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Multi-level facility location as the maximization of a submodular set function

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  • Ortiz-Astorquiza, Camilo
  • Contreras, Ivan
  • Laporte, Gilbert
Abstract
In this paper we model the multi-level uncapacitated facility location problem as two different combinatorial optimization problems. The first model is the classical representation of the problem which uses a set of vertices as combinatorial objects to represent solutions whereas in the second model we propose the use of a set of paths. An interesting observation is that the real-valued set function associated with the first combinatorial problem does not satisfy the submodular property, whereas the set function associated with the second problem does satisfy this property. This illustrates the fact that submodularity is not a property intrinsic to an optimization problem but rather to its mathematical representation.

Suggested Citation

  • Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2015. "Multi-level facility location as the maximization of a submodular set function," European Journal of Operational Research, Elsevier, vol. 247(3), pages 1013-1016.
    • Handle: RePEc:eee:ejores:v:247:y:2015:i:3:p:1013-1016
    DOI: 10.1016/j.ejor.2015.05.082
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    Cited by:

    1. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2017. "Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 767-779, November.
    2. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    3. Jean-Paul Arnaout, 2018. "Worm optimization for the multiple level warehouse layout problem," Annals of Operations Research, Springer, vol. 269(1), pages 29-51, October.
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    5. Jean-Paul Arnaout & Caline ElKhoury & Gamze Karayaz, 2020. "Solving the multiple level warehouse layout problem using ant colony optimization," Operational Research, Springer, vol. 20(1), pages 473-490, March.
    6. Mohammadi, Mehrdad & Jula, Payman & Tavakkoli-Moghaddam, Reza, 2017. "Design of a reliable multi-modal multi-commodity model for hazardous materials transportation under uncertainty," European Journal of Operational Research, Elsevier, vol. 257(3), pages 792-809.

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