Abstract: We consider a competition between two parties maximizing their profit from servicing customers. A decision making process is assumed to be organized in a Stackelberg game framework. In the model, we are given with two finite sets: a set of customers and a set of potential facilities’ locations. The parties, called the Leader and the Follower, sequentially open their facilities in some of the potential locations. A party opening the most preferable facility for a customer captures him or her. Facilities’ capacities are assumed to be finite, and the problem is to decide where to open facilities and how to assign them to service captured customers provided that capacity constraints are satisfied. The Leader’s problem is formalized as an optimistic bi-level mixed-integer program. We show that it can be considered as a problem to maximize a pseudo-Boolean function depending on a “small” number of Boolean variables. To find an optimal solution of this problem, we suggest a branch-and-bound algorithm where an estimating problem in a form of mixed-integer programming is utilized to calculate an upper bound for values of the objective function. In computational experiments, we study the quality of the upper bound and the performance of the method on randomly generated inputs

Cite: Beresnev V. , Melnikov A.
Exact method for the capacitated competitive facility location problem
Computers and Operations Research. 2018. V.95. P.73-82. DOI: 10.1016/j.cor.2018.02.013 WOS Scopus OpenAlex

Identifiers:

Web of science:	WOS:000432767600006
Scopus:	2-s2.0-85043594642
OpenAlex:	W2791530219

Citing:

DB	Citing
Scopus	25
OpenAlex	27
Web of science	18

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