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An approximation algorithm for a competitive facility location problem with network effects

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  • Kung, Ling-Chieh
  • Liao, Wei-Hung

Abstract

When facilities are built to serve end consumers directly, it is natural that consumer demands are affected by the number of open facilities. Moreover, sometimes a facility becomes more attractive if other facilities around it are built. To capture these factors, in this study we construct a discrete location model for profit maximization with endogenous consumer demands and network effects. The effective demand is then a concave function of the sum of benefits of open facilities due to the diminishing marginal benefit effect. When the function is linear, we design a polynomial-time algorithm to find an optimal solution. When it is nonlinear, we show that the problem is NP-hard and develop an approximation algorithm based on demand function approximation, linear relaxation, decomposition, and sorting. It is demonstrated that the proposed algorithm has worst-case performance guarantees for some special cases of our problem. Numerical studies are conducted to demonstrate the average performance and general applicability of our algorithms.

Suggested Citation

  • Kung, Ling-Chieh & Liao, Wei-Hung, 2018. "An approximation algorithm for a competitive facility location problem with network effects," European Journal of Operational Research, Elsevier, vol. 267(1), pages 176-186.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:1:p:176-186
    DOI: 10.1016/j.ejor.2017.11.037
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    2. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
    3. Wuyang Yu, 2019. "A leader-follower model for discrete competitive facility location problem under the partially proportional rule with a threshold," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-16, December.

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