Variable Neighborhood Search Algorithms for a Competitive Location Problem with Elastic Demand

Abstract

Under consideration is the situation in a competitive market when a new Company plans to make profit from opening its own facilities that offer goods or services. The Company have to take it into account that there are several projects for opening each facility, and similar facilities of the Competitor are already placed on the market. Moreover, customers themselves choose the places to meet their demand in dependence on where and which facilities are located. The Company’s goal is to choose locations and projects for opening new facilities in order to attract the largest share of all customer demand. The special type of demand leads to nonlinearity of the objective function and to additional difficulties in finding an optimal solution. In this article we construct some variants of variable neighborhood search algorithms, perform their experimental analysis by using the upper estimates, obtain a posteriori accuracy estimates, and discuss the results.

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ACKNOWLEDGMENTS

The authors are grateful to N. Mladenović and Yu.A.Kochetov for helpful advice.

Funding

Sections 1 and 2 are performed by T.V. Levanova with the support by the Program for Fundamental Scientific Research of the State Academies of Sciences for 2013–2020 No. I.5 (project no. 0314–2019–0019). Section 3 is performed by A.Yu. Gnusarev with the support by the Russian Foundation for Basic Research (project no. 18–07–00599).

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Correspondence to T. V. Levanova or A. Yu. Gnusarev.

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Translated by L.B. Vertgeim

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Levanova, T.V., Gnusarev, A.Y. Variable Neighborhood Search Algorithms for a Competitive Location Problem with Elastic Demand. J. Appl. Ind. Math. 14, 693–705 (2020). https://doi.org/10.1134/S1990478920040080

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Keywords

  • location problem
  • competition
  • elastic demand
  • heuristic
  • variable neighborhood search