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Robust facility location

Author

Listed:
  • Emilio Carrizosa
  • Stefan Nickel

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 ω a , 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. Copyright Springer-Verlag 2003

Suggested Citation

  • Emilio Carrizosa & Stefan Nickel, 2003. "Robust facility location," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 331-349, November.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:2:p:331-349
    DOI: 10.1007/s001860300294
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    Citations

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    Cited by:

    1. De Rosa, Vincenzo & Gebhard, Marina & Hartmann, Evi & Wollenweber, Jens, 2013. "Robust sustainable bi-directional logistics network design under uncertainty," International Journal of Production Economics, Elsevier, vol. 145(1), pages 184-198.
    2. Frauke Liers & Lars Schewe & Johannes Thürauf, 2022. "Radius of Robust Feasibility for Mixed-Integer Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 243-261, January.
    3. Marc Ciligot-Travain & Sado Traoré, 2014. "On a robustness property in single-facility location in continuous space," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 321-330, April.
    4. Nikulin, Yury, 2006. "Robustness in combinatorial optimization and scheduling theory: An extended annotated bibliography," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 606, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2022. "The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments," European Journal of Operational Research, Elsevier, vol. 296(3), pages 749-763.
    6. Albareda-Sambola, Maria & Fernández, Elena & Saldanha-da-Gama, Francisco, 2011. "The facility location problem with Bernoulli demands," Omega, Elsevier, vol. 39(3), pages 335-345, June.
    7. Péter Egri & Balázs Dávid & Tamás Kis & Miklós Krész, 2023. "Robust facility location in reverse logistics," Annals of Operations Research, Springer, vol. 324(1), pages 163-188, May.
    8. M. A. Goberna & V. Jeyakumar & G. Li, 2021. "Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semi-definite Programs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 597-622, May.
    9. Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    10. Paul Berglund & Changhyun Kwon, 2014. "Robust Facility Location Problem for Hazardous Waste Transportation," Networks and Spatial Economics, Springer, vol. 14(1), pages 91-116, March.
    11. Li, Na & Jiang, Yue & Zhang, Zhi-Hai, 2021. "A two-stage ambiguous stochastic program for electric vehicle charging station location problem with valet charging service," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 149-171.
    12. Nicolas Fröhlich & Stefan Ruzika, 2022. "Interdicting facilities in tree networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 95-118, April.
    13. Blanquero, R. & Carrizosa, E. & Hendrix, E.M.T., 2011. "Locating a competitive facility in the plane with a robustness criterion," European Journal of Operational Research, Elsevier, vol. 215(1), pages 21-24, November.

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