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Multi-index transportation problems with 1-nested structure

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Abstract

Consideration was given to the solution of the multi-index transportation problems of linear and integer-linear programming. It was proposed to use the approach based on studying the reducibility of the multi-index transportation problems to the problem of the minimal cost in the treelike network. It was proved that within the framework of the reduction scheme the condition for 1-nesting of the multi-index problems is necessary and sufficient for reducibility to the problem of the minimal-cost flow problem on a treelike network. An algorithm was proposed to solve the 1-nested multi-index problems requiring as many computer operations as the square of variables in the original problem.

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Authors and Affiliations

  1. Lobachevsky State University, Nizhny Novgorod, Russia

    L. G. Afraimovich, A. S. Katerov & M. Kh. Prilutskii

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  1. L. G. Afraimovich
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  2. A. S. Katerov
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  3. M. Kh. Prilutskii
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Correspondence to L. G. Afraimovich.

Additional information

Original Russian Text © L.G. Afraimovich, A.S. Katerov, M.Kh. Prilutskii, 2016, published in Avtomatika i Telemekhanika, 2016, No. 11, pp. 18–42.

This paper was recommended for publication by A.A. Lazarev, a member of the Editorial Board

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Afraimovich, L.G., Katerov, A.S. & Prilutskii, M.K. Multi-index transportation problems with 1-nested structure. Autom Remote Control 77, 1894–1913 (2016). https://doi.org/10.1134/S0005117916110023

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