Abstract
In this paper we consider the weighted minimax (1-center) location problem in the plane when the weights are not given but rather drawn from independent uniform distributions. The problem is formulated and analyzed. For certain parameters of the uniform distributions the objective function is proven to be convex and thus can be easily solved by standard software such as the Solver in Excel. Computational experience is reported.
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References
Berman, O. and tD. Krass. (2001). “Facility Location with Stochastic Demands and Congestion.” In Z. Drezner and H.W. Hamacher (eds.), Facility Location: Applications and Theory. Berlin: Springer.
Berman, O. and tJ. Wang. (2001). “The 1-Median and 1-Antimedian Problems with Uniform Distributed Demands.” Working Paper, University of Toronto.
Berman, O., tJ. Wang, Z. Drezner, and G.O. Wesolowsky. (2003). “The Minimax and Maximin Location Problems with Uniform Distributed Weights.” IIE Transactions, in press.
Drezner, T. and Z. Drezner. (2001). “Finding the Optimal Solution to the Huff Competitive Location Model.” Working Paper, California State University, Fullerton, CA.
Drezner, Z., tA. Mehrez, and G.O. Wesolowsky. (1991). “The Facility Location Problem with Limited Distances.” Transportation Science 25, 183–187.
Drezner, Z. and tA. Suzuki. (2004). “The Big Triangle Small Triangle Method for the Solution of Non-Convex Facility Location Problems.” Operations Research, in press.
Drezner, Z., tG.O. Wesolowsky, and T. Drezner. (2001). “The Gradual Covering Problem.” Submitted for publication.
Elzinga, D.J. and D.W. Hearn. (1972). “The Minimum Covering Sphere Problem.” Management Science 19, 96–104.
Frank, H. (1966a). “Optimum Location on a Graph with Probabilistic Demands.” Operations Research 14, 404–321.
Frank, H. (1966b). “Optimum Location on a Graph with Correlated Normal Demands.” Operations Research 14, 552–557.
Hansen, P., tD. Peeters, and J.-F. Thisse. (1981). “On the Location of an Obnoxious Facility.” Sistemi Urbani 3, 299–317.
Hearn, D.W. and tJ. Vijay. (1982). “Efficient Algorithms for the (Weighted) Minimum Circle Problem.” Operations Research 30, 777–795.
Love, R.F., tJ.G. Morris, and G.O. Wesolowsky. (1988). Facilities Location: Models and Methods. New York: North Holland.
Maranas, C.D. and tC.A. Floudas. (1994). “A Global OptimizationMethod forWeber's Problem with Attraction and Repulsion.” In W.W. Hager, D.W Hearn, and P.M. Pardalos (eds.), Large Scale Optimization: State of the Art. Dordrecht: Kluwer.
Plastria, F. (1992). “GBSSS, the Generalized Big Square Small Square Method for Planar Single Facility Location.” European Journal of Operational Research 62, 163–174.
Sylvester, J.J. (1857). “A Question in the Geometry of Situation.” Quarterly Journal of Pure and Applied Mathematics 1, 79.
Tuy, H., tF. Al-Khayyal, and F. Zhou. (1995). “A D.C. Optimization Method for Single Facility Location Problems.” Journal of Global Optimization 7, 209–227.
Wesolowsky, G.O. (1977). “Probabilistic Weights in the One-Dimensional Facility Location Problem.” Management Science 24, 224–229.
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Berman, O., Wang, J., Drezner, Z. et al. A Probabilistic Minimax Location Problem on the Plane. Annals of Operations Research 122, 59–70 (2003). https://doi.org/10.1023/A:1026134121255
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DOI: https://doi.org/10.1023/A:1026134121255