The total completion time open shop scheduling problem with a given sequence of jobs on one machine

Authors:
Ching-Fang Liaw;Chun-Yuan Cheng;Mingchih Chen
Affiliations:
Department of Industrial Engineering and Management, Chaoyang University of Technology, 168 Gifeng East Road, Wufeng, Taichung, Taiwan;Department of Industrial Engineering and Management, Chaoyang University of Technology, 168 Gifeng East Road, Wufeng, Taichung, Taiwan;Department of Industrial Engineering and Management, Chaoyang University of Technology, 168 Gifeng East Road, Wufeng, Taichung, Taiwan
Venue:
Computers and Operations Research
Year:
2002

Citing 3
Cited 1

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)
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness

Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop

Mathematical and Computer Modelling: An International Journal

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Abstract

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.