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On the Optima Localization for the Three-Machine Routing Open Shop

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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

A tight optima localization interval for the classical open shop scheduling problem with three machines was established by S. Sevastyanov and I. Chernykh in 1998. It was proved that for any problem instance its optimal makespan does not exceed \(\frac{4}{3}\) times the standard lower bound. The process of proof involved massive computer-aided enumeration of the subsets of instances of the problem considered and took about 200 h of the running time to complete. This makes it seemingly impossible to use the same approach for more complicated problems, i.e. the four machine open shop for which the optima localization interval is still unknown. In this paper we apply that computer-aided approach to the three-machine routing open shop problem on a two-node transportation network. For this generalization of the plain open shop problem we derive some extreme instance properties and prove that the optimal makespan does not exceed \(\frac{4}{3}\) times the standard lower bound, thus generalizing the result previously known for the three-machine open shop.

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 20-01-00045 and 18-01-00747.

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Authors and Affiliations

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

    Ilya Chernykh

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

    Olga Krivonogova

Authors
  1. Ilya Chernykh
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  2. Olga Krivonogova
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Corresponding author

Correspondence to Ilya Chernykh .

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., Krivonogova, O. (2020). On the Optima Localization for the Three-Machine Routing Open Shop. 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_19

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