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.
Verfasserangaben: | Stefan Nickel, Emilio Carrizosa |
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URN (Permalink): | urn:nbn:de:hbz:386-kluedo-4787 |
Schriftenreihe (Bandnummer): | Report in Wirtschaftsmathematik (WIMA Report) (35) |
Dokumentart: | Preprint |
Sprache der Veröffentlichung: | Englisch |
Jahr der Fertigstellung: | 1998 |
Jahr der Veröffentlichung: | 1998 |
Veröffentlichende Institution: | Technische Universität Kaiserslautern |
Datum der Publikation (Server): | 03.04.2000 |
Fachbereiche / Organisatorische Einheiten: | Fachbereich Mathematik |
DDC-Sachgruppen: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Lizenz (Deutsch): |