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Parallel Machine Scheduling of Deteriorating Jobs With Rejection and An Availability Constraint

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  • Guanghua Wu
  • Huan Liu
  • Yongping Liang

Abstract

In this paper, we explored the nonresumable deteriorating job scheduling with machine availability constraints and rejection. The research presented here has focused on two key issues. First, it is assumed that jobs have a different basic processing time and the same deterioration rate. The objective is to minimize the total completion times of the accepted jobs plus the total penalty of the rejected jobs. We present a pseudopolynomial‐time dynamic programming exact algorithm and subsequently develop it into a fully polynomial‐time approximation scheme for the case where machine disruptions occur only on one of the machines. Second, we consider the scheduling problem in which the actual processing time of the job is a proportional function of its starting time. The objective is to minimize the weighted sum of completion times of the accepted jobs plus the total penalty of the rejected jobs. We present an alternative fully polynomial‐time approximation scheme for the case where machine disruptions occur only on one of the machines.

Suggested Citation

  • Guanghua Wu & Huan Liu & Yongping Liang, 2025. "Parallel Machine Scheduling of Deteriorating Jobs With Rejection and An Availability Constraint," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:4623702
    DOI: 10.1155/jom/4623702
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    References listed on IDEAS

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    1. Zheng-Guo Lv & Li-Han Zhang & Xiao-Yuan Wang & Ji-Bo Wang, 2024. "Single Machine Scheduling Proportionally Deteriorating Jobs with Ready Times Subject to the Total Weighted Completion Time Minimization," Mathematics, MDPI, vol. 12(4), pages 1-15, February.
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    3. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    4. Gerhard J. Woeginger, 2000. "When Does a Dynamic Programming Formulation Guarantee the Existence of a Fully Polynomial Time Approximation Scheme (FPTAS)?," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 57-74, February.
    5. Jia-Xuan Yan & Na Ren & Hong-Bin Bei & Han Bao & Ji-Bo Wang, 2022. "Scheduling with Resource Allocation, Deteriorating Effect and Group Technology to Minimize Total Completion Time," Mathematics, MDPI, vol. 10(16), pages 1-15, August.
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