Competitive Location Models

This chapter first provides a review of the foundations of competitive location models. It then traces subsequent developments through the decades under special consideration of customer behavior. After developing a general framework for customers’ decision making, the main results are put into this framework. The conclusion outlines a number of areas, in which existing models can be refined and made more realistic.

[1]  Ying Zhang,et al.  The competitive facility location problem under disruption risks , 2016 .

[2]  David Delgado-Gómez,et al.  Cournot–Stackelberg games in competitive delocation , 2017, Ann. Oper. Res..

[3]  Jacques-François Thisse,et al.  Competition in Multi-Characteristics Spaces: Hotelling Was Almost Right , 1996 .

[4]  Simon P. Anderson Spatial competition and price leadership , 1987 .

[5]  Ralph M. Braid Retail competition along intersecting roadways , 1989 .

[6]  Ralph M. Braid,et al.  The locations of firms on intersecting roadways , 2013 .

[7]  Damien Neven,et al.  Market efficiency with combinable products , 1989 .

[8]  Fu-Chuan Lai,et al.  Spatial competition with quadratic transport costs and one online firm , 2014 .

[9]  Paolo Giudici,et al.  Data mining of association structures to model consumer behaviour , 2002 .

[10]  Ahmad Makui,et al.  A firefly algorithm for solving competitive location-design problem: a case study , 2016 .

[11]  Jean Jaskold Gabszewicz,et al.  Spatial competition and the location of firms , 1986 .

[12]  B. Eaton,et al.  FREE ENTRY IN ONE‐DIMENSIONAL MODELS: PURE PROFITS AND MULTIPLE EQUILIBRIA* , 1976 .

[13]  Z. John Zhang,et al.  Price-Matching Policy and the Principle of Minimum Differentiation , 1995 .

[14]  Uni Martinsen,et al.  Environmental practices as offerings and requirements on the logistics market , 2014, Logist. Res..

[15]  Roberta Capello,et al.  One or infinite optimal city sizes? In search of an equilibrium size for cities , 2013 .

[16]  Pierre Hansen,et al.  Algorithms for Voting and Competitive Location on a Network , 1988, Transp. Sci..

[17]  P. Zarembka Frontiers in econometrics , 1973 .

[18]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[19]  Zvi Drezner,et al.  Solving the multiple competitive facilities location problem , 2002, Eur. J. Oper. Res..

[20]  H. Singer,et al.  Some Notes on Duopoly and Spatial Competition , 1937, Journal of Political Economy.

[21]  Lee G. Cooper,et al.  Parameter Estimation for a Multiplicative Competitive Interaction Model—Least Squares Approach , 1974 .

[22]  T. Drezner Optimal continuous location of a retail facility, facility attractiveness, and market share: An interactive model , 1994 .

[23]  Artem A. Panin,et al.  Bilevel competitive facility location and pricing problems , 2014, Autom. Remote. Control..

[24]  Bahar Yetis Kara,et al.  Hub location under competition , 2016, Eur. J. Oper. Res..

[25]  Gilbert Laporte,et al.  The Existence of Equilibria in the 3-Facility Hotelling Model in a Tree , 1993, Transp. Sci..

[26]  Said Salhi,et al.  Facility Location: A Survey of Applications and Methods , 1996 .

[27]  Jacques-François Thisse,et al.  OPTIMAL TRANSPORTATION POLICY WITH STRATEGIC LOCATIONAL CHOICE , 1995 .

[28]  Simon P. Anderson,et al.  Cournot Competition Yields Spatial Agglomeration , 1991 .

[29]  André de Palma,et al.  Spatial competition under uniform delivered pricing , 1987 .

[30]  Gilbert Laporte,et al.  OBJECTIVES IN LOCATION PROBLEMS. , 1995 .

[31]  Jacques-François Thisse,et al.  Mixed Oligopoly With Differentiated Products , 1991 .

[32]  A. Shaked Existence and Computation of Mixed Strategy Nash Equilibrium for 3-Firms Location Problem , 1982 .

[33]  Blas Pelegrín,et al.  Single facility location on a network under mill and delivered pricing , 2006 .

[34]  Andrew Caplin,et al.  Aggregation and Imperfect Competition: On the Existence of Equilibrium , 1991 .

[35]  Oded Berman,et al.  Flow-Interception Problems , 1995 .

[36]  Jacques-François Thisse,et al.  Competitive location on networks under delivered pricing , 1990 .

[37]  M. Teitz LOCATIONAL STRATEGIES FOR COMPETITIVE SYSTEMS , 1968 .

[38]  Robert Rothschild,et al.  The effect of sequential entry on choice of location , 1979 .

[39]  H. A. Elselt Perception and information in a competitive location model , 1998, Eur. J. Oper. Res..

[40]  Vladimir Marianov,et al.  On agglomeration in competitive location models , 2016, Ann. Oper. Res..

[41]  V. Marianov,et al.  Finding locations for public service centres that compete with private centres: Effects of congestion , 2004 .

[42]  José Fernández,et al.  Location equilibria for a continuous competitive facility location problem under delivered pricing , 2014, Comput. Oper. Res..

[43]  Phillip J. Lederer,et al.  Competition of Firms: Discriminatory Pricing and Location , 1986 .

[44]  Atsuyuki Okabe,et al.  Stability of Spatial Competition for a Large Number of Firms on a Bounded Two-Dimensional Space , 1987 .

[45]  Gilbert Laporte,et al.  Locational equilibrium of two facilities on a tree , 1990 .

[46]  Athanasios Migdalas,et al.  Nash type games in competitive facilities location , 2016 .

[47]  Elon Kohlberg,et al.  Equilibrium store locations when consumers minimize travel time plus waiting time , 1983 .

[48]  J. Tsai,et al.  Spatial duopoly with triangular markets , 2005 .

[49]  M. J. Hodgson A Flow-Capturing Location-Allocation Model , 2010 .

[50]  Charles ReVelle,et al.  Competitive Location and Pricing on Networks , 1999 .

[51]  Blas Pelegrín,et al.  On tie breaking in competitive location under binary customer behavior , 2015 .

[52]  Dominik Kress,et al.  Sequential competitive location on networks , 2013, Eur. J. Oper. Res..

[53]  Jacques-François Thisse,et al.  Spatial discrimination: Bertrand vs. Cournot in a model of location choice , 1989 .

[54]  H. A. Eiselt Different pricing policies in Hotelling's duopoly model , 1991 .

[55]  Stefano Benati,et al.  An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem , 2003, Ann. Oper. Res..

[56]  Dominik Kress,et al.  Competitive Location and Pricing on Networks with Random Utilities , 2015, Networks and Spatial Economics.

[57]  D. Serra,et al.  Market capture by two competitors: The pre-emptive location problem , 1994 .

[58]  Vladimir Marianov,et al.  Optimal location of public health centres which provide free and paid services , 2001, J. Oper. Res. Soc..

[59]  Jacques-François Thisse,et al.  The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity , 1985 .

[60]  R. Selten Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[61]  Equilibrium existence in the linear model: Concave versus convex transportation costs* , 2005 .

[62]  Juan José Salazar González,et al.  A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem , 2003, Oper. Res..

[63]  Oded Berman,et al.  Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities , 1998 .

[64]  Horst A. Eiselt,et al.  Stability Of Nash Equilibria In Locational Games , 1995 .

[65]  Charles ReVelle,et al.  Surviving in a Competitive Spatial Market: The Threshold Capture Model , 1999 .

[66]  James J. H. Liou,et al.  A novel decision rules approach for customer relationship management of the airline market , 2009, Expert Syst. Appl..

[67]  R. Lipsey,et al.  The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition , 1975 .

[68]  Hans-Christoph Wirth,et al.  (r, P)-centroid Problems on Paths and Trees , 2009, Theor. Comput. Sci..

[69]  Zvi Drezner,et al.  Facility location - applications and theory , 2001 .

[70]  A. Shared Non-existence of Equilibrium for the Two-dimensional Three-firms Location Problem , 1975 .

[71]  Noriaki Matsushima,et al.  Cost differentials and mixed strategy equilibria in a Hotelling model , 2009 .

[72]  Simon P. Anderson Equilibrium existence in the linear model of spatial competition , 1988 .

[73]  Avijit Ghosh,et al.  Multiple Outlets in a Duopoly: A First Entry Paradox , 2010 .

[74]  H. Hotelling Stability in Competition , 1929 .

[75]  W. DeSarbo,et al.  Product Positioning Under Price Competition , 1990 .

[76]  Tammy Drezner,et al.  A review of competitive facility location in the plane , 2014, Logist. Res..

[77]  André de Palma,et al.  SPATIAL EQUILIBRIUM WITH FOOTLOOSE FIRMS , 1992 .

[78]  H. A. Eiselt,et al.  Reachability of locational Nash equilibria , 1998 .

[79]  Rafael Suárez-Vega,et al.  The follower location problem with attraction thresholds , 2007 .

[80]  M. Tombak,et al.  Endogenous location leadership , 2009 .

[81]  José Muñoz-Pérez,et al.  Competitive location with rectilinear distances , 1995 .

[82]  E. Prescott,et al.  Sequential location among firms with foresight , 1977 .

[83]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics) , 2007 .

[84]  Aleksandr V. Plyasunov,et al.  A Leader-Follower Hub Location Problem Under Fixed Markups , 2016, DOOR.

[85]  Jacques-François Thisse,et al.  Asymmetric equilibria in spatial competition , 1995 .

[86]  Atsuyuki Okabe,et al.  Existence of equilibrium configurations of competitive firms on an infinite two-dimensional space , 1991 .

[87]  Zvi Drezner,et al.  A leader-follower model for discrete competitive facility location , 2015, Comput. Oper. Res..

[88]  Vladimir Marianov,et al.  Author ' s personal copy Discrete Optimization Facility location for market capture when users rank facilities by shorter travel and waiting times , 2006 .

[89]  H. A. Eiselt,et al.  Market Capture Models under Various Customer-Choice Rules , 1999 .

[90]  Frank Plastria,et al.  On destination optimality in asymmetric distance Fermat-Weber problems , 1993, Ann. Oper. Res..

[91]  Oded Berman,et al.  Competitive facility location model with concave demand , 2007, Eur. J. Oper. Res..

[92]  D. Serra,et al.  Competitive location in discrete space , 1994 .

[93]  Charles ReVelle,et al.  THE MAXIMUM CAPTURE OR “SPHERE OF INFLUENCE” LOCATION PROBLEM: HOTELLING REVISITED ON A NETWORK* , 1986 .

[94]  Subhash C. Narula,et al.  Where shall we shop today? A theory of multiple-stop, multiple-purpose shopping trips , 1983 .

[95]  David L. Huff,et al.  Defining and Estimating a Trading Area , 1964 .

[96]  Z. Drezner Competitive location strategies for two facilities , 1982 .

[97]  Amoz Kats,et al.  More on Hotelling's stability in competition , 1995 .

[98]  Z. Drezner,et al.  Replacing continuous demand with discrete demand in a competitive location model , 1997 .

[99]  Daisuke Shimizu,et al.  Cournot and Bertrand in shipping models with circular markets , 2006 .

[100]  Victor Ginsburgh,et al.  Competitive Location with Random Utilities , 1989, Transp. Sci..

[101]  Theodore C. Bergstrom,et al.  Hotelling Location Problems with Directional Constraints: An Application to Television News Scheduling , 1995 .

[102]  W. J. Lane Product Differentiation in a Market with Endogenous Sequential Entry , 1980 .

[103]  Carolyn Pitchik,et al.  Equilibrium in Hotelling's Model of Spatial Competition , 1987 .

[104]  S. Louis Hakimi,et al.  Market and Locational Equilibrium for Two Competitors , 1991, Oper. Res..

[105]  G Laporte,et al.  TABU SEARCH ALGORITHMS FOR THE (R/XP)-MEDIANOID AND (R/P)-CENTROID PROBLEMS , 1994 .

[106]  Soung Hie Kim,et al.  Mining the change of customer behavior in an internet shopping mall , 2001, Expert Syst. Appl..

[107]  Vladimir Marianov,et al.  Location of hubs in a competitive environment , 1999, Eur. J. Oper. Res..

[108]  Peter J. Slater,et al.  Maximin facility location , 1975 .

[109]  Rafael Suárez-Vega,et al.  Location and quality selection for new facilities on a network market , 2014 .

[110]  Donald Hay,et al.  Sequential Entry and Entry-Deterring Strategies in Spatial Competition , 1976 .

[111]  Oded Berman,et al.  Optimizing pricing and location decisions for competitive service facilities charging uniform price , 2008, J. Oper. Res. Soc..

[112]  Joyendu Bhadury,et al.  COMPETITIVE LOCATION UNDER UNCERTAINTY OF COSTS , 1996 .

[113]  C. Michelot,et al.  Geometrical properties of the Fermat-Weber problem , 1985 .

[114]  Jacques-François Thisse,et al.  On hotelling's "Stability in competition" , 1979 .

[115]  Stefano Colombo,et al.  A Model of Three Cities , 2016 .

[116]  H. A. Eiselt,et al.  Consumers in Competitive Location Models , 2002 .

[117]  Ralph M. Braid THE OPTIMAL LOCATIONS OF BRANCH FACILITIES AND MAIN FACILITIES WITH CONSUMER SEARCH , 1996 .

[118]  Takatoshi Tabuchi,et al.  Two-stage two-dimensional spatial competition between two firms , 1994 .

[119]  Phillip J. Lederer,et al.  Spatial duopoly with discriminatory pricing , 1985 .

[120]  Tammy Drezner,et al.  Competitive Facility Location in the Plane , 1995 .

[121]  Milad Gorji Ashtiani,et al.  Competitive location: a state-of-art review , 2016 .

[122]  Stefano Benati,et al.  The maximum capture problem with heterogeneous customers , 1999, Comput. Oper. Res..

[123]  Arsalan Rahmani,et al.  Competitive facility location problem with attractiveness adjustment of the follower on the closed supply chain , 2016 .

[124]  Eligius M. T. Hendrix On competition in a Stackelberg location-design model with deterministic supplier choice , 2016, Ann. Oper. Res..

[125]  A. Smithies Optimum Location in Spatial Competition , 1941, Journal of Political Economy.

[126]  Changhyun Kwon,et al.  Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms , 2014 .

[127]  Frank Plastria,et al.  Static competitive facility location: An overview of optimisation approaches , 2001, Eur. J. Oper. Res..

[128]  H. A. Eiselt,et al.  Sequential Location Models , 2011 .

[129]  Carolyn Pitchik,et al.  The Nature of Equilibrium in a Location Model , 1986 .

[130]  Gilbert Laporte,et al.  A Continuous Model for Multistore Competitive Location , 2005, Oper. Res..

[131]  D. McFadden Conditional logit analysis of qualitative choice behavior , 1972 .

[132]  Andreas T. Ernst,et al.  A Stackelberg hub arc location model for a competitive environment , 2014, Comput. Oper. Res..

[133]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[134]  José Fernández,et al.  An approach for solving competitive location problems with variable demand using multicore systems , 2014, Optim. Lett..

[135]  B. Curtis Eaton,et al.  Spatial Competition Revisited , 1972 .

[136]  R. Suárez-Vega,et al.  Competitive Multifacility Location on Networks: The (R|Xp)-Medianoid Problem , 2004 .

[137]  Horst A. Eiselt,et al.  Hotelling's duopoly on a tree , 1993, Ann. Oper. Res..

[138]  H. A. Eiselt Equilibria in Competitive Location Models , 2011 .

[139]  Z. Drezner Note-On a Modified One-Center Model , 1981 .

[140]  W. Reilly The law of retail gravitation , 1931 .

[141]  Martin J. Beckmann,et al.  Spatial cournot oligopoly , 1972 .

[142]  E. Maskin,et al.  The Existence of Equilibrium in Discontinuous Economic Games, I: Theory , 1986 .

[143]  Daniel Serra,et al.  Consumer choice and optimal locations models: Formulations and heuristics , 2001 .

[144]  N. Economides Minimal and maximal product differentiation in Hotelling's duopoly , 1986 .

[145]  André de Palma,et al.  A Non-Cooperative Analysis of Hotelling's Location Game , 1996 .

[146]  Damien J. Neven,et al.  Endogenous sequential entry in a spatial model , 1987 .

[147]  Ralph M. Braid Heterogeneous preferences and non-central agglomeration of firms , 1988 .

[148]  Blas Pelegrín,et al.  All Stackelberg Location Equilibria in the Hotelling's Duopoly Model on a Tree with Parametric Prices , 2003, Ann. Oper. Res..

[149]  Gilbert Laporte,et al.  Competitive Location Models: A Framework and Bibliography , 1993, Transp. Sci..

[150]  Blas Pelegrín,et al.  A discrete long-term location-price problem under the assumption of discriminatory pricing: Formulations and parametric analysis , 2007, Eur. J. Oper. Res..

[151]  N. Megiddo,et al.  The Maximum Coverage Location Problem , 1983 .

[152]  Atsuyuki Okabe,et al.  Spatial competition of firms in a two-dimensional bounded market , 1993 .

[153]  William J. Cook,et al.  The Traveling Salesman Problem: A Computational Study , 2007 .

[154]  Tammy Drezner,et al.  Locating a single new facility among existing unequally attractive facilities , 1994 .

[155]  G. Bonanno Location Choice, Product Proliferation and Entry Deterrence , 1987 .

[156]  Victor Ginsburgh,et al.  On Existence of Location Equilibria in the 3-firm Hotelling Problem , 1987 .

[157]  Zvi Drezner,et al.  Consistent and Inconsistent Rules in Competitive Facility Choice , 1996 .

[158]  Dan Yakir,et al.  Global enzymes: Sphere of influence , 2002, Nature.

[159]  Simon P. Anderson,et al.  Social Surplus and Profitability Under Different Spatial Pricing Policies , 1992 .

[160]  Elon Kohlberg,et al.  Equilibrium in a simple price-location model , 1982 .

[161]  Benjamin H. Steven,et al.  An application of game theory to a problem in location strategy , 1961 .

[162]  S. Hakimi On locating new facilities in a competitive environment , 1983 .