**Wednesday, 15:15 - 15:40 h, Room: H 3008**

**Vladimir Beresnev**

Algorithms for discrete competitive facility location problem

**Abstract:**

We consider a mathematical model generalizing the well-known facility location problem. In this model two rival sides (Leader and Follower) sequentially open their facilities and aim to capture clients in order to make maximal profit. We state the problem as a bilevel integer programming problem. It includes the upper level (Leader’s) problem and the lower level (Follower’s) problem. We consider so-called optimal noncooperative solutions to the problem, where from all possible optimal solutions to Follower’s problem we choose the solution which yields the smallest value of the objective function of the Leader’s problem. We represent our problem as the problem of maximizing a pseudo-Boolean function. We propose a local search algorithm for constructing an approximate solution to the problem and a branch-and-bound algorithm for finding an optimal solution of the problem. An important ingredient of the algorithms is a method for calculating an upper bound for the values of the pseudo-Boolean function on subsets of solutions.

Talk 1 of the contributed session Wed.3.H 3008

**"Competitive and multi-objective facility location"** [...]

Cluster 2

**"Combinatorial optimization"** [...]