Opened Access Robust facility location

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Author: Carrizosa Priego, Emilio José
Nickel, Stefan
Department: Universidad de Sevilla. Departamento de Estadística e Investigación Operativa
Date: 2003-11
Published in: Mathematical Methods of Operations Research, 58 (2), 331-349.
Document type: Article
Abstract: Let A be a nonempty finite subset of the plane 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∈A if the facility is located at x∈S is proportional to dist(x,a) — the distance from x to a — and that demand of point a is given by ωa, minimizing the total transportation cost TC(ω,x) amounts to solving the Weber problem. In practice, it may be the case, however, that the demand vector ω is not known, and only an estimator ωcirc; can be provided. Moreover the errors in such estimation process may be non-negligible. We propose a new model for this situation: select a threshold value B>0 representing the highest admissible transportation cost. Define the robustness ρ of a location x as the minimum increase in demand needed to become inadmissible, i.e. ρ(x)=min{|ω−ωcirc;|:TC(ω,x)>B,ω≥0} and find the x maximizing ρ to get the most robust location.
Cite: Carrizosa Priego, E.J. y Nickel, S. (2003). Robust facility location. Mathematical Methods of Operations Research, 58 (2), 331-349.
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DOI: 10.1007/s001860300294

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