Competitive facility location and design with reactions of competitors already in the market

A new retail facility is to locate and its service quality is to determine where similar facilities of competitors offering the same goods are already present. The market share captured by each facility depends on its distance to customers and its quality, which is described by a probabilistic Huff-like model. In order to maximize the profit of the new facility, a two-stage method is developed, which takes into account the reactions of the competitors. In the quality decision stage, the competitive decision process occurring among facilities is modelled as a game, whose solution is given by its Nash equilibrium. The solution, which can be represented as functions of the location of the new facility, is obtained by analytical resolution of a system of equations in the case of one facility in the market or by polynomial approximation in the case of multiple facilities. In the location decision stage, an interval based global optimization method is used to determine the best location of the new facility. Numerical experiments on randomly generated instances demonstrate the effectiveness of the method.

[1]  R. B. Kearfott Rigorous Global Search: Continuous Problems , 1996 .

[2]  S. Hakimi p-Median theorems for competitive locations , 1986 .

[3]  F. Plastria GBSSS: The generalized big square small square method for planar single-facility location , 1992 .

[4]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

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

[6]  Said Salhi,et al.  Discrete Location Theory , 1991 .

[7]  Ronald R. Willis,et al.  New Computer Methods for Global Optimization , 1990 .

[8]  Cuthbert Daniel,et al.  Fitting Equations to Data: Computer Analysis of Multifactor Data , 1980 .

[9]  A. Kononov,et al.  Competitive facility location models , 2009 .

[10]  Daniel Scholz,et al.  The big cube small cube solution method for multidimensional facility location problems , 2010, Comput. Oper. Res..

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

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

[13]  Blas Pelegrín,et al.  Sequential versus simultaneous approach in the location and design of two new facilities using planar Huff-like models , 2009, Comput. Oper. Res..

[14]  Blas Pelegrín,et al.  Solving a Huff-like competitive location and design model for profit maximization in the plane , 2007, Eur. J. Oper. Res..

[15]  K. Bellmann Daniel, C., F. S. WOOD, J. W. GORMAN: Fitting Equations to Data. Computer Analysis of Multifactor Data for Scientists and Engineers. John Wiley & Sons, New York-London-Sydney-Toronto 1974. XIV, 342 S., 132 Abb., 33 Tab., £6.50 , 1975 .

[16]  José Fernández,et al.  Sensitivity analysis of a continuous multifacility competitive location and design problem , 2008 .

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

[18]  A. Volgenant,et al.  Facility location: a survey of applications and methods , 1996 .

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

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

[21]  David Simchi-Levi,et al.  Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era (International Series in Operations Research & Management Science) , 2004 .

[22]  Tomas Sauer,et al.  Computational aspects of multivariate polynomial interpolation , 1995, Adv. Comput. Math..

[23]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

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

[25]  O. Knüppel,et al.  PROFIL/BIAS—A fast interval library , 1994, Computing.

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

[27]  D. Huff A Programmed Solution for Approximating an Optimum Retail Location , 1966 .

[28]  T. Friesz,et al.  Incorporating competitors' reactions in facility location decisions: A market equilibrium approach , 1995 .

[29]  T. Sauer,et al.  On multivariate Lagrange interpolation , 1995 .

[30]  E. Carrizosa,et al.  LOCATION AND DESIGN OF A COMPETITIVE FACILITY FOR PROFIT MAXIMISATION , 2003 .

[31]  Gilbert Laporte,et al.  Sequential location problems , 1997 .

[32]  T. Friesz,et al.  Equilibrium Facility Location on Networks , 1995 .