Abstract:
The problem of a sequential traversal of sets is considered, which is complicated by the necessity of fulfilling (internal) tasks on the sets as well as by restrictions in the form of precedence conditions. It is assumed that the method of aggregating the losses is additive. For the appearing extremal problem with dependent variables, an equivalent transformation is built for the optimization problem on a Cartesian product. Based on this, an iteration method is constructed that uses a reconstructible model of the courier problem (a traveling salesman problem complicated by precedence conditions).
Citation:
A. A. Chentsov, A. G. Chentsov, P. A. Chentsov, “Iteration method in the routing problem with internal losses”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 270–289; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S48–S68
\Bibitem{CheCheChe09}
\by A.~A.~Chentsov, A.~G.~Chentsov, P.~A.~Chentsov
\paper Iteration method in the routing problem with internal losses
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 270--289
\mathnet{http://mi.mathnet.ru/timm443}
\elib{https://elibrary.ru/item.asp?id=12952772}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S48--S68
\crossref{https://doi.org/10.1134/S0081543810060064}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962467093}
Linking options:
https://www.mathnet.ru/eng/timm443
https://www.mathnet.ru/eng/timm/v15/i4/p270
This publication is cited in the following 8 articles:
A. A. Petunin, A. A. Chentsov, A. G. Chentsov, P. A. Chentsov, “Elements of dynamic programming in local improvement constructions for heuristic solutions of routing problems with constraints”, Autom. Remote Control, 78:4 (2017), 666–681
A. A. Petunin, A. G. Chentsov, P. A. Chentsov, “Lokalnye vstavki na osnove dinamicheskogo programmirovaniya v zadache marshrutizatsii s ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 56–75
A. A. Chentsov, A. G. Chentsov, P. A. Chentsov, “Elements of dynamic programming in extremal route problems”, Automation and Remote Control, 75:3 (2014), 537–550
A. A. Chentsov, A. G. Chentsov, “Metod iteratsii v obobschennoi zadache kurera s osobennostyu v opredelenii funktsii stoimosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 3, 88–113
Chentsov A.G., Chentsov A.A., “Dynamic Programming in the Routing Problem with Constraints and Costs Depending on a List of Tasks”, Dokl. Math., 88:3 (2013), 637–640
A. A. Chentsov, A. G. Chentsov, “On an iterative procedure for solving a routing problem with constraints”, Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 24–45
A. G. Chentsov, P. A. Chentsov, “Ob odnoi nestatsionarnoi zadache marshrutizatsii s ogranicheniyami”, Model. i analiz inform. sistem, 19:4 (2012), 5–24
Salii Ya.V., Chentsov A.G., “Ob odnoi marshrutnoi zadache na uzkie mesta s vnutrennimi rabotami”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 17:3 (2012), 827–847
On a bottleneck routing problem with internal tasks
Citation in format AMSBIB
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