (Observation 7). For the RC strategy to be feasible in this range, we need to show that This is true provided which obviously holds since Hence, in this range the RC is the optimal strategy. Case 2: In this range, we consider three sub cases:

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128 In this range, strategies DC and RC are both feasible (strategy OC is infeasible). However, based on Observations 1 and 3, it is obvious that and hence, DC is the optimal strategy. In this range, both strategies RC and OC are infeasible and the only feasible strategy is DC (Observatio n 5). Hence, DC is the optimal strategy in this range. In this range, strategies DC and OC are both feasible (strategy RV is infeasible). However, based on Observation 2 and 4, it is obvious that and hence DC is the optimal strategy. Case 3: We start by assuming that this is a feasible range (i.e., ). Then we observe that in this range: (a) strategy DC is infeasible (Observation 6); and (b) strategy RC is i nfeasible (Observation 5). For the OC strategy to be feasible in this range, we need to show that This is true provided which obviously holds since Hence, in this range the OC is the optimal strategy. This concludes our proof of Theorem 1. Proof of Corollary 1 and 2 in Chapter 2 Proof: The optimal prices for the dual channel stochastic model are as follows: (A 1 1 ) (A 1 2) where , and

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129 Analyzing further, we find that In this expression, we find that , and Since then Taking the derivative of with respect to various parameters, we find that (A 1 3) (A 1 4) (A 1 5) (A 1 6) (A 1 7) (A 1 8) (A 1 9) The results for are similar to those for and are omitted.

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130 APPENDIX B PROOFS OF THEOREMS AND COROLLARIES IN CHAPTER 3 Proof of Corollary 1 in Chapter 3 Corollary 1: profit by setting up the capacity which satisfies The supply ision variables and : Proof of Corollary 1: The optimal satisfied: Since , End of the proof. Proof of Theorem 1 in Chapter 3 Thus the optimal value of satisfies:

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131 Consider ing which is independent of the value of which equal s to the one that Let th e contract terms are determined as follows. From centralized supply chain, unique optimal capacity decision that maximizes in Theorem 1 A ny other set s of decision variables generate the profit smaller than Given or and Therefore the optimal solution under the forced compliance traditional policy is worse than centralized supply chain. The equat ion only holds when and which is quite a rare case in power rental industry. Thus coordinate the supply chain. End of the proof.

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132 Proof of Theorem 4 in Chapter 3 First ly we assume ( ), then prove the supply chain is coordinated. Since substitute it T he supply chain achieves coordination. Second ly when which is we prove this policy coordinate the supply chain with that assumption Substitute it :

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133 Compare with the profit and optimal capacity in centralized supply chain, s ince , according to Corollary 2: This policy cannot coordinate the supply chain under the assumption that End of the proof. Proof of Theorem 6 in Chapter 3 The optimal that maximizes : when Thus is the solution that makes and is the solution that maximize s profit, and also is the optimal solution for the supplier. Substitute and back into we get: The express ion of is the only value that coordinate the supply chain, thus option and exercise fe es are independent of the penalty cost:

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134 The upper bound is the same as in Corollary positive. End of the proof. Proof of Theorem 7 in Chapter 3 When Thus, it coordinates the supply chain; otherwise it cannot coordinate the supply chain. From the optimal solution we get: With where End of the proof.

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135 APPENDIX C PROOFS OF THEOREMS IN CHAPTER 4 Proof of Theorem 1 in Chapter 4 Under the case firstly the supplier consider to provide two option contracts to the buyers To solve Equation (4 6 ) and Equation (4 7 ) those two constraints in the optimization such that buyer city is the one that maximize his profit, consider the following analysis: Let then: and identify the value of would earn under the walk in scenario. By substituting this result back into the expression of we eliminate the term and only cost decision variables are involved in the expression of the profit expression such that:

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136 From , we get Therefore, the expressions for and are: In which Alternatively, the supplier considers the other strategy such that she provides priority contract service to buyer 1 and walk in service to buyer 2. It is used as an example of how to use the general steps to find the solutions for the optimization problems in other cases. When the supplier provides priority contract service to buyer 1 and walk in service to buyer 2, the optimization model for the supplier is following with decision variables : s.t.

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137 profit is: Let ( supply chain) or Thus which is Substitute

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138 contract to the buyer 1.

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144 BIOGRAPHICAL SKETCH Ruoxuan Wang earned her Bachelor of Engineering in Industrial Engineering from Tsinghua University in 2008. Prior to entering the doctoral program, she worked as an industrial engineering intern at Nissan Motor Corporation at Guangzhou, China. Her research interests encompass the areas of supply chain management, green supply chains and sustainability, capacity planning, outsourcing contracts and supply chain coordination. Ruoxuan received her Ph.D. in business administration from the University of Florida in August 2014 and will join San Diego State University as an assistant professor in Fall 2014.