Scheduling two-machine preemptive open shops to minimize total completion time

Authors:
Ching-Fang Liaw
Affiliations:
Department of Industrial Engineering and Management, Chaoyang University of Technology, 168 Gifeng East Road, Wufeng, Taichung, Taiwan
Venue:
Computers and Operations Research
Year:
2004

Citing 5
Cited 0

Scheduling ordered open shops

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Minimizing total tardiness on one machine is NP-hard

Mathematics of Operations Research
A branch & bound algorithm for the open-shop problem

GO-II Meeting Proceedings of the second international colloquium on Graphs and optimization
Open Shop Scheduling to Minimize Finish Time

Journal of the ACM (JACM)
Scheduling Algorithms

Scheduling Algorithms

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Abstract

This paper deals with the problem of scheduling two-machine preemptive open shops to minimize total completion time. The un-weighted version of this problem is known to be NP-hard in the ordinary sense, while the weighted version of this problem is known to be NP-hard in the strong sense. Based on the analysis of problem characteristics, several fundamental properties are presented. A dynamic programming (DP) algorithm is developed to optimally solve both the un-weighted and weighted versions of the problem. Also, an efficient heuristic is proposed for solving large-sized problems. Computational results show that the proposed DP algorithm can handle problems with up to 30 jobs within a reasonable amount of time, and that the proposed heuristic has an average percentage deviation of less than 0.5% from the optimal solution value for problems with up to 30 jobs.