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How the Difference in Travel Times Affects the Optima Localization for the Routing Open Shop

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

The routing open shop problem, being a generalization of the metric TSP and the open shop scheduling problem, is known to be NP-hard even in case of two machines with a transportation network consisting of two nodes only. We consider a generalization of this problem with unrelated travel times of each machine. We determine a tight optima localization interval for the two-machine problem in the case when the transportation network consists of at most three nodes. As a byproduct of our research, we present a linear time \(\frac{5}{4}\)-approximation algorithm for the same problem. We prove that the algorithm has the best theoretically possible approximation ratio with respect to the standard lower bound.

This research was supported by the Russian Foundation for Basic Research, projects 17-01-00170, 17-07-00513 and 18-01-00747.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Ilya Chernykh

  2. Novosibirsk State University, Novosibirsk, Russia

    Ilya Chernykh & Ekaterina Lgotina

  3. Novosibirsk State Technical University, Novosibirsk, Russia

    Ilya Chernykh

Authors
  1. Ilya Chernykh
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  2. Ekaterina Lgotina
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Corresponding author

Correspondence to Ilya Chernykh .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Chernykh, I., Lgotina, E. (2019). How the Difference in Travel Times Affects the Optima Localization for the Routing Open Shop. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_14

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

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