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Batch scheduling of simple linear deteriorating jobs on a single machine to minimize makespan

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  • Ji, Min
  • Cheng, T.C.E.

Abstract

We consider a scheduling problem in which n jobs are to be processed on a single machine. The jobs are processed in batches and the processing time of each job is a simple linear function of its waiting time, i.e., the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. The objective is to minimize the makespan, i.e., the completion time of the last job. We first show that the problem is strongly NP-hard. Then we show that, if the number of batches is B, the problem remains strongly NP-hard when B[less-than-or-equals, slant]U for a variable U[greater-or-equal, slanted]2 or B[greater-or-equal, slanted]U for any constant U[greater-or-equal, slanted]2. For the case of B[less-than-or-equals, slant]U, we present a dynamic programming algorithm that runs in pseudo-polynomial time and a fully polynomial time approximation scheme (FPTAS) for any constant U[greater-or-equal, slanted]2. Furthermore, we provide an optimal linear time algorithm for the special case where the jobs are subject to a linear precedence constraint, which subsumes the case where all the job growth rates are equal.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:90-98
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    Cited by:

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    3. Shaojun Lu & Min Kong & Zhiping Zhou & Xinbao Liu & Siwen Liu, 2022. "A hybrid metaheuristic for a semiconductor production scheduling problem with deterioration effect and resource constraints," Operational Research, Springer, vol. 22(5), pages 5405-5440, November.
    4. Wenhua Li & Libo Wang & Xing Chai & Hang Yuan, 2020. "Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    5. Pei, Jun & Liu, Xinbao & Fan, Wenjuan & Pardalos, Panos M. & Lu, Shaojun, 2019. "A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers," Omega, Elsevier, vol. 82(C), pages 55-69.
    6. 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.

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