NDLI: A note on the preemptive scheduling to minimize total completion time with release time and deadline constraints

Content Provider	Springer Nature Link
Author	Geng, Zhichao Wan, Long Yuan, Jinjiang
Copyright Year	2014
Abstract	In this paper, we consider two problems about the preemptive scheduling of a set of jobs with release times on a single machine. In the first problem, each job has a deadline. The objective is to find a feasible schedule which minimizes the total completion time of the jobs. In the second problem (called two-agent scheduling problem), the set of jobs is partitioned into two subsets $$\mathcal{J}^{(1)}$$ and $$\mathcal{J}^{(2)}$$ . Each job in $$\mathcal{J}^{(2)}$$ has a deadline. The objective is to find a feasible schedule which minimizes the total completion time of the jobs in $$\mathcal{J}^{(1)}$$ . For the first problem, Du and Leung (Journal of Algorithms 14:45–68, 1993) showed that the problem is NP-hard. We show in this paper that there is a flaw in their NP-hardness proof. For the second problem, Leung et al. (Operations Research 58:458–469, 2010) showed that the problem can be solved in polynomial time. Yuan et al. (Private Communication) showed that their polynomial-time algorithm is invalid so the complexity of the second problem is still open. In this paper, by a modification of Du and Leung’s NP-hardness proof, we show that the first problem is NP-hard even when the jobs have only two distinct deadlines. Using the same reduction, we also show that the second problem is NP-hard even when the jobs in $$\mathcal{J}^{(2)}$$ has a common deadline $$D>0$$ and a common release time 0.
Ending Page	323
Page Count	9
Starting Page	315
File Format	PDF
ISSN	10946136
e-ISSN	10991425
Journal	Journal of Scheduling
Issue Number	3
Volume Number	18
Language	English
Publisher	Springer US
Publisher Date	2014-02-04
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Preemptive scheduling NP-hard Calculus of Variations and Optimal Control; Optimization Operations Research/Decision Theory Deadline Release time Artificial Intelligence (incl. Robotics) Production/Logistics/Supply Chain Scheduling theory, deterministic Combinatorial optimization Optimization
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Management Science and Operations Research Engineering Software

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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