Additional Constraints for Dynamic Competitive Facility Location Problem

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 consisting a known number of time periods. It is assumed 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 that is based on using HP-relaxation of the bilevel 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 paper, we propose new families of additional constraints to strengthen the HP-relaxation that allow computing nontrivial upper bounds.