Geodesic
Branch-and-bound method for the competitive facility location problem with prescribed choice of suppliers
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 3-23

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The mathematical model is being considered, where two competing sides sequentially open their facilities with the goal to capture customers and maximize profit. The model can be written as the bi-level integer programming problem. Optimal noncooperative solutions are considered as optimal solutions of the problem. In order to provide appproximate and exact solutions of the problem the branch-and-bound method is proposed. Computational experiments show capability of the method to solve small and medium instances. Tab. 2, bibliogr. 18.
Keywords: bi-level programming, optimal noncooperative solution, pseudo-Boolean function, branch-and-bound method. 
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     title = {Branch-and-bound method for the competitive facility location problem with prescribed choice of suppliers},
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V. L. Beresnev; A. A. Melnikov. Branch-and-bound method for the competitive facility location problem with prescribed choice of suppliers. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 2, pp. 3-23. http://geodesic.mathdoc.fr/item/DA_2014_21_2_a0/