A capacitated competitive facility location problem
- Authors: Beresnev V.L.1,2, Melnikov A.A.1,2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 10, No 1 (2016)
- Pages: 61-68
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212240
- DOI: https://doi.org/10.1134/S1990478916010075
- ID: 212240
Cite item
Abstract
We consider a mathematical model similar in a sense to competitive location problems. There are two competing parties that sequentially open their facilities aiming to “capture” customers and maximize profit. In our model, we assume that facilities’ capacities are bounded. The model is formulated as a bilevel integer mathematical program, and we study the problem of obtaining its optimal (cooperative) solution. It is shown that the problem can be reformulated as that of maximization of a pseudo-Boolean function with the number of arguments equal to the number of places available for facility opening. We propose an algorithm for calculating an upper bound for values that the function takes on subsets which are specified by partial (0, 1)-vectors.
About the authors
V. L. Beresnev
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: beresnev@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
A. A. Melnikov
Sobolev Institute of Mathematics; Novosibirsk State University
Email: beresnev@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090