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Avtomatika i Telemekhanika, 2016, Issue 11, Pages 18–42 (Mi at14595)  
This article is cited in 4 scientific papers (total in 4 papers)

Topical issue

Multi-index transportation problems with $1$-nested structure

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

Lobachevsky State University, Nizhny Novgorod, Russia
Full-text PDF (733 kB) Citations (4)
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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.
Funding agency Grant number
Russian Science Foundation 15-11-30022
This work was supported in part by the grant “Global Optimization, Supercomputer Calculations, and Applications” of the Russian Science Foundation, project no. 15-11-30022.
Presented by the member of Editorial Board: A. A. Lazarev

Received: 04.02.2016
English version:
Automation and Remote Control, 2016, Volume 77, Issue 11, Pages 1894–1913
DOI: https://doi.org/10.1134/S0005117916110023
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. G. Afraimovich, A. S. Katerov, M. Kh. Prilutskii, “Multi-index transportation problems with $1$-nested structure”, Avtomat. i Telemekh., 2016, no. 11, 18–42; Autom. Remote Control, 77:11 (2016), 1894–1913
Citation in format AMSBIB
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\jour Autom. Remote Control
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:36
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