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

Ilya Chernykh, Olga Krivonogova

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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.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Proceedings
EditorsAlexander Kononov, Michael Khachay, Valery A. Kalyagin, Panos Pardalos
PublisherSpringer Gabler
Pages274-288
Number of pages15
ISBN (Print)9783030499877
DOIs
Publication statusPublished - 1 Jan 2020
Event19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020 - Novosibirsk, Russian Federation
Duration: 6 Jul 202010 Jul 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12095 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020
CountryRussian Federation
CityNovosibirsk
Period06.07.202010.07.2020

Keywords

  • Approximation algorithm
  • Computer-aided proof
  • Open shop
  • Optima localization
  • Routing open shop

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