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Two-Machine Flowshop Batching and Scheduling

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  • B. Lin
  • T. Cheng

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. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • B. Lin & T. Cheng, 2005. "Two-Machine Flowshop Batching and Scheduling," Annals of Operations Research, Springer, vol. 133(1), pages 149-161, January.
    • Handle: RePEc:spr:annopr:v:133:y:2005:i:1:p:149-161:10.1007/s10479-004-5029-7
    DOI: 10.1007/s10479-004-5029-7
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    References listed on IDEAS

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    1. C.A. Glass & C.N. Potts & V.A. Strusevich, 2001. "Scheduling Batches with Sequential Job Processing for Two-Machine Flow and Open Shops," INFORMS Journal on Computing, INFORMS, vol. 13(2), pages 120-137, May.
    2. Javad H. Ahmadi & Reza H. Ahmadi & Sriram Dasu & Christopher S. Tang, 1992. "Batching and Scheduling Jobs on Batch and Discrete Processors," Operations Research, INFORMS, vol. 40(4), pages 750-763, August.
    3. 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.
    4. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    5. 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.
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    Cited by:

    1. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    2. Jae-Min Yu & Rong Huang & Dong-Ho Lee, 2017. "Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops," International Journal of Production Research, Taylor & Francis Journals, vol. 55(11), pages 3266-3282, June.
    3. 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.
    4. Xinxin Hu & James D Blocher & Hans Sebastian Heese & Feng Zhou, 2016. "Scheduling products with subassemblies and changeover time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1025-1033, August.
    5. Zhou, Feng & Blocher, James D. & Hu, Xinxin & Sebastian Heese, H., 2014. "Optimal single machine scheduling of products with components and changeover cost," European Journal of Operational Research, Elsevier, vol. 233(1), pages 75-83.

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