Seminar on Applied Mathematics
Yury Kochetov, Sobolev Institute of Mathematics, Novosibirsk, Russia; e-mail: firstname.lastname@example.org
HEURISTIC AND EXACT METHODS FOR THE COMPETITIVE p-MEDIAN PROBLEM
Sadrzaj: In the competitive p-median problem two decision makers, a leader and a follower, compete to attract clients from a given market. The leader opens p facilities, anticipating that the follower will react to the decision by opening his own r facilities. The decision makers try to maximize their own profits. This Stackelberg game is P2 -hard. We develop a hybrid memetic algorithm for it where probabilistic tabu search heuristic is applied for improving the offspring. To obtain an upper bound, we reformulate the problem as a mixed integer program with large number of constraints and variables. Selecting some of them, we get the desired upper bound. To find optimal solutions, we iteratively modify the subset of the constraints and variables. This approach is tested on the benchmarks from the library Discrete Location Problems. The optimal solutions are found for r = p = 5, 100 clients, and 100 facilities.