Generalized Benders decomposition for competitive facility location with concave demand and zone-specialized variable attractiveness

Abstract

We study a competitive facility location problem, in which a company enters a market where competitor’s facilities exist. Customers with elastic buying powers make choices following the gravity rule. Each facility, once open, has an intrinsic fixed attraction to customers. Besides, zone-specialized variable attractiveness can be provided to increase the total attraction of a facility to a specific customer zone. The objective of the company is to maximize profit by determining the locations of the facilities and the facility-customer pairwise attractiveness level, accounting for the expected revenue and the cost. The problem is formulated as a mixed-integer nonlinear program and subsequently solved by a tailored generalized Benders decomposition algorithm with tunable parameters. We then conduct extensive computational studies to demonstrate the efficiency of the algorithm. Finally, we analyze the solution structures under different scenarios and provide managerial implications for real-world applications.