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 Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2011, Volume 11, Issue 1, Pages 15–34 (Mi vngu65)

Uniform Capacitated Facility Location Problem with Random Input Data

E. Kh. Gimadiab, A. A. Kurochkina

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: 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, transportation problem, graph with random edges, perfect matching, asymptotically exact algorithm, Chebyshev inequality, Petrov theorem.

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English version:
Journal of Mathematical Sciences, 2013, 188:4, 359–377

UDC: 519.8

Citation: E. Kh. Gimadi, A. A. Kurochkin, “Uniform Capacitated Facility Location Problem with Random Input Data”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:1 (2011), 15–34; J. Math. Sci., 188:4 (2013), 359–377

Citation in format AMSBIB
\Bibitem{GimKur11}
\paper Uniform Capacitated Facility Location Problem with Random Input Data
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2011
\vol 11
\issue 1
\pages 15--34
\mathnet{http://mi.mathnet.ru/vngu65}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 188
\issue 4
\pages 359--377
\crossref{https://doi.org/10.1007/s10958-012-1134-3}