Abstract
In this paper, the problem of locating new facilities in a competitive environment is considered. The problem is formulated as the firm expected profit maximization and a set of nodes is selected in a graph representing the geographical zone. Profit depends on fixed and deterministic location costs and, since customers are independent decision-makers, on the expected market share. The problem is an instance of nonlinear integer programming, because the objective function is concave and submodular. Due to this complexity a branch & bound method is developed for solving small size problems (that is, when the number of nodes is less than 50), while a heuristic is necessary for larger problems. The branch & bound is called data-correcting method, while the approximate solutions are obtained using the heuristic-concentration method.
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Benati, S. An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem. Annals of Operations Research 122, 43–58 (2003). https://doi.org/10.1023/A:1026182020346
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DOI: https://doi.org/10.1023/A:1026182020346