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Two‐machine flow shop scheduling with common due window to minimize weighted number of early and tardy jobs

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  • Wing‐Kwan Yeung
  • Ceyda Oğuz
  • Tai‐Chiu Edwin Cheng

Abstract

This article studies two due window scheduling problems to minimize the weighted number of early and tardy jobs in a two‐machine flow shop, where the window size is externally determined. These new scheduling models have many practical applications in real life. However, results on these problems have rarely appeared in the literature because of a lack of structural and optimality properties for solving them. In this article, we derive several dominance properties and theorems, including elimination rules and sequencing rules based on Johnsos order, lower bounds on the penalty, and upper bounds on the window location, which help to significantly trim the search space for the problems. We further show that the problems are NP‐hard in the ordinary sense only. We finally develop efficient pseudopolynomial dynamic programming algorithms for solving the problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

Suggested Citation

  • Wing‐Kwan Yeung & Ceyda Oğuz & Tai‐Chiu Edwin Cheng, 2009. "Two‐machine flow shop scheduling with common due window to minimize weighted number of early and tardy jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(7), pages 593-599, October.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:7:p:593-599
    DOI: 10.1002/nav.20356
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    References listed on IDEAS

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    1. W.K. Yeung & Ceyda Oğuz & T.C. Cheng, 2001. "Minimizing Weighted Number of Early and Tardy Jobs with a Common Due Window Involving Location Penalty," Annals of Operations Research, Springer, vol. 108(1), pages 33-54, November.
    2. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    3. Gordon, Valery & Proth, Jean-Marie & Chu, Chengbin, 2002. "A survey of the state-of-the-art of common due date assignment and scheduling research," European Journal of Operational Research, Elsevier, vol. 139(1), pages 1-25, May.
    4. Koulamas, Christos, 1996. "Single-machine scheduling with time windows and earliness/tardiness penalties," European Journal of Operational Research, Elsevier, vol. 91(1), pages 190-202, May.
    5. Michael X. Weng & Jose A. Ventura, 1994. "Scheduling about a large common due date with tolerance to minimize mean absolute deviation of completion times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 843-851, October.
    6. Della Croce, Federico & Gupta, Jatinder N. D. & Tadei, Roberto, 2000. "Minimizing tardy jobs in a flowshop with common due date," European Journal of Operational Research, Elsevier, vol. 120(2), pages 375-381, January.
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