Geodesic
Additional constraints for dynamic competitive facility location problem
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 43-56.

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We consider a competitive facility location model, where competing parties (Leader and Follower) make decisions considering changes of the set of customers happening during the planing horizon, having known number of time periods. It is supposed that the Leader makes a decision on opening their facilities at the beginning of the planning horizon, while the Follower can revise their decision in each time period. In the present paper, we study perspectives to apply a method for finding the best solution which is based on using HP-relaxation of the bi-level problem considered. The key element of this method is construction of additional inequalities strengthening the HP-relaxation and computation of upper bounds for the objective function of the problem. In the work, new families of additional constraints are proposed to strengthen the HP-relaxation, that allow us to compute non-trivial upper bounds. Bibliogr. 13.
Keywords: Stackelberg game, bi-level programming, competitive location, valid inequalities. 
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V. L. Beresnev; A. A. Melnikov. Additional constraints for dynamic competitive facility location problem. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 43-56. http://geodesic.mathdoc.fr/item/DA_2023_30_3_a1/

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