**Seminar on Applied Mathematics**

**PROGRAM**

Matematički fakultet

Fakultet organizacionih nauka

JUPIM

IEEE Computer Chapter, Srbija

MI SANU, Knez Mihailova 36, sala 301f

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** Ponedeljak, 27.09.2010. u 14:15, Sala 301f, MI SANU: **

** Yury Kochetov, Sobolev Institute of Mathematics, Novosibirsk, Russia; e-mail: jkochet@math.nsc.ru 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. **

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** RUKOVODIOCI SEMINARA **

** Vera Kovačević-Vujčić Milan Dražić **