## Equilibrium Facility Location on NetworksThis 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 |

223 | |

List of Figures | 235 |

List of Tables | 237 |

241 | |

### Other editions - View all

Equilibrium Facility Location on Networks Tan C. Miller,Terry L. Friesz,Roger L. Tobin Limited preview - 2013 |

Equilibrium Facility Location on Networks Tan C. Miller,Terry L. Friesz,Roger L. Tobin No preview available - 2014 |

Equilibrium Facility Location on Networks Tan C. Miller,Terry L. Friesz,Roger L. Tobin No preview available - 2010 |

### Common terms and phrases

approach assumed assumptions bilevel capacity Chapter competitors constraints cost functions Cournot firms Cournot reaction function Cournot-Nash equilibrium Data for Problem delivered price denotes developed diagonal dynamic economic equilibrium enumeration equi equilibrium facility location equilibrium problem equilibrium solution facility location models facility sizing facility sizing/location Firm 1 Firm firm locates firm of interest Fixed Sol'n FOB mill price Friesz implicit function inverse demand iteration Jacobian librium linear approximation locating firm location problem location submodel market equilibria mathematical programming Nash Equilibrium node non-negative nonlinear nonlinear complementarity problem Notation objective function oligopolistic oligopoly optimal period plant location price equilibrium model price function production and shipping production facility production levels profit function profit maximizing quantities represents revenue function Scenario Section sensitivity analysis sizing and location sizing/location in SPE SNC equilibrium solve spatial network spatial price equilibrium SPE model SPE submodel Stackelberg firm Step Table tion Tobin variational inequality vector

### Popular passages

Page 229 - Department of Decision Sciences and Information Systems, College of Business Administration, Florida International University...

Page 232 - Iterative methods for variational and complementarity problems...

Page 234 - Wendell, RE and McKelvey, RD, 1981, New Perspectives in Competitive Location Theory, European Journal of Operations Research 6, 174-182.