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Single-machine scheduling of proportionally deteriorating jobs by two agents

Author

Listed:
  • S Gawiejnowicz

    (Adam Mickiewicz University, Poznań, Poland)

  • W-C Lee

    (Feng Chia University, Taichung, Taiwan)

  • C-L Lin

    (Feng Chia University, Taichung, Taiwan)

  • C-C Wu

    (Feng Chia University, Taichung, Taiwan)

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:p:1983-1991
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    Citations

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    Cited by:

    1. Baruch Mor & Gur Mosheiov, 2017. "A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1454-1468, May.
    2. Ren-Xia Chen & Shi-Sheng Li, 2019. "Two-agent single-machine scheduling with cumulative deterioration," 4OR, Springer, vol. 17(2), pages 201-219, June.
    3. 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.
    4. 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.
    5. 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.
    6. Zhenyou Wang & Cai-Min Wei & Yu-Bin Wu, 2016. "Single Machine Two-Agent Scheduling with Deteriorating Jobs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-17, October.
    7. Perez-Gonzalez, Paz & Framinan, Jose M., 2014. "A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 1-16.
    8. Cheng, Mingbao & Tadikamalla, Pandu R. & Shang, Jennifer & Zhang, Shaqing, 2014. "Bicriteria hierarchical optimization of two-machine flow shop scheduling problem with time-dependent deteriorating jobs," European Journal of Operational Research, Elsevier, vol. 234(3), pages 650-657.
    9. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    10. 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.
    11. Tang, Lixin & Zhao, Xiaoli & Liu, Jiyin & Leung, Joseph Y.-T., 2017. "Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine," European Journal of Operational Research, Elsevier, vol. 263(2), pages 401-411.

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