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Single-machine batch delivery scheduling with an assignable common due window


  • Yin, Yunqiang
  • Cheng, T.C.E.
  • Hsu, Chou-Jung
  • Wu, Chin-Chia


This paper addresses a batch delivery single-machine scheduling problem in which jobs have an assignable common due window. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find the optimal size and location of the window, the optimal dispatch date for each job, as well as an optimal job sequence to minimize a cost function based on earliness, tardiness, holding time, window location, window size, and batch delivery. We show that the problem can be optimally solved in O(n8) time by a dynamic programming algorithm under a reasonable assumption on the relationships among the cost parameters. A computational experiment is also conducted to evaluate the performance of the proposed algorithm. We also show that some special cases of the problem can be optimally solved by lower order algorithms.

Suggested Citation

  • Yin, Yunqiang & Cheng, T.C.E. & Hsu, Chou-Jung & Wu, Chin-Chia, 2013. "Single-machine batch delivery scheduling with an assignable common due window," Omega, Elsevier, vol. 41(2), pages 216-225.
  • Handle: RePEc:eee:jomega:v:41:y:2013:i:2:p:216-225
    DOI: 10.1016/

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    References listed on IDEAS

    1. Liman, Surya D. & Panwalkar, Shrikant S. & Thongmee, Sansern, 1996. "Determination of common due window location in a single machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 93(1), pages 68-74, August.
    2. 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.
    3. Herrmann, Jeffrey W. & Lee, Chung-Yee, 1993. "On scheduling to minimize earliness-tardiness and batch delivery costs with a common due date," European Journal of Operational Research, Elsevier, vol. 70(3), pages 272-288, November.
    4. Yeung, W. K. & Oguz, Ceyda & Edwin Cheng, T. C., 2004. "Two-stage flowshop earliness and tardiness machine scheduling involving a common due window," International Journal of Production Economics, Elsevier, vol. 90(3), pages 421-434, August.
    5. Cheng, T.C.E. & Yang, Suh-Jenq & Yang, Dar-Li, 2012. "Common due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity," International Journal of Production Economics, Elsevier, vol. 135(1), pages 154-161.
    6. 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.
    7. Shabtay, Dvir, 2010. "Scheduling and due date assignment to minimize earliness, tardiness, holding, due date assignment and batch delivery costs," International Journal of Production Economics, Elsevier, vol. 123(1), pages 235-242, January.
    8. Cheng, T. C. E. & Gupta, M. C., 1989. "Survey of scheduling research involving due date determination decisions," European Journal of Operational Research, Elsevier, vol. 38(2), pages 156-166, January.
    9. Chen, Zhi-Long, 1996. "Scheduling and common due date assignment with earliness-tardiness penalties and batch delivery costs," European Journal of Operational Research, Elsevier, vol. 93(1), pages 49-60, August.
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    Cited by:

    1. Roca-Riu, Mireia & Fernández, Elena & Estrada, Miquel, 2015. "Parking slot assignment for urban distribution: Models and formulations," Omega, Elsevier, vol. 57(PB), pages 157-175.
    2. Shabtay, Dvir & Steiner, George & Zhang, Rui, 2016. "Optimal coordination of resource allocation, due date assignment and scheduling decisions," Omega, Elsevier, vol. 65(C), pages 41-54.
    3. repec:wsi:apjorx:v:34:y:2017:i:03:n:s0217595917400140 is not listed on IDEAS
    4. Yang, Lixing & Zhou, Xuesong & Gao, Ziyou, 2014. "Credibility-based rescheduling model in a double-track railway network: a fuzzy reliable optimization approach," Omega, Elsevier, vol. 48(C), pages 75-93.
    5. Yang, Dar-Li & Lai, Chien-Jung & Yang, Suh-Jenq, 2014. "Scheduling problems with multiple due windows assignment and controllable processing times on a single machine," International Journal of Production Economics, Elsevier, vol. 150(C), pages 96-103.
    6. Yin, Yunqiang & Cheng, Shuenn-Ren & Cheng, T.C.E. & Wang, Du-Juan & Wu, Chin-Chia, 2016. "Just-in-time scheduling with two competing agents on unrelated parallel machines," Omega, Elsevier, vol. 63(C), pages 41-47.


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