Two-machine flowshop batching and scheduling

Research output: Journal article publicationJournal articleAcademic researchpeer-review

25 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)149-161
Number of pages13
JournalAnnals of Operations Research
Issue number1-4
Publication statusPublished - 1 Jan 2005


  • Batch processing
  • Flowshop
  • Heuristics
  • Lower bound
  • Makespan
  • Production scheduling
  • Strong NP-hardness

ASJC Scopus subject areas

  • Management Science and Operations Research
  • General Decision Sciences


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