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Optimal delivery time quotation to minimize total tardiness penalties with controllable processing times

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  • Yaron Leyvand
  • Dvir Shabtay
  • George Steiner

Abstract

Scheduling problems with due date assignment and controllable processing times are studied in this paper. It is assumed that the job processing time is a linear function of the amount of resource allocated to the job, and all jobs share the same due date, which is a decision variable. The problems have many applications, e.g., in optimal delivery time quotation and order sequencing when outsourcing is an option. The quality of a schedule is measured by two different criteria. The first is the total weighted number of tardy jobs plus due date assignment cost, and the second one is the total weighted resource consumption. Four different problems for treating the two criteria are considered. It is shown that three of these problems are NP-hard in the ordinary sense, although the problem of minimizing an integrated objective function can be solved in polynomial time. A pseudo-polynomial time optimization algorithm is provided for the three NP-hard versions of the problem. A fully polynomial time algorithm for approximating a Pareto-optimal solution is also presented. Finally, important polynomially solvable special cases are highlighted.

Suggested Citation

  • Yaron Leyvand & Dvir Shabtay & George Steiner, 2010. "Optimal delivery time quotation to minimize total tardiness penalties with controllable processing times," IISE Transactions, Taylor & Francis Journals, vol. 42(3), pages 221-231.
    • Handle: RePEc:taf:uiiexx:v:42:y:2010:i:3:p:221-231
    DOI: 10.1080/07408170903394322
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    Citations

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    Cited by:

    1. 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.
    2. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    3. George Steiner & Rui Zhang, 2011. "Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries," Annals of Operations Research, Springer, vol. 191(1), pages 171-181, November.
    4. Dujuan Wang & Yugang Yu & Huaxin Qiu & Yunqiang Yin & T. C. E. Cheng, 2020. "Two‐agent scheduling with linear resource‐dependent processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 573-591, October.
    5. Dujuan Wang & Yunqiang Yin & T.C.E. Cheng, 2017. "A bicriterion approach to common flow allowances due window assignment and scheduling with controllable processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 41-63, February.

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