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Trudy Inst. Mat. i Mekh. UrO RAN, 2017, Volume 23, Number 1, Pages 275–292 (Mi timm1402)  

This article is cited in 2 scientific papers (total in 2 papers)

A discrete-continuous routing problem with precedence conditions

A. G. Chentsovab, A. A. Chentsova

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: We consider the problem of visiting closed sets in a compact metric space complicated by constraints in the form of precedence conditions and a possible dependence of the cost function on a list of tasks. We study a variant of the approximate realization of the extremum by applying models that involve problems of sequential visits to megalopolises (nonempty finite sets). This variant is naturally embedded into a more general construction that implements sequential visits to nonempty closed sets (NCSs) from a finite system in a metrizable compactum. The space of NCSs is equipped with the Hausdorff metric, which is used to estimate (under the corresponding condition that the sections of the cost functions are continuous) the proximity of the extrema in the problem of sequential visits for any two systems of NCSs (it is assumed that the numbers or NCSs in the systems are the same). The constraints in the form of precedence conditions are preserved.

Keywords: route, path, precedence conditions.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-07909
16-01-00505
16-01-00649
Ural Branch of the Russian Academy of Sciences 15-16-1-8


DOI: https://doi.org/10.21538/0134-4889-2017-23-1-275-292

Full text: PDF file (642 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2018, 300, suppl. 1, 56–71

Bibliographic databases:

UDC: 519.6
MSC: 49L20, 90C39
Received: 21.06.2016

Citation: A. G. Chentsov, A. A. Chentsov, “A discrete-continuous routing problem with precedence conditions”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 1, 2017, 275–292; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 56–71

Citation in format AMSBIB
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\paper A discrete-continuous routing problem with precedence conditions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2017
\vol 23
\issue 1
\pages 275--292
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\crossref{https://doi.org/10.21538/0134-4889-2017-23-1-275-292}
\elib{http://elibrary.ru/item.asp?id=28409386}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2018
\vol 300
\issue , suppl. 1
\pages 56--71
\crossref{https://doi.org/10.1134/S0081543818020074}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Petunin, A. G. Chentsov, P. A. Chentsov, “K voprosu o marshrutizatsii peremeschenii pri listovoi rezke detalei”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:3 (2017), 25–39  mathnet  crossref  elib
    2. Alexander G. Chentsov, Alexey M. Grigoriev, Alexey A. Chentsov, “Optimizing the starting point in a precedence constrained routing problem with complicated travel cost functions”, Ural Math. J., 4:2 (2018), 43–55  mathnet  crossref  mathscinet
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