Sequential Competitive Facility Location: Exact and Approximate Algorithms

Mingyao Qi (), Ruiwei Jiang () and Siqian Shen ()
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Mingyao Qi: Logistics and Transportation Division, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518071, China
Ruiwei Jiang: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109
Siqian Shen: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109

Operations Research, 2024, vol. 72, issue 1, 300-316

Abstract: We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation and exploit the problem structures to derive two valid inequalities based on submodularity and concave overestimation, respectively. We use the two valid inequalities in a branch-and-cut algorithm to find globally optimal solutions. Then, we propose an approximation algorithm to find good-quality solutions with a constant approximation guarantee. We develop several extensions by considering general facility-opening costs and outside competitors as well as diverse facility-planning decisions, and we discuss solution approaches for each extension. We conduct numerical studies to demonstrate that the exact algorithm significantly accelerates the computation of CFLP on large-sized instances that have not been solved optimally or even heuristically by existing methods, and the approximation algorithm can quickly find high-quality solutions. We derive managerial insights based on sensitivity analysis of different settings that affect customers’ probabilistic choices and the ensuing demand.

Keywords: Optimization; competitive facility location; mixed-integer nonlinear programming; branch-and-cut; submodularity; concave overestimation; approximation algorithm (search for similar items in EconPapers)
Date: 2024
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