An Approximation Algorithm for a Competitive Facility Location Problem with Network Effects
European Journal of Operational Research, 267(1) 176-186, Forthcoming
32 Pages Posted: 3 May 2018
Date Written: November 23, 2017
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.
Keywords: location, competitive facility location problem, network effect, approximation algorithm
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