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

Camilo Ortiz-Astorquiza, Ivan Contreras and Gilbert Laporte

European Journal of Operational Research, 2015, vol. 247, issue 3, 1013-1016

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.

Keywords: Submodularity; Multi-level facility location (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:247:y:2015:i:3:p:1013-1016

DOI: 10.1016/j.ejor.2015.05.082

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