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The Due Window Assignment Problems with Deteriorating Job and Delivery Time

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  • Jin Qian

    (College of Science, Northeastern University, Shenyang 110819, China)

  • Yu Zhan

    (College of Science, Northeastern University, Shenyang 110819, China)

Abstract

This paper considers the single machine scheduling problem with due window, delivery time and deteriorating job, whose goal is to minimize the window location, window size, earliness and tardiness. Common due window and slack due window are considered. The delivery time depends on the actual processing time of past sequences. The actual processing time of the job is an increasing function of the start time. Based on the small perturbations technique and adjacent exchange technique, we obtain the propositions of the problems. For common and slack due window assignment, we prove that the two objective functions are polynomial time solvable in O ( n l o g n ) time. We propose the corresponding algorithms to obtain the optimal sequence, window location and window size.

Suggested Citation

  • Jin Qian & Yu Zhan, 2022. "The Due Window Assignment Problems with Deteriorating Job and Delivery Time," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1672-:d:815042
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    References listed on IDEAS

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    1. S. S. Panwalkar & M. L. Smith & A. Seidmann, 1982. "Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem," Operations Research, INFORMS, vol. 30(2), pages 391-399, April.
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    3. Ji-Bo Wang & Bo Cui & Ping Ji & Wei-Wei Liu, 2021. "Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 290-303, February.
    4. Koulamas, Christos & Kyparisis, George J., 2008. "Single-machine scheduling problems with past-sequence-dependent setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1045-1049, June.
    5. Yue, Qing & Zhou, Shenghai, 2021. "Due-window assignment scheduling problem with stochastic processing times," European Journal of Operational Research, Elsevier, vol. 290(2), pages 453-468.
    6. Xinyu Sun & Xin-Na Geng, 2019. "Single-machine scheduling with deteriorating effects and machine maintenance," International Journal of Production Research, Taylor & Francis Journals, vol. 57(10), pages 3186-3199, May.
    7. Gang Li & Mei-Ling Luo & Wen-Jie Zhang & Xiao-Yuan Wang, 2015. "Single-machine due-window assignment scheduling based on common flow allowance, learning effect and resource allocation," International Journal of Production Research, Taylor & Francis Journals, vol. 53(4), pages 1228-1241, February.
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    Cited by:

    1. Zheng-Guo Lv & Li-Han Zhang & Xiao-Yuan Wang & Ji-Bo Wang, 2024. "Single Machine Scheduling Proportionally Deteriorating Jobs with Ready Times Subject to the Total Weighted Completion Time Minimization," Mathematics, MDPI, vol. 12(4), pages 1-15, February.
    2. Rong-Rong Mao & Yi-Chun Wang & Dan-Yang Lv & Ji-Bo Wang & Yuan-Yuan Lu, 2023. "Delivery Times Scheduling with Deterioration Effects in Due Window Assignment Environments," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    3. Xiang Li & Shuo Zhang & Wei Zhang, 2023. "Applied Computing and Artificial Intelligence," Mathematics, MDPI, vol. 11(10), pages 1-4, May.

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