The gravity p

Abstract In this paper we propose a new model for the p -median problem. In the standard p -median problem it is assumed that each demand point is served by the closest facility. In many situations (for example, when demand points are communities of customers and each customer makes his own selection of the facility) demand is divided among the facilities. Each customer selects a facility which is not necessarily the closest one. In the gravity p -median problem it is assumed that customers divide their patronage among the facilities with the probability that a customer patronizes a facility being proportional to the attractiveness of that facility and to a decreasing utility function of the distance to the facility. The model is analyzed and heuristic solution procedures are proposed. Computational experiments using a set of test problems, provide excellent results.

[1]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[2]  M. J. Hodgson.  A location—allocation model maximizing consumers' welfare , 1981 .

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

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

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

[6]  G. O. Wesolowsky,et al.  On the Logit Approach to Competitive Facility Location , 1998 .

[7]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[8]  Zvi Drezner,et al.  A Note on Applying the Gravity Rule to the Airline Hub Problem , 2001 .

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

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

[11]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

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

[13]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[14]  Mark S. Daskin,et al.  3 Discrete Network Location Models , 2001 .

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

[16]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[17]  S. Hakimi.  Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems , 1965 .

[18]  Christopher S. Tang,et al.  Determining Where to Shop: Fixed and Variable Costs of Shopping , 1998 .