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Threshold robustness in discrete facility location problems: a bi-objective approach

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Abstract

The two best studied facility location problems are the \(p\)-median problem and the uncapacitated facility location problem (Daskin, Network and discrete location: models, algorithms, and applications. Wiley, New York, 1995; Mirchandani and Francis, Discrete location theory. Wiley, New York, 1990). Both seek the location of the facilities minimizing the total cost, assuming no uncertainty in costs exists, and thus all parameters are known. In most real-world location problems the demand is not certain, because it is a long-term planning decision, and thus, together with the minimization of costs, optimizing some robustness measure is sound. In this paper we address bi-objective versions of such location problems, in which the total cost, as well as the robustness associated with the demand, are optimized. A dominating set is constructed for these bi-objective nonlinear integer problems via the \(\varepsilon \)-constraint method. Computational results on test instances are presented, showing the feasibility of our approach to approximate the Pareto-optimal set.

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    http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/.

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    http://math.nsc.ru/AP/benchmarks/english.html.

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Author information

Correspondence to Anton Ushakov.

Additional information

The research of the E. Carrizosa is supported by Grants MTM2012-36163, Spain, P11-FQM-7603 and FQM-329, Andalucía, all financed in part with EU ERD Funds. The study of the A. Ushakov and I. Vasilyev is partially supported by RFBR, research project NO. 14–07–00382-a.

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Carrizosa, E., Ushakov, A. & Vasilyev, I. Threshold robustness in discrete facility location problems: a bi-objective approach. Optim Lett 9, 1297–1314 (2015). https://doi.org/10.1007/s11590-015-0892-5

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Keywords

  • Discrete facility location
  • Robustness
  • Bi-objective combinatorial optimization
  • \(p\)-Median problem
  • UFLP
  • \(\varepsilon \)-Constraint method
  • \(\delta \)-Dominating set