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On Location-Allocation Problems for Dimensional Facilities

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Abstract

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities, and we prove the existence of optimal solutions under mild assumptions. To achieve these results, we borrow tools from optimal transport mass theory that allow us to give explicit solution structure of the considered lower level problem. We also provide a discretization approach that can approximate, up to any degree of accuracy, the optimal solution of the original problem. This discrete approximation can be optimally solved via a mixed-integer linear program. To address very large instance sizes, we also provide a GRASP heuristic that performs rather well according to our experimental results. The paper also reports some experiments run on test data.

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Acknowledgements

This paper was originated during a visit of Prof. L. Mallozzi at the University of Seville supported by the Ph.D. Program Mathematics. The authors want to thanks Prof. A. Lewis for his suggestion to tackle the general location-allocation problem using a discretization scheme suggested during a presentation of this material in a seminar given during the previously mentioned visit. Finally, we would also like to thank the Ministry of Economy and Competitiveness of Spanish Government for partially funding our research via Project MTM2016-74983-C2-1-R.

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Authors and Affiliations

  1. University of Naples Federico II, Naples, Italy

    Lina Mallozzi

  2. IMUS, Universidad de Sevilla, Seville, Spain

    Justo Puerto & Moisés Rodríguez-Madrena

Authors
  1. Lina Mallozzi
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  2. Justo Puerto
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  3. Moisés Rodríguez-Madrena
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Correspondence to Justo Puerto.

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Communicated by Michel Théra.

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Mallozzi, L., Puerto, J. & Rodríguez-Madrena, M. On Location-Allocation Problems for Dimensional Facilities. J Optim Theory Appl 182, 730–767 (2019). https://doi.org/10.1007/s10957-018-01470-y

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