Robust facility location

  • Let A be a nonempty finite subset of R^2 representing the geographical coordinates of a set of demand points (towns, ...), to be served by a facility, whose location within a given region S is sought. Assuming that the unit cost for a in A if the facility is located at x in S is proportional to dist(x,a) - the distance from x to a - and that demand of point a is given by w_a, minimizing the total trnsportation cost TC(w,x) amounts to solving the Weber problem. In practice, it may be the case, however, that the demand vector w is not known, and only an estimator {hat w} can be provided. Moreover the errors in sich estimation process may be non-negligible. We propose a new model for this situation: select a threshold valus B 0 representing the highest admissible transportation cost. Define the robustness p of a location x as the minimum increase in demand needed to become inadmissible, i.e. p(x) = min{||w^*-{hat w}|| : TC(w^*,x) B, w^* = 0} and solve then the optimization problem max_{x in S} p(x) to get the most robust location.

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Author:Stefan Nickel, Emilio Carrizosa
URN (permanent link):urn:nbn:de:hbz:386-kluedo-4787
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (35)
Document Type:Preprint
Language of publication:English
Year of Completion:1998
Year of Publication:1998
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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