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Efficient Algorithms for the Routing Open Shop with Unrelated Travel Times on Cacti

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Optimization and Applications (OPTIMA 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1145))

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Abstract

The object of investigation is the routing open shop problem, in which a fleet of machines have to visit all the nodes of a given transportation network to perform operations on some jobs located at those nodes. Each machine has to visit each node, to process each job and to return back to the common initial location—the depot. Operations of each job can be processed in an arbitrary sequence, any machine may perform at most one operation at a time. The goal is to construct a feasible schedule to minimize the makespan. The routing open shop problem is known to be NP-hard even in the simplest two-machine case with the transportation network consisting of just two nodes (including the depot). We consider a certain generalization of this problem in which travel times are individual for each of the two machines and the structure of the transportation network is an arbitrary cactus. We generalize an instance reduction algorithm known for the problem on a tree with identical travel times, and use it to describe new polynomially solvable cases for the problem, as well as an efficient approximation algorithm for another special case with a tight approximation ratio guarantee.

This research was supported by the program of fundamental scientific researches of the SB RAS No I.5.1., project No 0314-2019-0014, and by the Russian Foundation for Basic Research, projects 17-01-00170, 17-07-00513 and 18-01-00747, and by the Russian Ministry of Science and Education under the 5–100 Excellence Programme.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Koptyug Avenue 4, Novosibirsk, 630090, Russia

    Ilya Chernykh

  2. Novosibirsk State University, Pirogova Street 2, Novosibirsk, 630090, Russia

    Ilya Chernykh & Olga Krivonogova

  3. Novosibirsk State Technical University, Marksa Avenue 20, Novosibirsk, 630073, Russia

    Ilya Chernykh

Authors
  1. Ilya Chernykh
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  2. Olga Krivonogova
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Correspondence to Ilya Chernykh .

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Editors and Affiliations

  1. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  2. Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  3. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

  4. FRC CSC RAS, Moscow, Russia

    Mikhail Posypkin

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Chernykh, I., Krivonogova, O. (2020). Efficient Algorithms for the Routing Open Shop with Unrelated Travel Times on Cacti. In: Jaćimović, M., Khachay, M., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2019. Communications in Computer and Information Science, vol 1145. Springer, Cham. https://doi.org/10.1007/978-3-030-38603-0_1

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  • DOI: https://doi.org/10.1007/978-3-030-38603-0_1

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