@inproceedings{e9940e38d569489f9369d7d424fa44b8,

title = "On the Optima Localization for the Three-Machine Routing Open Shop",

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.",

keywords = "Approximation algorithm, Computer-aided proof, Open shop, Optima localization, Routing open shop",

author = "Ilya Chernykh and Olga Krivonogova",

year = "2020",

month = jan,

day = "1",

doi = "10.1007/978-3-030-49988-4_19",

language = "English",

isbn = "9783030499877",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Gabler",

pages = "274--288",

editor = "Alexander Kononov and Michael Khachay and Kalyagin, {Valery A.} and Panos Pardalos",

booktitle = "Mathematical Optimization Theory and Operations Research - 19th International Conference, MOTOR 2020, Proceedings",

address = "Germany",

note = "19th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2020 ; Conference date: 06-07-2020 Through 10-07-2020",

}