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Single-machine scheduling of proportionally deteriorating jobs by two agents

Author

Listed:
  • S Gawiejnowicz

    (Adam Mickiewicz University)

  • W-C Lee

    (Feng Chia University)

  • C-L Lin

    (Feng Chia University)

  • C-C Wu

    (Feng Chia University)

Abstract

We consider a problem of scheduling a set of independent jobs by two agents on a single machine. Every agent has its own subset of jobs to be scheduled and uses its own optimality criterion. The processing time of each job proportionally deteriorates with respect to the starting time of the job. The problem is to find a schedule that minimizes the total tardiness of the first agent, provided that no tardy job is allowed for the second agent. We prove basic properties of the problem and give a lower bound on the optimal value of the total tardiness criterion. On the basis of these results, we propose a branch-and-bound algorithm and an evolutionary algorithm for the problem. Computational experiments show that the exact algorithm solves instances up to 50 jobs in a reasonably short time and that solutions obtained by the metaheuristic are close to optimal ones.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:62:y:2011:i:11:d:10.1057_jors.2010.171
    DOI: 10.1057/jors.2010.171
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    References listed on IDEAS

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    1. Su, Ling-Huey & Lien, Chun-Yuan, 2009. "Scheduling parallel machines with resource-dependent processing times," International Journal of Production Economics, Elsevier, vol. 117(2), pages 256-266, February.
    2. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    3. 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.
    4. Gupta, Sushil K & Kunnathur, Anand S & Dandapani, Krishnan, 1987. "Optimal repayment policies for multiple loans," Omega, Elsevier, vol. 15(4), pages 323-330.
    5. Gawiejnowicz, Stanislaw & Kononov, Alexander, 2010. "Complexity and approximability of scheduling resumable proportionally deteriorating jobs," European Journal of Operational Research, Elsevier, vol. 200(1), pages 305-308, January.
    6. Chung-Lun Li, 2008. "A note on unrelated parallel machine scheduling with time-dependent processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(12), pages 1696-1697, December.
    7. C-C He & C-C Wu & W-C Lee, 2009. "Branch-and-bound and weight-combination search algorithms for the total completion time problem with step-deteriorating jobs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1759-1766, December.
    8. W-H Kuo & C-J Hsu & D-L Yang, 2009. "A note on unrelated parallel machine scheduling with time-dependent processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(3), pages 431-434, March.
    9. C. T. Ng & T. C. E. Cheng & J. J. Yuan, 2006. "A note on the complexity of the problem of two-agent scheduling on a single machine," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 387-394, December.
    10. Ji, Min & Cheng, T.C.E., 2010. "Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan," European Journal of Operational Research, Elsevier, vol. 202(1), pages 90-98, April.
    11. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    12. 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.
    13. Lee, Wen-Chiung & Shiau, Yau-Ren & Chen, Shiuan-Kang & Wu, Chin-Chia, 2010. "A two-machine flowshop scheduling problem with deteriorating jobs and blocking," International Journal of Production Economics, Elsevier, vol. 124(1), pages 188-197, March.
    14. Cheng, T.C.E. & Ng, C.T. & Yuan, J.J., 2008. "Multi-agent scheduling on a single machine with max-form criteria," European Journal of Operational Research, Elsevier, vol. 188(2), pages 603-609, July.
    15. Lodree Jr., Emmett J. & Geiger, Christopher D., 2010. "A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration," European Journal of Operational Research, Elsevier, vol. 201(2), pages 644-648, March.
    16. Dar-Li Yang & Wen-Hung Kuo, 2009. "Single-machine scheduling with both deterioration and learning effects," Annals of Operations Research, Springer, vol. 172(1), pages 315-327, November.
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    Cited by:

    1. Jun Pei & Jinling Wei & Baoyu Liao & Xinbao Liu & Panos M. Pardalos, 2020. "Two-agent scheduling on bounded parallel-batching machines with an aging effect of job-position-dependent," Annals of Operations Research, Springer, vol. 294(1), pages 191-223, November.
    2. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    3. Shesh Narayan Sahu & Yuvraj Gajpal & Swapan Debbarma, 2018. "Two-agent-based single-machine scheduling with switchover time to minimize total weighted completion time and makespan objectives," Annals of Operations Research, Springer, vol. 269(1), pages 623-640, October.
    4. Hongfeng Wang & Min Huang & Junwei Wang, 2019. "An effective metaheuristic algorithm for flowshop scheduling with deteriorating jobs," Journal of Intelligent Manufacturing, Springer, vol. 30(7), pages 2733-2742, October.

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