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

Ilya Chernykh, Olga Krivonogova

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

2 Цитирования (Scopus)

## Аннотация

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.

Язык оригинала английский Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Proceedings Alexander Kononov, Michael Khachay, Valery A. Kalyagin, Panos Pardalos Springer Gabler 274-288 15 9783030499877 https://doi.org/10.1007/978-3-030-49988-4_19 Опубликовано - 1 янв 2020 19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020 - Novosibirsk, Российская ФедерацияПродолжительность: 6 июл 2020 → 10 июл 2020

### Серия публикаций

Название Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 12095 LNCS 0302-9743 1611-3349

### Конференция

Конференция 19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020 Российская Федерация Novosibirsk 06.07.2020 → 10.07.2020

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