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Outer approximation and submodular cuts for maximum capture facility location problems with random utilities
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DOI：10.1016/j.ejor.2017.09.023.png)
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Abstract
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We consider a family of competitive facility location problems in which a newcomer company enters the market and has to decide where to locate a set of new facilities so as to maximize its market share. The multinomial logit model is used to estimate the captured customer demand. We propose a first branch-and-cut approach for this family of difficult mixed-integer non-linear problems. Our approach combines two types of cutting planes that exploit particular properties of the objective function: the first one are the outer-approximation cuts and the second one are the submodular cuts. The approach is computationally evaluated on three datasets from the recent literature. The obtained results show that our new branch-and-cut drastically outperforms state-of-the-art exact approaches, both in terms of the computing times, and in terms of the number of instances solved to optimality. (C) 2017 Elsevier B.V. All rights reserved.
Keywords:
Combinatorial optimization
Branch-and-cut
Maximum capture
Random utility model
Competitive facility location
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