Upper bound for the competitive facility location problem with demand uncertainty

We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenario. The problem to find the best solutions for the parties is formulated as a discrete bi-level mathematical programming problem. In the paper, we suggest a procedure to compute an upper bound for the objective function on subsets. The procedure could be employed in implicit enumeration schemes capable to compute an optimal solution for the problem under study. Within the procedure, additional constraints iteratively augment the high-point relaxation of the initial bi-level problem, what strengthens the relaxation and improves the upper bound’s quality. New procedure to generate such cuts allows to construct the strongest cuts without enumerating the parameters encoding them.