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Pareto‐optimization of three‐agent scheduling to minimize the total weighted completion time, weighted number of tardy jobs, and total weighted late work

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  • Yuan Zhang
  • Jinjiang Yuan
  • Chi To Ng
  • Tai Chiu E. Cheng

Abstract

We consider three‐agent scheduling on a single machine in which the criteria of the three agents are to minimize the total weighted completion time, the weighted number of tardy jobs, and the total weighted late work, respectively. The problem is to find the set of all the Pareto‐optimal points, that is, the Pareto frontier, and their corresponding Pareto‐optimal schedules. Since the above problem is unary NP‐hard, we study the problem under the restriction that the jobs of the first agent have inversely agreeable processing times and weights, that is, the smaller the processing time of a job is, the greater its weight is. For this restricted problem, which is NP‐hard, we present a pseudo‐polynomial‐time algorithm to find the Pareto frontier. We also show that, for various special versions, the time complexity of solving the problem can be further reduced.

Suggested Citation

  • Yuan Zhang & Jinjiang Yuan & Chi To Ng & Tai Chiu E. Cheng, 2021. "Pareto‐optimization of three‐agent scheduling to minimize the total weighted completion time, weighted number of tardy jobs, and total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 378-393, April.
    • Handle: RePEc:wly:navres:v:68:y:2021:i:3:p:378-393
    DOI: 10.1002/nav.21961
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    References listed on IDEAS

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    1. Wan, Long & Yuan, Jinjiang & Wei, Lijun, 2016. "Pareto optimization scheduling with two competing agents to minimize the number of tardy jobs and the maximum cost," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 912-923.
    2. E. L. Lawler & J. M. Moore, 1969. "A Functional Equation and its Application to Resource Allocation and Sequencing Problems," Management Science, INFORMS, vol. 16(1), pages 77-84, September.
    3. Jinjiang Yuan, 2017. "Multi-agent scheduling on a single machine with a fixed number of competing agents to minimize the weighted sum of number of tardy jobs and makespans," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 433-440, August.
    4. Oron, Daniel & Shabtay, Dvir & Steiner, George, 2015. "Single machine scheduling with two competing agents and equal job processing times," European Journal of Operational Research, Elsevier, vol. 244(1), pages 86-99.
    5. C. N. Potts & L. N. Van Wassenhove, 1992. "Single Machine Scheduling to Minimize Total Late Work," Operations Research, INFORMS, vol. 40(3), pages 586-595, June.
    6. Yunqiang Yin & Du‐Juan Wang & Chin‐Chia Wu & T.C.E. Cheng, 2016. "CON/SLK due date assignment and scheduling on a single machine with two agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(5), pages 416-429, August.
    7. 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.
    8. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    9. Du-Juan Wang & Yunqiang Yin & Shuenn-Ren Cheng & T.C.E. Cheng & Chin-Chia Wu, 2016. "Due date assignment and scheduling on a single machine with two competing agents," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1152-1169, February.
    10. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    11. Yuan, Jinjiang & Ng, C.T. & Cheng, T.C.E., 2020. "Scheduling with release dates and preemption to minimize multiple max-form objective functions," European Journal of Operational Research, Elsevier, vol. 280(3), pages 860-875.
    12. Rubing Chen & Jinjiang Yuan & Yuan Gao, 2019. "The complexity of CO-agent scheduling to minimize the total completion time and total number of tardy jobs," Journal of Scheduling, Springer, vol. 22(5), pages 581-593, October.
    13. Omri Dover & Dvir Shabtay, 2016. "Single machine scheduling with two competing agents, arbitrary release dates and unit processing times," Annals of Operations Research, Springer, vol. 238(1), pages 145-178, March.
    14. A. M. A. Hariri & C. N. Potts & L. N. Van Wassenhove, 1995. "Single Machine Scheduling to Minimize Total Weighted Late Work," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 232-242, May.
    15. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    16. Yuan Zhang & Jinjiang Yuan, 2019. "A note on a two-agent scheduling problem related to the total weighted late work," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 989-999, April.
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