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Single-machine scheduling to minimize total absolute differences in waiting times with deteriorating jobs

Author

Listed:
  • L-H Sun

    (School of Business Administration, Xi’an University of Technology
    Knowledge Management & Innovation Research Centre, Xi’an Jiaotong University
    The State Key Laboratory on Mechanic Manufacturing, Xi’an Jiaotong University)

  • L-Y Sun

    (The State Key Laboratory on Mechanic Manufacturing, Xi’an Jiaotong University
    Management School, Xi'an Jiaotong University
    The Key Laboratory of the Ministry of Education on Process Control and Efficiency, Xi’an Jiaotong University)

  • J-B Wang

    (Knowledge Management & Innovation Research Centre, Xi’an Jiaotong University
    Operations Research and Cybernetics Institute, School of Science, Shenyang Institute of Aeronautical Engineering)

Abstract

In this paper we consider a single-machine scheduling problem with simple linear deterioration. By simple linear deterioration, we mean that the processing time of a job is a simple linear function of its execution starting time and its deterioration rate. The objective is to find a schedule that minimizes total absolute differences in waiting times. We show that the optimal schedule is V-shaped: 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 prove other several properties of an optimal schedule, and introduce two efficient heuristic algorithms that are tested against a lower bound. We also provide computational results to evaluate the performance of the heuristic algorithms.

Suggested Citation

  • L-H Sun & L-Y Sun & J-B Wang, 2011. "Single-machine scheduling to minimize total absolute differences in waiting times with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 768-775, April.
    • Handle: RePEc:pal:jorsoc:v:62:y:2011:i:4:d:10.1057_jors.2010.26
    DOI: 10.1057/jors.2010.26
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    References listed on IDEAS

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    1. B Alidaee & N K Womer, 1999. "Scheduling with time dependent processing times: Review and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 711-720, July.
    2. Wu, Chin-Chia & Lee, Wen-Chiung, 2008. "Single-machine group-scheduling problems with deteriorating setup times and job-processing times," International Journal of Production Economics, Elsevier, vol. 115(1), pages 128-133, September.
    3. T C E Cheng & L Y Kang & C T Ng, 2007. "Due-date assignment and parallel-machine scheduling with deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1103-1108, August.
    4. Uttarayan Bagchi, 1989. "Simultaneous Minimization of Mean and Variation of Flow Time and Waiting Time in Single Machine Systems," Operations Research, INFORMS, vol. 37(1), pages 118-125, February.
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