Abstract
This paper investigates a new variation in the continuous single facility location problem. Specifically, we address the problem of locating a new facility on a plane with different distance norms on different sides of a boundary line. Special cases and extensions of the problem, where there are more than two regions are also discussed. Finally, by investigating the properties of the models, efficient solution procedures are proposed.
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References
Batta, R. and tU.S. Palekar. (1988). “Mixed Planar/Network Facility Location Problems.” Computers & Operations Research 15(1), 61–67.
Brimberg, J. and tR.F. Love. (1993). “Global Convergence of a Generalized Iterative Procedure for the Minisum Location Problem with _p Distances.” Operations Research 41(6), 1153–1163.
Carrizosa, E. and tA.M. Rodriguez-Chia. (1997). “Weber Problems with Alternative Transportation Systems.” European Journal of Operational Research 97, 87–93.
Hansen, P., tJ. Perreur, and J.F. Thisse. (1980). “Location Theory, Dominance and Convexity: Some Further Results.” Operations Research 28(5), 1241–1250.
Love, R.E., tJ.G. Morris, and G.O. Wesolowsky. (1988). Facilities Location, Models and Methods. New York: North-Holland.
Mitchell, J.S.B. and tC.H. Papadimitriou. (1991). “The Weighted Region Problem: Finding Shortest Paths Through a Weighted Planar Subdivision.” Journal of the Association for Computing Machinery 38(1), 18–73.
Parlar, M. (1994). “Single Facility Location Problem with Region-Dependent Distance Metrics.” International Journal of Systems Sciences 25(3), 513–525.
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Brimberg, J., Kakhki, H.T. & Wesolowsky, G.O. Location Among Regions with Varying Norms. Annals of Operations Research 122, 87–102 (2003). https://doi.org/10.1023/A:1026190322164
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DOI: https://doi.org/10.1023/A:1026190322164