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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
Baruch Mor, G. Mosheiov (2016)
A two-agent single machine scheduling problem with due-window assignment and a common flow-allowanceJournal of Combinatorial Optimization, 33
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
- ISSN
- 1862-4472
- eISSN
- 1862-4480
- DOI
- 10.1007/s11590-022-01967-6
- Publisher site
- See Article on Publisher Site
Abstract
We consider two-agent scheduling on a single-machine with release dates. There are two agents, namely, A and B. Each agent has his own job set. Each job has a release date and a processing time. All jobs need to be scheduled on a single machine. The objective function of each agent is the makespan with respect to his jobs, i.e., the maximum completion time. We consider two problems, namely the problem to minimize the makespans of agent A with the makespan of agent B not greater than a positive number Q given in advance, and the problem to minimize the weighted sum of both agents’ makespans. For the first problem, we drive an approximation algorithm with a worst-case ratio of 32\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\frac{3}{2}$$\end{document}. Furthermore, we show that this problem admits a fully polynomial-time approximation scheme(FPTAS). For the second problem, we propose an improved approximation algorithm with a worst-case ratio of 1+θ(1+θ)2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$1 +\frac{\theta }{(1+\theta )^2}$$\end{document}, where θ>0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta >0$$\end{document} is the weight of agent B.
Journal
Optimization Letters – Springer Journals
Published: Nov 1, 2023
Keywords: Two-agent scheduling; Makespan; Release date; Approximation algorithm; FPTAS