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Single machine scheduling of deteriorating jobs to minimize total absolute differences in completion times

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  • Li, Yongqiang
  • Li, Gang
  • Sun, Linyan
  • Xu, Zhiyong

Abstract

This paper investigates a single machine scheduling problem with deteriorating jobs. By a deteriorating job, we mean that the processing time is an increasing function of its execution starting time. Job deterioration is described by a function which is proportional to a linear function of time. The objective is to find a schedule that minimizes total absolute differences in completion times (TADC). We show that the optimal schedule is V-shaped, i.e., jobs are arranged in descending order of their deterioration rates if they are placed before the job with the smallest deterioration rate, but in ascending order of their deterioration rates if placed after it. We also prove some other properties of an optimal schedule, and propose two heuristic algorithms that are tested against a lower bound. We also provide computational results to evaluate the performance of the heuristic algorithms.

Suggested Citation

  • Li, Yongqiang & Li, Gang & Sun, Linyan & Xu, Zhiyong, 2009. "Single machine scheduling of deteriorating jobs to minimize total absolute differences in completion times," International Journal of Production Economics, Elsevier, vol. 118(2), pages 424-429, April.
    • Handle: RePEc:eee:proeco:v:118:y:2009:i:2:p:424-429
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    References listed on IDEAS

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    Cited by:

    1. Baruch Mor & Gur Mosheiov, 2018. "A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection," Annals of Operations Research, Springer, vol. 271(2), pages 1079-1085, December.
    2. Rubing Chen & Jinjiang Yuan, 2020. "Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices," 4OR, Springer, vol. 18(2), pages 177-196, June.
    3. Zhao, Chuan-Li & Tang, Heng-Yong, 2010. "Scheduling deteriorating jobs under disruption," International Journal of Production Economics, Elsevier, vol. 125(2), pages 294-299, June.
    4. Jin, Xianfei & Li, Kunpeng & Sivakumar, Appa Iyer, 2013. "Scheduling and optimal delivery time quotation for customers with time sensitive demand," International Journal of Production Economics, Elsevier, vol. 145(1), pages 349-358.
    5. Wang, Ling & Sun, Lin-Yan & Sun, Lin-Hui & Wang, Ji-Bo, 2010. "On three-machine flow shop scheduling with deteriorating jobs," International Journal of Production Economics, Elsevier, vol. 125(1), pages 185-189, May.
    6. S Gawiejnowicz & W-C Lee & C-L Lin & C-C Wu, 2011. "Single-machine scheduling of proportionally deteriorating jobs by two agents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 1983-1991, November.

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