Shioura, A, Strusevich, VA and Chakhlevitch, NV orcid.org/0000-0002-5225-4008 (2024) Preemptive scheduling of parallel jobs of two sizes with controllable processing times. Journal of Scheduling, 27. pp. 203-224. ISSN 1094-6136
Abstract
In parallel machine scheduling, a size of a job is defined as the number of machines that are simultaneously required for its processing. This paper considers a scheduling problem in which the set of jobs consists of jobs of two sizes: the conventional jobs (each job requires a single machine for its processing) and parallel jobs (each job to be simultaneously processed on more than one machine). The processing times are controllable, and they have to be chosen from given intervals in order to guarantee the existence of a preemptive schedule in which all jobs are completed by a common deadline. The objective is to minimize the total compression cost which reflects possible reductions in processing times. Unlike problems of classical scheduling with conventional jobs, the model under consideration cannot be directly handled by submodular optimization methods. We reduce the problem to maximizing the total weighted work of all jobs parametrized with respect to total work of the parallel jobs. The solution is delivered by separately finding the breakpoints for the maximum total weighted work of the parallel jobs and for the maximum total weighted work of the conventional jobs. This results in a polynomial-time algorithm that is no slower than needed to perform sorting of jobs’ parameters.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Multi-processor jobs; Submodular optimization; Parallel machine scheduling; Controllable processing times |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/T01461X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Mar 2023 16:18 |
Last Modified: | 21 May 2024 12:13 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10951-023-00782-w |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:197256 |