The Regionally Constrained p-Median Problem

In many applications involving the location of public facilities, the activity that is being located is added to the landscape of existing public facilities and services. Further, there also exists a political and behavioral landscape of differing jurisdictions, representations, and perceptions. This paper presents a new form of the p-median problem which addresses two types of “regional” constraints that can arise in public facilities planning. A formulation is given for this specially constrained median problem along with a solution approach. Several examples are presented with computational results which indicate that this type of constrained problem could lead to better facilities planning.

[1]  D. H. Marks,et al.  An Analysis of Private and Public Sector Location Models , 1970 .

[2]  R. A. Whitaker.  A Tight Bound Drop Exchange Algorithm for Solving the p Median Problem , 1981 .

[3]  Donald Erlenkotter,et al.  A Dual-Based Procedure for Uncapacitated Facility Location , 1978, Oper. Res..

[4]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[5]  M. Rao,et al.  An Algorithm for the M-Median Plant Location Problem , 1974 .

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

[7]  E. Hillsman.  The p-Median Structure as a Unified Linear Model for Location—Allocation Analysis , 1984 .

[8]  C. Revelle,et al.  Central Facilities Location under an Investment Constraint , 2010 .

[9]  A. M. Geoffrion,et al.  Lagrangean Relaxation Applied to Capacitated Facility Location Problems , 1978 .

[10]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

[11]  Richard L. Church,et al.  A location model based on multiple metrics and multiple facility assignment , 1986 .

[12]  Subhash C. Narula,et al.  Technical Note - An Algorithm for the p-Median Problem , 1977, Oper. Res..

[13]  Oded Berman,et al.  Developments in network location with mobile and congested facilities , 1981 .

[14]  Charles ReVelle,et al.  Central Facilities Location , 2010 .

[15]  Lazaros P. Mavrides.  An Indirect Method for the Generalized k-Median Problem Applied to Lock-Box Location , 1979 .

[16]  Nicos Christofides,et al.  A tree search algorithm for the p-median problem , 1982 .

[17]  Roberto D. Galvão,et al.  A Dual-Bounded Algorithm for the p-Median Problem , 1980, Oper. Res..

[18]  Lawrence M. Ostresh.  The Stepwise Location-Allocation Problem: Exact Solutions in Continuous and Discrete Spaces , 2010 .

[19]  Dominique Peeters,et al.  A comparison of two dual-based procedures for solving the p-median problem , 1985 .

[20]  R. Swain.  A Parametric Decomposition Approach for the Solution of Uncapacitated Location Problems , 1974 .

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

[22]  A. Odoni,et al.  Locations of Medians on Stochastic Networks , 1979 .