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- W4320343083 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, outside competitors, as well as diverse facility-planning decisions, and 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." @default.
- W4320343083 created "2023-02-13" @default.
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- W4320343083 date "2021-03-06" @default.
- W4320343083 modified "2023-09-23" @default.
- W4320343083 title "Sequential Competitive Facility Location: Exact and Approximate Algorithms" @default.
- W4320343083 doi "https://doi.org/10.48550/arxiv.2103.04259" @default.
- W4320343083 hasPublicationYear "2021" @default.
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