Shioura, A., Strusevich, V.A. and Shakhlevich, N.V. orcid.org/0000-0002-5225-4008 (2024) Generalizing Horn's conditions for preemptive scheduling on identical parallel machines via network flow techniques. Networks, 83 (3). pp. 527-546. ISSN 0028-3045
Abstract
We study the use of flow-based algorithmic and proof techniques applied to preemptive scheduling of jobs on parallel identical machines. For the classical problem in which the jobs have individual release dates and must be finished by a common deadline, we present and prove unified necessary and sufficient conditions for the existence of a feasible schedule by examining the structure of minimum cuts in a special network. We then study an enhanced model that allows the presence of additional resources, provided that some jobs at any time of their processing require one unit of a particular resource. We extend our argument developed for the classical case to this enhanced model. The generalized necessary and sufficient conditions for the existence of a feasible schedule are presented and proved using the max-flow/min-cut reasoning.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 The Authors. Networks published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | maximum-flow problem; minimum-cut problem; optimality conditions; parallel-machine scheduling; preemption; scheduling under resource constraints; scheduling with 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: | 21 Nov 2023 10:43 |
Last Modified: | 15 Oct 2024 13:20 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1002/net.22202 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:205518 |