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

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 15-01-0790916-01-0050516-01-00649 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

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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

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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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
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
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