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A Polynomial-Time Algorithm for the Routing Flow Shop Problem with Two Machines: An Asymmetric Network with a Fixed Number of Nodes

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Mathematical Optimization Theory and Operations Research (MOTOR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12095))

Abstract

We consider the routing flow shop problem with two machines on an asymmetric network. For this problem we discuss properties of an optimal schedule and present a polynomial time algorithm assuming the number of nodes of the network to be bounded by a constant. To the best of our knowledge, this is the first positive result on the complexity of the routing flow shop problem with an arbitrary structure of the transportation network, even in the case of a symmetric network. This result stands in contrast with the complexity of the two-machine routing open shop problem, which was shown to be NP-hard even on the two-node network.

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 20-07-00458 and 18-01-00747.

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Notes

  1. 1.

    The relationship between the routing flow shop problem and the problem of planning the construction of country houses in England was proposed by Natalia Shakhlevich in a private communication.

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Author information

Authors and Affiliations

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

    Ilya Chernykh, Alexander Kononov & Sergey Sevastyanov

  2. Novosibirsk State University, Pirogov str. 2, Novosibirsk, 630090, Russia

    Ilya Chernykh

Authors
  1. Ilya Chernykh
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  2. Alexander Kononov
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  3. Sergey Sevastyanov
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Corresponding author

Correspondence to Sergey Sevastyanov .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Alexander Kononov

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

    Michael Khachay

  3. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A Kalyagin

  4. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Chernykh, I., Kononov, A., Sevastyanov, S. (2020). A Polynomial-Time Algorithm for the Routing Flow Shop Problem with Two Machines: An Asymmetric Network with a Fixed Number of Nodes. In: Kononov, A., Khachay, M., Kalyagin, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Lecture Notes in Computer Science(), vol 12095. Springer, Cham. https://doi.org/10.1007/978-3-030-49988-4_21

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