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Title: Two-machine flowshop batching and scheduling
Authors: Lin, B. M. T.
Cheng, T. C. Edwin
Subjects: Production scheduling
Batch processing
Strong NP-hardness
Lower bound
Issue Date: 2005
Publisher: Springer Netherlands
Source: Annals of operations research, Jan. 2005, v. 133, no. 1-4, p. 149-161.
Abstract: We consider in this paper a two-machine flowshop scheduling problem in which the first machine processes jobs individually while the second machine processes jobs in batches. The forming of each batch on the second machine incurs a constant setup time. The objective is to minimize the makespan. This problem was previously shown to be NP-hard in the ordinary sense. In this paper, we first present a strong NP-hardness result of the problem. We also identify a polynomially solvable case with either anticipatory or non-anticipatory setups. We then establish a property that an optimal solution for the special case is a lower bound for the general problem. To obtain near-optimal solutions for the general problem, we devise some heuristics. The lower bound is used to evaluate the quality of the heuristic solutions. Results of computational experiments reveal that the heuristics produce solutions with small error ratios. They also suggest that the lower bound is close to the optimal solution.
Rights: © 2005 Springer Science + Business Media. The original publication is available at
Type: Journal/Magazine Article
DOI: 10.1007/s10479-004-5029-7
ISSN: 0254-5330 (print)
1572-9338 (online)
Appears in Collections:LMS Journal/Magazine Articles

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