On an approach to the robustness in the case of the $p$-median problem

I. L. Vasilyev, A. V. Ushakov

Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, 134, Lermontov St., Irkutsk, 664033

Abstract: In this paper we study an approach to the robustness of discrete facility location problems by the example of the $p$-median problem. For that purpose a bicriteria facility location problem of $p$ points of service in order to minimize the total cost of satisfying the demands of all clients and to maximize the robustness of obtained solutions is considered. An algorithm of finding an approximation of the weak Pareto solution set based on the $\varepsilon$-constraint method has been proposed.

Keywords: discrete facility location, robustness, bi-objective combinatorial optimization, $p$-median problem, $\varepsilon$-constraint method.

UDC: 519.854.2