{"Affiliation":[{"label":"Affiliation","value":"Business, Sauder School of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Sosic, Greys","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2009-10-05T20:00:27Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"2002","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree","value":"Doctor of Philosophy - PhD","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"DegreeGrantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"The three essays in this thesis address various problems in the general area of supply\r\nchain management. In general, supply chain management is concerned with management\r\nof the flow of goods, information, and funds among supply chain members, such as\r\nsuppliers, manufacturers, distributors, retailers, and consumers. As such, its scope\r\nincludes timing and quantity of material flow, logistics, improving efficiencies in\r\nproblems with several decision makers, etc. The first essay in this thesis considers the\r\nproblem of improving coordination in a decentralized system of retailers, while the\r\nsecond one addresses stability and profitability of Internet-based supply exchange\r\nalliances. The third essay analyzes a logistics problem, of finding an optimal route for a\r\ncapacitated vehicle which travels on a graph and which can perform pickups and\r\ndeliveries.\r\nIn the first essay, we study a three-stage model of a decentralized distribution system\r\nwith n retailers who each faces a stochastic demand for an identical product. In the first\r\nstage, before the demand is realized, each retailer independently orders her initial\r\ninventory. In the second stage, after the realization of the demand, each retailer decides\r\nwhat portion of her residual supply\/demand she wants to share with the other retailers. In\r\nthe third stage, residual inventories are transshipped in order to possibly meet residual\r\ndemands, and an additional profit is allocated among the retailers. We study the effect of\r\nimplementing various allocations rules in the third stage on the levels of the residual\r\nsupply\/demand the retailers are willing to share with others in the second stage, and the\r\ntradeoff involved in achieving a solution which is also optimal for the corresponding\r\ncentralized system.\r\nThe second essay is concerned with the formation of Internet-based supply exchange\r\nalliances among three or fewer retailers of possibly substitutable products. We provide\r\nsome conditions, in terms of product substitutability and quality of suppliers, which\r\n\r\nwould lead to the formation of a three member alliance, or a two member alliance, or no\r\nalliance at all. We also study the effect of alliance structure and quality of suppliers on\r\nthe profit of a retailer.\r\nThe third essay considers a vehicle routing problem with pickups and deliveries (VRPD\r\nproblem) on some special graphs. Some vertices on the graph represent delivery\r\ncustomers, and other vertices represent pickup customers. The objective is to find a\r\nminimum length tour for a capacitated vehicle, which starts at a depot and travels on the\r\ngraph while satisfying all the requests by the customers without violating the vehicle\r\ncapacity constraint, and returns to a depot. We have developed linear time algorithms for\r\nthe VRPD problem on a path and on tree graphs, linear and O (|V| log |V|) algorithm for a\r\nVRPD problem defined on a path with parametric initial capacity, and quadratic and\r\nO (|V|\u00b2 log |V|) algorithms for a VRPD problem defined over a cycle graph.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/13611?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"Extent":[{"label":"Extent","value":"7082068 bytes","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/extent","classmap":"dpla:SourceResource","property":"dcterms:extent"},"iri":"http:\/\/purl.org\/dc\/terms\/extent","explain":"A Dublin Core Terms Property; The size or duration of the resource."}],"FileFormat":[{"label":"FileFormat","value":"application\/pdf","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/elements\/1.1\/format","classmap":"edm:WebResource","property":"dc:format"},"iri":"http:\/\/purl.org\/dc\/elements\/1.1\/format","explain":"A Dublin Core Elements Property; The file format, physical medium, or dimensions of the resource.; Examples of dimensions include size and duration. Recommended best practice is to use a controlled vocabulary such as the list of Internet Media Types [MIME]."}],"FullText":[{"label":"FullText","value":"THREE ESSAYS IN SUPPLY CHAIN MANAGEMENT by GREYS SOSIC B.Sc. (Mathematics), University of Zagreb, 1988 M.Sc. (Mathematics), University of Zagreb, 1996 A THESIS SUBMITTED IN PARTIAL F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (THE F A C U L T Y OF C O M M E R C E A N D BUSINESS ADMINISTRATION) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A July 2002 \u00a9 Greys Sosic, 2002 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Operations and Logistics Division Faculty of Commerce and Business Administration The University of British Columbia 2053 Main Mall Vancouver BC, Canada V6T 1Z2 Date 11 Abstract The three essays in this thesis address various problems in the general area of supply chain management. In general, supply chain management is concerned with management of the flow of goods, information, and funds among supply chain members, such as suppliers, manufacturers, distributors, retailers, and consumers. As such, its scope includes timing and quantity of material flow, logistics, improving efficiencies in problems with several decision makers, etc. The first essay in this thesis considers the problem of improving coordination in a decentralized system of retailers, while the second one addresses stability and profitability of Internet-based supply exchange alliances. The third essay analyzes a logistics problem, of finding an optimal route for a capacitated vehicle which travels on a graph and which can perform pickups and deliveries. In the first essay, we study a three-stage model of a decentralized distribution system with n retailers who each faces a stochastic demand for an identical product. In the first stage, before the demand is realized, each retailer independently orders her initial inventory. In the second stage, after the realization of the demand, each retailer decides what portion of her residual supply\/demand she wants to share with the other retailers. In the third stage, residual inventories are transshipped in order to possibly meet residual demands, and an additional profit is allocated among the retailers. We study the effect of implementing various allocations rules in the third stage on the levels of the residual supply\/demand the retailers are willing to share with others in the second stage, and the tradeoff involved in achieving a solution which is also optimal for the corresponding centralized system. The second essay is concerned with the formation of Internet-based supply exchange alliances among three or fewer retailers of possibly substitutable products. We provide some conditions, in terms of product substitutability and quality of suppliers, which Ill would lead to the formation of a three member alliance, or a two member alliance, or no alliance at all. We also study the effect of alliance structure and quality of suppliers on the profit of a retailer. The third essay considers a vehicle routing problem with pickups and deliveries (VRPD problem) on some special graphs. Some vertices on the graph represent delivery customers, and other vertices represent pickup customers. The objective is to find a minimum length tour for a capacitated vehicle, which starts at a depot and travels on the graph while satisfying all the requests by the customers without violating the vehicle capacity constraint, and returns to a depot. We have developed linear time algorithms for the VRPD problem on a path and on tree graphs, linear and O (| V\\ log | V\\) algorithm for a VRPD problem defined on a path with parametric initial capacity, and quadratic and O (| V\\2 log | V\\) algorithms for a VRPD problem defined over a cycle graph. Table of Contents Abstract... ii Table of Contents iv List of Figures vii List of Tables viii Acknowledgements ix CHAPTER 1 Introduction 1 1.1 Supply chain management 1 1.3 Game-theoretical concepts 2 1.2.1 Non-cooperative games 3 1.2.2 Cooperative games 4 1.2.3 Monotonic allocation rules 7 1.3 Summary of contributions 8 CHAPTER 2 A three-stage model for a decentralized distribution system of retailers 11 2.1 Introduction 11 2.2 The A B Z distribution model 14 2.3 The three-stage model and some related models 17 2.3.1 A decentralized system without transshipments 19 2.3.2 A centralized system with transshipments 20 2.3.3 A decentralized system with transshipments 21 2.4 Game-theoretical concepts... 24 2.4.1 Core allocations for transshipment games. ; : 25 2.4.2 Monotonic allocation rules for transshipment games 25 V 2.5 Allocations based on dual prices 27 2.6 Core allocations 30 2.6.1 Two players 30 2.6.2 Three players 31 2.6.3 Four players 33 2.6.4 General case 35 2.7 Achieving a first best solution 35 2.8 Conclusion 37 2.9 Appendix 39 CHAPTER 3 Formation of alliances in Internet-based supply exchanges 56 3.1 Introduction 56 3.2 The model 60 3.3 Profit as a function of alliance structure 63 3.3.1 Two-retailer alliance \u2022\u2022 64 3.3.2 Three-retailer alliance 67 3.4 Preference for a partner 70 3.4.1 Preference for a partner in a two-retailer alliance 70 3.4.2 Participation in a two-retailer alliance when profit decreases 71 3.5 Stability criteria : 73 3.6 Stable coalition structures 77 3.7 Concluding remarks 81 3.8 Appendix 85 CHAPTER 4 The vehicle routing problem with pickups and deliveries (VRPD) on some special graphs 98 4.1 Introduction 98 VI 4.2 Preliminary and notation 99 4.3 The VRPD problem on a path 101 4.4 The VRPD problem on a tree graph 104 4.4.1 The case where s = t 105 4.4.2 The tree case where 5 and t are predetermined 106 4.4.3 The case where t is endogenously determined 107 4.4.4 The tree case with s and t endogenously determined 109 4.5 The VRPD problem on a cycle graph I l l 4.5.1 The VRPD (C, r, N) problem with s and \/ endogenously determined 112 4.5.2 The VRPD problem on a cycle graph when s and t are predetermined and s\u00b1t..\\\\4 4.5.3 The VRPD problem on a cycle graph when 5 and \/ are predetermined and s = r..l28 4.6 Appendix 129 Bibliography 140 List of Figures vu CHAPTER 4 Figure 4.1 Form(l) 1 1 7 119 Figure 4.2 Form (2) 120 Figure 4.3 Form (3) 121 Figure 4.4 Form (4) Figure 4.5 Example ^ 5 List of Tables V l l l CHAPTER 2 Table 2.1 Payoffs for a discrete transshipment game with two players 45 CHAPTER 3 Table 3.1 Conditions for an increase in a retailer i's profit in the alliance (ij) 66 Table 3.2 Conditions for an increase in retailers' profit when k joins the alliance (if) 68 Table 3.3 Conditions for an increase in i's profit when independent retailers join in (ijk).... 69 Table 3.4 Retailer i's preferences for pairing when A'', > A ' , 71 CHAPTER 4 Table 4.1 Demands in the vertices 125 Table 4.2 Lengths of the arcs 126 Table 4.3 Step 1, w(7\/,) = 46 126 Table 4.4 Step 2, w(T2) = 46 127 Table 4.5 Step 3, w(T}) = 44 127 Table 4.6 Step 4, w(T4) = 50 127 Table 4.7 Step 5, w(T5) = 46 128 Acknowledgements IX First of all, I would like to thank Professors Daniel and Frieda Granot, my research supervisors, for their continuous support and encouragement through my years spent at UBC. They both provided me with the essential guidance, and I consider myself very lucky for the opportunity of working with them. I am extremely grateful to Danny for introducing me to the field of Game Theory and spending many hours discussing my research and reviewing my work. My thanks also go to Professors Derek Atkins and Charles Weinberg, who served on my supervisory committee and provided valuable comments on my work, and many other faculty members at U B C , who were always willing to offer their assistance. I am also grateful to Professors Luka Neralic and Sanjo Zlobec, who served on the supervisory committee for my Masters thesis in Zagreb, and provided me with the advice and guidance, that eventually resulted in my joining the Doctoral program at U B C . And finally, my deepest thanks go to my family - my parents, my sister, and my fiancee - who were always there when I needed them. Chapter 1 Introduction 1.1 Supply chain management The essays in this thesis address various problems in the general area of supply chain management. In general, supply chain management is concerned with management of the flow of goods, information, and funds among supply chain members, such as suppliers, manufacturers, distributors, retailers, and consumers. Although the term supply chain management became increasingly popular in recent years, some of the problems that supply chain management deals with are not as new. As an exam-ple, inventory control, which is nowadays a topic in supply chain management, was considered by scientists at the beginning of the 20th century, when Harris published two papers (1913, 1915) that dealt with decisions in inventory control. In addition to analyzing timing and quantity of material flow, which is the topic of multi-echelon inventory theory, research in supply chain management covers much broader topics, such as product design, production, contracts, performance measures and quality control, logistics, etc. While the early research in supply chain management analyzed mostly problems with the objective of minimizing the cost of a single decision maker, current work in 1 CHAPTER 1. INTRODUCTION 2 this area broadened the nature of the problems being considered. Thus, recent papers are often concerned with profit maximization instead of cost minimization, and the fo-cus has shifted from a single company to the more realistic case, wherein relationships among several companies are being studied. One of the important problems addressed by supply chain management today is improving efficiencies in models with several decision makers, where each decision maker is a member of the supply chain who optimizes his individual goals, which may lead to a solution that is not globally opti-mal (e.g. double marginalization). Situations with multiple decision makers required a new paradigm for modeling, and the use of game theory is becoming increasingly popular in this area. Thus, non-cooperative game theory is used for modeling com-petitive framework, wherein each decision maker is concerned with optimizing his individual objectives, while cooperative games are being used to study cooperative behavior among the companies that may lead to an increase in profit realized by com-panies involved. Since the first two essays in the thesis fall into this category and use game-theoretical framework, let us briefly introduce here some concepts from game theory. 1.2 Game-theoretical concepts We start with some definitions related to non-cooperative games, which are used as a framework for modeling competitive behavior among the firms. This subsection is mostly based on Fudenberg and Tirole (1991). We then proceed by introducing some elements from cooperative game theory, which will be used for modeling cooperation among the firms, and some monotonicity concepts, which will be used in the first essay. CHAPTER 1. INTRODUCTION 3 1.2.1 Non-cooperative games A game in a strategic form has three elements: the set of players N = {1,2,... ,n}, the pure strategy space Si for each player i, and payoff functions Ui(s) for each strategy profile s = ( s i , S 2 , . . . , sn), Sj 6 5j. A mixed strategy <7j is a probability distribution over pure strategies. Let z_i :\u2014 (zi,..., Zi_i, Zi+\\,..., z^), V Z e i R n . \u2022 A mixed-strategy profile a* is a Aas\/j equilibrium if, for all players i , Mi (^ ' ^ I i ) > VSi e Si. A pure-strategy Nash equilibrium is a pure-strategy profile that satisfies the same conditions. When a game has several \"stages\", we may want to impose some additional re-strictions on the Nash equilibria, in order to \"pick\" those equilibria that are more \"credible\" or \"reasonable\". More formally, we will say that a multi-stage game with observed actions is a game where all players knew the actions chosen at all previous stages, 0 , 1 , . . . , k \u2014 1 , when choosing their actions at stage k, and where all players move simultaneously in each stage. Let hk+1 denote the history at the end of stage k, that is, the sequence of actions in the previous periods. Further, let G(hk) denote the game from stage k on with history hk, and let a strategy profile s\\hk be defined in a following way: For each player i, Si\\hk is the restriction of sz to the histories consistent with hk. \u2022 A strategy profile s of a multi-stage game with observed actions is a subgame-perfect Nash equilibrium if, for every hk, the restriction s\\hk to G(hk) is a Nash equilibrium of G(hk). Besides considering only games wherein players act unilaterally, noncooperative framework can also be used for the analysis of coalition deviation. Some of the approaches are given below. CHAPTER 1. INTRODUCTION 4 \u2022 A strategy profile is said to be a strong Nash equilibrium (Aumann, 1959) if no set of players can jointly deviate and make all of its members better off. Un-like Nash equilibrium, which considers only unilateral deviations, strong Nash equilibrium considers deviations by all proper coalitions. Although applied to noncooperative environment, this solution concept requires some form of bind-ing agreement among the players - players have to follow strategies they have agreed upon, even if some of them might profit by deviating. \u2022 Coalition-Proof Nash equilibrium (Bernheim, Peleg and Whinston, 1987) in-volves \"self-enforcing\" agreements among the members of a coalition. That is, an agreement is coalition-proof if it is efficient within the class of self-enforcing agreements, where self-enforceability requires that no coalition can benefit by deviating in a self-enforcing way. Coalition-Proof Nash equilibrium is farsighted, in the sense that it takes into consideration possible future deviations by play-ers, but the attention is restricted to deviations that are immune to deviations by subcoalitions. In other words, it does not take into account the possibility that some members of the deviating coalition may further deviate with someone outside that coalition. 1.2.2 Cooperative games A pair (N,v), where N \u2014 {1,2,... ,n} is the set of players, and v : 2N -> IR is a function such that w(0) = 0, is called a (revenue) cooperative game, or an n-person game in coalitional form. A subset S C N is called a coalition, N is called the grand coalition, and v is called the characteristic function of the game. In general, v(S) represents the revenue that coalition S can achieve on its own. A coalition structure, B, is a partition on N. That is, B = {Bu ..., Bm}, B, C N for all i, U\u2122 ^ = N, B3r\\Bk = $,j^k. A mapping $ which assigns to every cooperative game (N,v) a subset $(u) C IRn is called a solution concept. $ is a one-point solution concept if $(v) assigns a single vector, cp = (cpi,..., cpn) \u00a3 MN, to every cooperative game (N, v).- We will refer to CHAPTER 1. INTRODUCTION 5 one-point solution concepts as allocation rules, and the value,
f \u00b0 r a u Some of the solution concepts which are often used and have some desirable properties are given below. \u2022 The fractional rule - it allocates a fixed portion of the value of the grand coali-tion to each player, ipi = jiv(N), ji > 0, Y,N7I \u2014 1- Clearly, the egalitarian rule is a special case of the fractional rule with 7* = 1\/n V i \u2022 The core (Gillies, 1959) - an allocation ip is a member of the core of (N,v) if it satisfies If $(w) is an element of the core for every cooperative game (N,v), then $ will be referred to as a core allocation rule. When core allocations are used, no subset of players has an incentive to secede from the grand coalition and form its own coalition, because they collectively receive at least as much as what they can obtain as a coalition. In general, the core can be an empty set. \u2022 Nucleolus (Schmeidler, 1969) - the unique allocation ip that lexicographically minimizes the vector of excesses e(S,tp) = v(S) \u2014 Y^sVi-, S C N, when these excesses are arranged in nonincreasing order. The nucleolus is always in the core when the core is nonempty, and it is a piecewise linear function of v. \u2022 Shapley value (Shapley, 1953) - an allocation rule that satisfies the following axioms: 1. Symmetry: for all permutations ir of N, Q^fav) = $i{v), where by irv we mean u(= nv) such that, for any S = i2, \u2022 \u2022 \u2022, is}, \u00ab(Mi i ) ,7r( i2) , . . . ,7r(is)}) = v(S); TZ=1 0, i = l ,2 ,3,4 > minimi , z = 2,3,4 1 1 (2.17) > m i n { # i , \u00a3 i + \u00a3,\u2022}, i,j = 2,3,4, i 4 = 0. CHAPTER 2. A THREE-STAGE MODEL 49 Since (fi + p3 + y?4 > i>({l,3,4}) = 8, we must have 8. 2. Either player 3 or player 4 decides to share only 2, all other players share everything. For simplicity, assume that Hx = H2 = 12, E3 = 2, EA = 4, E5 = 6, E6 = 10. As it was done in the first case, it is easy to verify that in every core allocation for this instance, player 3 receives at least 2 units, while the total additional profit decreases by 2 units. To avoid such a case, the allocations to players 3 and 4 cannot be smaller than 2 => cp3, cp4 > 2. 3. Player 5 decides to share only 4, all other players share everything. We have Hi \u2014 H2 = 12, E3 = E4 = E5 = 4, E6 = 10; it is easy to verify, as it was done in the first case, that in every core allocation for this instance, player 5 never receives less than 2 units, while the total additional profit decreases by 2 units. To avoid such a case, the allocation to player 5 cannot be smaller than 2 => 3 = E3\/2, ip4 = E4\/2. However, when Hi + H2 < E3 + E4, a continuum of Nash equilibria exists, namely (HX,H2, E3, Hx + H2 - E3) with E3 G [max{0, Hx + H2- E4), E3}. None of these Nash equilibria is completely sharing, but all of them are value-preserving. Chapter 3 Formation of alliances in Internet-based supply exchanges 3.1 Introduction After its initial boom in the year 2000, which was followed by a period of a somewhat slower growth, business-to-business commerce is again getting stronger in the year 2002. While the volume of B2B commerce in 2000 was $226 billion, eMarketer, a provider of Internet and e-business statistics, estimates that it reached $449 billion in 20011. Many researchers predict huge B2B revenues for the year 2002: eMarketer predicts $820 billion, Forrester Research $2,061 trillion, Goldman Sachs $1.3 trillion, to mention just a few2. On-line marketplace sales accounted for less than one percent of total B2B transactions in 2000, which, nevertheless, represented a 585 percent increase from 19993. Ovum, a UK-based consulting company, predicts that this number will further grow, from five percent in 2001 to 35 percent in 20064. 1 \"E-Business Numbers 2001\", Line56 News, January 31, 2002 2\"eMarketer's Sunny B2B Outlook\", Line56 News, March 5, 2002 3 \"E-Markets: Back Again\", Line56 News, November 15, 2001 4 \"Ovum's E-Business Big Five\" ,Line56 News, January 17, 2002 56 CHAPTER 3. FORMATION OF ALLIANCES 57 In different industries, such as automobiles, chemicals, or retailing, competitors are joining forces in establishing electronic marketplaces in order to reduce inefficiencies in the purchasing process and cut the costs, by combining their buying power. With an electronic exchange, the seller needs to list his products only once, while currently suppliers have to notify buyers individually about the current availability of products, and buyers have to shop around. The saving of $250 million by I B M when buying $13 billion worth of parts on the Web in 19995 can serve as an illustration of the potential savings that can result from on-line purchases. Various companies, including Boeing, DuPont, Sears Roebuck, General Motors, and Ford, have joined with their rivals to form industry marketplaces. Exostar is a global e-marketplace founded by some of the world's largest aerospace and defense companies - B A E Systems, Boeing, Lockheed Martin Corp, Raytheon Co., and Rolls-Royce. ChemConnect is an online chemicals and plastics marketplace, which has among its members companies such as B A S F A G , BP, The Dow Chemical Com-pany, DuPont, ShellChemicals, and many others. Hitachi, I B M , Nortel Network, Seagate Technology, Toshiba, L G Electronics and Matsushita Electrics (Panasonic) have founded e2open.com, an e-marketplace for buyers and sellers of technology prod-ucts. The largest online exchange created so far is Covisint, initiated by the Big Three automakers. Ford and G M announced on February 25, 2000 that they will merge their Internet-based supply exchanges, and that DaimlerChrysler will join the venture. This exchange was joined by Nissan and Renault on April 14, 2000, and by Peugeot Citroen on May 22, 2001. The venture is planned to operate as an independent company, with each of the Big Three automakers having an equal ownership, for the purpose of creating a single auto-parts exchange for their suppliers. The Big Three, who spend around $247 billion annually on purchases from their 30,000 suppliers, plan to to hold auctions for equipment and supplies. In May 2001, one such auction was conducted, involving DaimlerChrysler and five suppliers. 1,200 parts worth over 3 billion euros were exchanged, making it the largest on-line auction ever conducted 5 \" I B M to unveil component marketplace on Net\", CNET News, May 1, 2000 CHAPTER 3. FORMATION OF ALLIANCES 58 on an exchange6. Kevin English, Covisint's president and C E O , announced that Covisint's auction site handled $51 billion in transactions in 2001, which was its first full year of service. Covisint expects that the auction and procurement functions will reduce unwanted inventory and cut bureaucracy and cost. According to Ford, labor and paperwork costs for a single purchase average $150, while corresponding online cost ranges $5-$157. Investment bankers have predicted, according to the Covisint webpage, that the exchange will yield a saving of $2,000-$3,000 per vehicle on a $19,000 vehicle. However, not all automakers are willing to join Covisint. Volkswagen announced8 its plans for establishing a rival exchange, that would lead to substantial savings through inventory reduction resulting from a more efficient supply chain and through lower prices. B M W also announced9 the intent to build its own marketplace, to solicit proposals from part suppliers and to conduct online buying auctions. Some key electronic companies, including Sun Microsystems and Oracle, are being more cautious before linking with their rivals. Their opinion is that huge market-places shared with competitors could compromise their confidential list of approved vendors10. A Merrill Lynch analyst has recently stated that some leading technology companies (Sun, Oracle, General Electrics) do not believe in big online exchanges, such as Covisint or e2open.com. Sun views its approved vendor list as \"top secret\" and cannot understand why HP wants to share information with Compaq, or Ford with G M . Instead, he argues that Sun believes that it is more useful to set up its own private auction exchange to ensure privacy and to keep its top vendors under wraps. Thus, on one hand, the decision to join a marketplace forces a company to share its suppliers with other alliance members. On the other hand, alliance membership leads to reduced costs, including those of possible rivals, since members share the develop-ment and operation costs, and a larger marketplace may also lead to a more intense 6 \"Largest auction ever?\", Line56 News, May 16, 2001 7 \" F T C green-lights Big Three Net exchange\", CNET News, September 11, 2000 8\"Volkswagen plans Internet exchange to rival G M , Ford\", CNET News, Apr i l 12, 2000 9 \" B M W builds Net marketplace with Ar iba\" , CNET News, Apr i l 20, 2000 1 0 \"Tech companies wary of online exchanges\", CNET News, June 13, 2000 CHAPTER 3. FORMATION OF ALLIANCES 59 competition among the increased number of suppliers. In addition, an alliance mem-ber may further benefit at the expense of companies left outside the alliance. Some natural questions that could arise are, then, when would a firm prefer to take part in an electronic marketplace joint venture, when would it prefer that other firms, possi-bly rivals, join the venture, and what are the financial consequences of either joining an alliance or remaining independent? In an attempt to gain a better understanding of the issues, we have constructed a model with three companies, wherein a certain degree of substitutability may exist between the products of any two companies. In particular, we provide some conditions, in terms of product substitutability and qual-ity of suppliers, that lead to the formation of an alliance of all three retailers, or the alliance of only two retailers, or the case where no alliance is formed because all retailers prefer to act independently. We also study the effect of alliance structure and quality of suppliers on the profit of a company. We note that our analysis can be extended to more general strategic alliances, in which membership in an alliance leads to a decrease in input prices and\/or operating costs. In our model, we assume that demands are linear and deterministic, and that all retailers have complete information. This is clearly a great simplification, but we believe it can be used for an initial approach to the problem. Although there is a large body of literature on strategic alliances, as far as we know, there is not much written about alliance formation in on-line exchanges. For some related work on supply chain contracting and supplier coalitions in electronic markets, see Jin and Wu (2000, 2001). For an analysis of general strategic alliances, see, e.g., Lewis (1990), and for an analysis of alliances in airline industry, see, e.g., Oum et al. (2000). . The structure of the essay is as follows. In the next section, we present our model with three retailers of possibly substitutable products, where the demand functions are obtained as natural extensions of the demand functions used in the two-retailers model introduced by McGuire and Staelin (1983). In Section 3.3 we study the changes in a retailer's profit as a function of the substitutability levels among products, qual-ity of suppliers, and market structure. Section 3.4 analyzes retailers' preference for a CHAPTER 3. FORMATION OF ALLIANCES 60 partner in a two-retailer alliance. Section 3.5 briefly introduces, as stability criteria, the farsighted coalitional stability and the largest consistent set, which are subse-quently used in our analysis. In Section 3.6, we characterize some stable alliance structures for some special cases, wherein all products are either non-substitutable or highly substitutable, and in Section 3.7, we demonstrate that our results shed some light on the issues discussed above, and we further discuss the applicability of our results to more general situations with more than three retailers. A l l proofs are given in the Appendix. 3.2 T h e model We are presenting a model with three retailers, where the demand functions are obtained as natural extensions of the demand functions used in the model of two retailers with possibly substitutable products and deterministic and linear demands, introduced by McGuire and Staelin (1983). Following their notation, let S represent a scale factor corresponding to the industry demand when the prices of all products are set to zero, while the \/i's and 0's represent two aspects of product differentiation - the absolute difference in demands and the substitutability of two products, respectively. Changes in \/i's alter the relative product preferences, while changes in #'s affect the substitutability of the two products. When % = 0, products i and j have independent demands; product substitutability increases with dij, and they become highly substitutable as 6%j \u2014> 1. The demand functions are given by: c L P Pi g pi 2 V k [i - e^ii - elk) with i,j,k e {1,2,3} such that i ^ j ^ k ^ i, 0 < (ii, \/i2, ^3 < 1, Mi + fJ-2 + M3 = 1) P > 0) 3 > 0, and 0 < % < 1. Notice that when there is no substitutability among the products, the term within the brackets reduces to 1 \u2014 Bp\\, which corresponds to a standard demand for a single product. Similarly, when one product, k, is not substitutable by the two remaining products, i and j, the equations for q[ and q'j coincide with the demand functions in the McGuire-Staelin model. CHAPTER 3. FORMATION OF ALLIANCES 61 We are assuming that the demands q\\ are non-negative, which can be written as 2(1 - 0\u201e-)(i - eik) - 2pp\\ + pelJ(2 - One)?', + peik{2 - el3)P'k > o, for k \u00a3 {1, 2, 3} such that i ^ j ^ k ^ i. This leads to the following assumption about the retailers' profits. Assumption 3.1 The profit realized by each retailer (in any alliance structure) is non-negative, !![ = q'i(p'i \u2014 w'^j > 0. Following the lead of McGuire-Staelin, we rescale the model in order to reduce the number of variables. The rescaled model will involve only the retail prices, Pi,p2,P3, and the coefficients of substitutability, #12, #13, #23- Thus, let Qi = HiS' P , P l ( i _ ^ . ) ( l - 0 l f c ) P \" P , (i - el3){i - elk)w^ for i,j,k \u00a3 {1,2,3} such that i 7^ j \/ k ^ i. Using the rescaled variables, the demands can be expressed in terms of the rescaled prices and coefficients of substi-tutability as qi = 1 - pi +.\u2014 2 - Oij Q 2 - 9ik a (3.1) 1 \u2014 Uij 1 \u2014 Uik for k \u00a3 {1, 2, 3}, i 7^ j 7^ k 7^ i, while the profits are given by Ui = (pt - Wi)qi, i = 1,2,3. The following relationships between profits and rescaled profits hold: n 2 = \u2014 ^ z \u2014 \/ T 7 1 \u2014 ^ n ; , i,j,k e {1,2,3}, % \u00b1 3 \u00b1 k \u00b1 i, or IT; = PiFlj. Observe that px does not depend on the variables pt and Wi, hence the analysis of the retailers' behavior based on IIj's will lead to the same results as the analysis based on 174's. CHAPTER 3. FORMATION OF ALLIANCES 62 The first order conditions that the rescaled profits Ui need to satisfy with respect to the rescaled retail prices pi result in the following system of equations: 1 - 2pi + 1 \u2014 9jk 2 \u2014 9, ik eljPj + 1 \u2014 6jk 2 \u2014 9i e. OikPk + Wi = 0, 2 i-elk ^J 2 i for i, j, k \u00a3 {1,2, 3}, i ^ j ^ k ^ i. Let us denote a = 32 - 923(2 - 9l3-9l2)(4- 913912)- 9213(2 - 923 - 912)(4- 9239l2)-- 922 (2 - 923 - 913)(4 - 9239l3) - 89239l39l2 + 9\\39\\39\\2. Then, the solution of the system (3.2) is given by (3.2) Vi 1 6 - ^ ( 2 - % ) ( 2 - ^ ik a (1 + Wi) + + (1 - 9jk)(2 - 9ik) _ 49ij + 9jk9ik{2 - %) ^ + w.^ + ( i - 9lk) a (1 \u2014 9jk){2 \u2014 9ij) 49ik + 9jk9ij(2 \u2014 9ik) (1 + VJk), (1 - 9l3) a for z,jf, A; \u20ac {1,2,3}, i ^ j ^ k ^ i. By substituting the expressions for p; in (3.1), we obtain: 16 - 9%(2 - 9lk)(2 - 9tJ) _ r _ 1 6 - ^ f c ( 2 - ^ ) ( 2 - % ) -ft = + (1 \u2014 fl?fc)(2 - i^fc) 4% + 9jk9ik(2 \u2014 Qjj) (1 - ' a (1 \u2014 9jk)(2 - 9ij) 49ik + 9jk9ij(2 - 9ik) (1 - %) a Let us now introduce the following notation: Ai = 16-92jk(2-9tJ)(2-9lk), Bi = 49jk + 9ij9ik(2 \u2014 9jk), 7z = 1+ 1 (1 + Wj)-(1 + lWfc). 1 \u2014 Observe that cn > 0, Ai > 0,Bi > 0, 7 i > 0. The above expressions for the retail prices and demands can, consequently, be rewritten as Pi = ^{Al{l + wi) + (l-9jk)[jjBk{l + wj)+jkBj{l + wk)}}, q, = ^ {A, - (a - A^w, + {1 - 9]k)[-fjBk{l + Wj) +-fkBj{l + wk)}} , (3.3) CHAPTER 3. FORMATION OF ALLIANCES 63 and therefore, the profit for retailer i is given by M (3.4) = ^{Ai-(a- Ai)wi + (1 - 9jk)[