Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 1, Pages 24–45
This article is cited in 2 scientific papers (total in 2 papers)
A model of “nonadditive” routing problem where the costs depend on the set of pending tasks
A. G. Chentsovab, Ya. V. Saliiab
a Krasovskii Institute of Mathematics and Mechanics, Ural Branch
of the Russian Academy of Sciences, Yekaterinburg, Russian Federation
b Ural Federal University Named after the First President of Russia B. N. Yeltsin, Yekaterinburg, Russian Federation
We consider a generalization of the bottleneck (minimax) routing problem. The problem is to successively visit a number of megalopolises, complicated by precedence of constraints imposed on the order of megalopolises visited and the fact that the cost functions (of movement between megalopolises and of interior tasks) may explicitly depend on the list of tasks that are not completed at the present time. The process of movement is considered to be a sequence of steps, which include the exterior movement to the respective megalopolis and the following completion of (essentially interior) jobs connected with the megalopolis. The quality of the whole process is represented by the maximum cost of steps it consists of; the problem is to minimize the mentioned criterion (which yields a minimax problem, usually referred to as a “bottleneck problem”). Optimal solutions, in the form of a route-track pair (a track, or trajectory, conforms to a specific instance of a tour over the megalopolises, which are numbered in accordance with the route; the latter is defined by the transposition of indices), are constructed through a “nonstandard” variant of the dynamic programming method, which allows to avoid the process of constructing of all the values of the Bellman function whenever precedence constraints are present.
dynamic programming; route; precedence constraints; sequential ordering problem.
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MSC: 90C90, 90C39
A. G. Chentsov, Ya. V. Salii, “A model of “nonadditive” routing problem where the costs depend on the set of pending tasks”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:1 (2015), 24–45
Citation in format AMSBIB
\by A.~G.~Chentsov, Ya.~V.~Salii
\paper A model of ``nonadditive'' routing problem where the costs depend on the set of pending tasks
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
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A. G. Chentsov, A. A. Chentsov, “Marshrutizatsiya peremeschenii pri dinamicheskikh ogranicheniyakh: zadacha “na uzkie mesta””, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:1 (2016), 121–140
A. G. Chentsov, A. A. Chentsov, “A discrete-continuous routing problem with precedence conditions”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 56–71
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