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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 4, Pages 569–592
DOI: https://doi.org/10.35634/vm220406
(Mi vuu827)
 

This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

Dynamic programming and questions of solvability of route bottleneck problem with resource constraints

A. G. Chentsovab, A. A. Chentsovb

a Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
b N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
References:
Abstract: The article deals with the problem of admissible routing for a system of cycles each of which contains exterior permutation and works connected with megalopolises (non-empty finite sets) visiting. In the initial setting, a resource constraint is given; this constraint should be fulfilled for every cycle under permutation. The solvability conditions in this problem are connected with the extremum of the auxiliary bottleneck routing problem without above-mentioned constraint, in which the apparatus of widely understood dynamic programming (DP) is used. A particular case of the setting is the known bottleneck courier problem which can be used (in particular) for routing a vehicle (airplane or helicopter) aiming to realize the given shipping system with a limited fuel reserve on each flight. An algorithm implemented on a personal computer is constructed.
Keywords: dynamic programming, route, precedence conditions.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-874
This work was funded within the framework of research at the Ural Mathematical Center supported by the Ministry of Science and Higher Education of the Russian Federation (agreement number 075-02-2022-874).
Received: 07.09.2022
Accepted: 10.10.2022
Bibliographic databases:
Document Type: Article
UDC: 519.8
MSC: 49L20, 90C39
Language: Russian
Citation: A. G. Chentsov, A. A. Chentsov, “Dynamic programming and questions of solvability of route bottleneck problem with resource constraints”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:4 (2022), 569–592
Citation in format AMSBIB
\Bibitem{CheChe22}
\by A.~G.~Chentsov, A.~A.~Chentsov
\paper Dynamic programming and questions of solvability of route bottleneck problem with resource constraints
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2022
\vol 32
\issue 4
\pages 569--592
\mathnet{http://mi.mathnet.ru/vuu827}
\crossref{https://doi.org/10.35634/vm220406}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4534872}
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  • https://www.mathnet.ru/eng/vuu/v32/i4/p569
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:23
     
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