Equilibrium Facility Location on Networks

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Springer Science & Business Media, Dec 12, 1995 - Science - 245 pages
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This is a book about the simultaneous location, production and distri bution decisions of a firm entering a competitive market whose spatial nature is describable by a network in which the market either achieves an equilibrium or is equilibrium tending. As such, the problem is of clear theoretical and practical importance, for it is a rather general version of the problem faced by real firms every day in deciding where to locate. Further, the timeliness of this subject manifests itself in the growing excitement and interest found both in the research/academic communities and in the practitioner/private industry communities for more comprehensive approaches to competitive facility location analy sis and equilibrium modeling of networks. The desire both for new conceptual approaches yielding enhanced insights and for practical methodologies to capture these insights drives this interest. While nor mative, deterministic facility location modeling techniques currently provide valuable input into the location decision-making process, re searchers and practitioners alike have realized the vast and relatively untapped potential of more advanced location decision making tech niques. In this book, we develop what we believe represents a major new line of research in the field of competitive facility location analysis; namely, equilibrium facility location modeling. In particular, this book offers a number of innovations in the mathe matical analysis and computation of solutions to location models which we have pioneered and which are collected under a single cover for the first time.
 

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Contents

Introduction
1
11 Location Decisions in Spatial Competition
2
12 Criteria for Evaluating Competitive Facility Location Models
3
122 Pricing
5
123 Demand
6
124 Market Conditions
7
125 Transport Markets
8
126 Infrastructure
9
612 The Firm of Interest
93
62 Formulations
94
622 The FOB Mill Price Sizing and Location Model
97
63 The Implicit Function
98
64 Existence Results
101
65 A Solution Algorithm
104
66 Numerical Results
108
661 An Exact or Simultaneous Algorithm
109

128 Algorithms
10
129 Evaluation of Selected Competitive Facility Location Models
11
14 What Motivates the Equilibrium Facility Location Problem?
17
15 Study Objectives
22
16 Organization of Book
23
Aspatial Stackelberg Nash Cournot Equilibria
27
22 Cournot Nash and Stackelberg Nash Cournot Equilibria
29
23 Derivatives of the Implicit Function Qx
31
24 Uniqueness of Stackelberg Nash Cournot Equilibria
35
25 Examples and Algorithm
39
Classical Plant Location on Networks
47
32 Capacitated Plant Location
49
33 Plant Location with Elastic Demands
50
34 Conclusion
54
Spatial Market Equilibria on Networks
55
411 Definition of Spatial Price Equilibrium Model
57
412 The SPE Model in Variational Inequality Form
59
413 Existence and Uniqueness
62
414 Algorithms for Spatial Price Equilibria
63
42 A Spatial Cournot Nash Network Equilibrium Model
69
422 Formulation as a Variational Inequality
73
423 Existence and Uniqueness for Spatial Cournot Nash Equilibria
75
424 Algorithms for Spatial Cournot Nash Equilibria
76
Sensitivity Analysis of Spatial Market Equilibria on Networks
79
51 Sensitivity Analysis for Variational Inequalities
80
512 Differentiability
81
52 Sensitivity Analysis of the Modified SPE Model
83
53 Sensitivity Analysis for Spatial Oligopoly
87
A Facility Sizing and Location in Spatial Price Equilibrium Models
91
61 Economic Settings
92
662 Results
111
Stackelberg Equilibria on Networks
139
72 Cournot Reaction Functions
142
73 Stackelberg Nash Cournot SNC Formulation
145
74 Existence and Uniqueness
147
75 A Sensitivity Based Algorithm for the SNC Equilibrium Problem
148
A Facility Sizing and Location in Stackelberg Nash Cournot Equilibrium Model
155
81 Economic Setting
156
82 Stackelberg Profit Maximization
158
83 Existence and Uniqueness
160
84 Algorithms for the Facility SizingLocation in Stackelberg Nash Cournot Equilibrium Model
161
841 The facility SizingLocation in SNC Equilibrium Algorithm Solved by Explicit Enumeration
163
842 Discussion of Algorithm
164
85 Numerical Results
167
The Importance of Including Reaction Functions and Analysis of Economic Equilibria in Facility Location Models An Example
181
Dynamic Models Equilibrium and Disequilibrium Approaches
193
101 Dynamic Stackelberg Profit Maximization
194
1011 Discussion of Potential Algorithms
202
1012 A Dynamic Profit Maximization Model for the Stackelberg Facility Location and Expansion Problem
203
102 A Dynamic Disequilibrium Facility Location Model
207
1021 Price Flow and Capacity Adjustment Processes
212
1022 A Disequilibrium Facility Location Model
214
103 Conclusion
217
Conclusion
219
Bibliography
223
List of Figures
235
List of Tables
237
Index
241
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Page 229 - Department of Decision Sciences and Information Systems, College of Business Administration, Florida International University...
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Page 234 - Wendell, RE and McKelvey, RD, 1981, New Perspectives in Competitive Location Theory, European Journal of Operations Research 6, 174-182.

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