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Makespan minimization in the two‐machine flowshop batch scheduling problem

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  • T.C.E. Cheng
  • B.M.T. Lin
  • A. Toker

Abstract

In this paper we consider a practical scheduling problem commonly arising from batch production in a flexible manufacturing environment. Different part‐types are to be produced in a flexible manufacturing cell organized into a two‐stage production line. The jobs are processed in batches on the first machine, and the completion time of a job is defined as the completion time of the batch containing it. When processing of all jobs in a batch is completed on the first machine, the whole batch of jobs is transferred intact to the second machine. A constant setup time is incurred whenever a batch is formed on any machine. The tradeoff between the setup times and batch processing times gives rise to the batch composition decision. The problem is to find the optimal batch composition and the optimal schedule of the batches so that the makespan is minimized. The problem is shown to be strongly NP‐hard. We identify some special cases by introducing their corresponding solution methods. Heuristic algorithms are also proposed to derive approximate solutions. We conduct computational experiments to study the effectiveness of the proposed heuristics. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 128–144, 2000

Suggested Citation

  • T.C.E. Cheng & B.M.T. Lin & A. Toker, 2000. "Makespan minimization in the two‐machine flowshop batch scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 128-144, March.
  • Handle: RePEc:wly:navres:v:47:y:2000:i:2:p:128-144
    DOI: 10.1002/(SICI)1520-6750(200003)47:23.0.CO;2-#
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    References listed on IDEAS

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    1. Teofilo Gonzalez & Sartaj Sahni, 1978. "Flowshop and Jobshop Schedules: Complexity and Approximation," Operations Research, INFORMS, vol. 26(1), pages 36-52, February.
    2. Chung-Yee Lee & T. C. E. Cheng & B. M. T. Lin, 1993. "Minimizing the Makespan in the 3-Machine Assembly-Type Flowshop Scheduling Problem," Management Science, INFORMS, vol. 39(5), pages 616-625, May.
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    4. Edward G. Coffman & Ardavan Nozari & Mihalis Yannakakis, 1989. "Optimal Scheduling of Products with Two Subassemblies on a Single Machine," Operations Research, INFORMS, vol. 37(3), pages 426-436, June.
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    6. Scott Webster & Kenneth R. Baker, 1995. "Scheduling Groups of Jobs on a Single Machine," Operations Research, INFORMS, vol. 43(4), pages 692-703, August.
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    Cited by:

    1. I. Van Nieuwenhuyse, 2008. "Lot sizing in stochastic flowshops. Striking the balance between capacity and flow," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 147-160.
    2. Gur Mosheiov & Daniel Oron, 2011. "Batch scheduling on a two‐machine jobshop with machine‐dependent setup times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(7), pages 676-684, October.
    3. B. Lin & T. Cheng, 2005. "Two-Machine Flowshop Batching and Scheduling," Annals of Operations Research, Springer, vol. 133(1), pages 149-161, January.
    4. F. Hwang & M. Kovalyov & B. Lin, 2014. "Scheduling for fabrication and assembly in a two-machine flowshop with a fixed job sequence," Annals of Operations Research, Springer, vol. 217(1), pages 263-279, June.

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