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Scheduling with or without precedence relations on a serial-batch machine to minimize makespan and maximum cost

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  • Geng, Zhichao
  • Yuan, Jinjiang
  • Yuan, Junling

Abstract

In this paper, we consider several scheduling problems on a serial-batch machine for scheduling jobs with or without precedence relations. Under the serial-batch setting, the jobs in a batch are processed in succession and are removed until the last job in this batch finishes its processing. Thus, the processing time of a batch is equal to the sum of processing times of jobs in the batch. When a new batch starts, a constant setup time is required for the machine. The objectives of the problems involve minimizing makespan and a maximum cost. For these problems, we either present polynomial-time algorithms to generate all Pareto optimal points and find a corresponding Pareto optimal schedule for each Pareto optimal point, or give the strong NP-hardness proof. Experimentation results show that the proposed algorithms for the considered problems are very efficient.

Suggested Citation

  • Geng, Zhichao & Yuan, Jinjiang & Yuan, Junling, 2018. "Scheduling with or without precedence relations on a serial-batch machine to minimize makespan and maximum cost," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 1-18.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:1-18
    DOI: 10.1016/j.amc.2018.03.001
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    References listed on IDEAS

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    1. Allahverdi, Ali, 2015. "The third comprehensive survey on scheduling problems with setup times/costs," European Journal of Operational Research, Elsevier, vol. 246(2), pages 345-378.
    2. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    3. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    4. Cheng He & Hao Lin & Yixun Lin & Ji Tian, 2013. "Bicriteria scheduling on a series-batching machine to minimize maximum cost and makespan," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 177-186, January.
    5. Scott Webster & Kenneth R. Baker, 1995. "Scheduling Groups of Jobs on a Single Machine," Operations Research, INFORMS, vol. 43(4), pages 692-703, August.
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    Cited by:

    1. Gais Alhadi & Imed Kacem & Pierre Laroche & Izzeldin M. Osman, 2020. "Approximation algorithms for minimizing the maximum lateness and makespan on parallel machines," Annals of Operations Research, Springer, vol. 285(1), pages 369-395, February.
    2. Yijie Li, 2023. "Bicriteria fabrication scheduling of two-component jobs on a single machine," Operational Research, Springer, vol. 23(4), pages 1-13, December.
    3. Cheng He & Chunqi Xu & Hao Lin, 2020. "Serial-batching scheduling with two agents to minimize makespan and maximum cost," Journal of Scheduling, Springer, vol. 23(5), pages 609-617, October.

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