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Optimal transport and a bilevel location-allocation problem

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Abstract

In this paper a two-stage optimization model is studied to find the optimal location of new facilities and the optimal partition of the consumers (location-allocation problem). The social planner minimizes the social costs, i.e. the fixed costs plus the waiting time costs, taking into account that the citizens are partitioned in the region according to minimizing the capacity costs plus the distribution costs in the service regions. By using optimal transport tools, existence results of solutions to the location-allocation problem are presented together with some examples.

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Acknowledgments

The authors grateful acknowledge valuable comments of two referees.

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Authors and Affiliations

  1. Department of Mathematics and Applications Renato Caccioppoli, University of Naples Federico II, via Claudio 21, 80125, Naples, Italy

    Lina Mallozzi

  2. Department of Mathematics and Applications Renato Caccioppoli, University of Naples Federico II, via Cinthia M.te S. Angelo, 80126, Naples, Italy

    Antonia Passarelli di Napoli

Authors
  1. Lina Mallozzi
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  2. Antonia Passarelli di Napoli
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Correspondence to Lina Mallozzi.

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Mallozzi, L., Napoli, A.P.d. Optimal transport and a bilevel location-allocation problem. J Glob Optim 67, 207–221 (2017). https://doi.org/10.1007/s10898-015-0347-7

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  • DOI: https://doi.org/10.1007/s10898-015-0347-7

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