Geodesic
Uniform Capacitated Facility Location Problem with Random Input Data
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 1, pp. 15-34

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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 
@article{VNGU_2011_11_1_a1,
     author = {E. Kh. Gimadi and A. A. Kurochkin},
     title = {Uniform {Capacitated} {Facility} {Location} {Problem} with {Random} {Input} {Data}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {15--34},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_1_a1/}
}
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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/