A new three-machine shop scheduling: complexity and approximation algorithm

Authors:
Jianming Dong;Yong Chen;An Zhang;Qifan Yang
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou, PR China 310027;Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, PR China 310018;Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, PR China 310018;Department of Mathematics, Zhejiang University, Hangzhou, PR China 310027
Venue:
Journal of Combinatorial Optimization
Year:
2013

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Abstract

The paper investigates a new three-machine shop scheduling problem that arises from many production systems, such as the garment assembly line, etc. In such scenarios, each job consists of three operations, each of which has to be non-preemptively processed by one specific machine. In contrast with the classical three-machine shop scheduling, the processing order of the operations of each job is partially restricted. In particular, the first two operations are ordered and all the same for all jobs, while the third operation is not restricted. The objective is to minimize the makespan. We show the problem is NP-hard in the ordinary sense and present a polynomial time approximation algorithm with a worst case performance ratio of $\frac{3}{2}$.