Geodesic
Uniform Capacitated Facility Location Problem with Random Input Data
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 1, pp. 15-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Capacitated Facility Location Problem with uniform capacitates and some specific demand restrictions is studied in this paper. Elements of cost matrix $(g_{ij})$ are assumed to take random values according to discrete uniform distribution. An approximation algorithm for solving this problem is suggested and the probabilistic analysis of its work is demonstrated. A key role in this algorithm belongs to the procedure of finding the perfect matching in graph with random edges. The conditions when the algorithm is asymptotically exact with time complexity $O(n \ln m)$ ($n$ — the number of clients, $m$ — the number of facilities) are found.
Keywords: facility location problem, graph with random edges, perfect matching, asymptotically exact algorithm, Chebyshev inequality, Petrov theorem.
Mots-clés : transportation problem 
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E. Kh. Gimadi; A. A. Kurochkin. Uniform Capacitated Facility Location Problem with Random Input Data. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 1, pp. 15-34. http://geodesic.mathdoc.fr/item/VNGU_2011_11_1_a1/

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