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Scheduling Piecewise Linear Deteriorating Jobs to Minimize Makespan in a Two-Machine Flowshop

Author

Listed:
  • Abbasali Jafari-Nodoushan

    (Meybod University)

  • Hassan Khademi Zare

    (Yazd University)

  • M. M. Lotfi

    (Yazd University)

  • R. Tavakkoli-Moghaddam

    (University of Tehran)

Abstract

A job processed later may consume more time in many realistic machine scheduling situations than the same job when processed earlier. This phenomenon is known as the deterioration of jobs. In this paper, two-machine flowshop scheduling problem under piecewise linear deteriorating jobs is investigated where the objective is to minimize the makespan. Deteriorating jobs may increase the makespan and it is important to obtain the optimal or near-optimal solution. Tab;At first, a Mixed Integer Non-Linear Programming (MINLP) model is presented for the problem and linearization of it is performed. After that, a branch and bound algorithm with dominance rules and lower bounds is established to solve the problem optimally. Several simple heuristics are also proposed to derive near-optimal solutions. The computational experiments are conducted through randomly generated examples to evaluate the performance of the proposed algorithms. The results demonstrate that the branch and bound algorithm can solve most medium-sized problems within a reasonable time. The heuristic algorithm is relatively accurate, with an average error percentage of less than 1.6%.

Suggested Citation

  • Abbasali Jafari-Nodoushan & Hassan Khademi Zare & M. M. Lotfi & R. Tavakkoli-Moghaddam, 2021. "Scheduling Piecewise Linear Deteriorating Jobs to Minimize Makespan in a Two-Machine Flowshop," SN Operations Research Forum, Springer, vol. 2(4), pages 1-29, December.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:4:d:10.1007_s43069-021-00096-7
    DOI: 10.1007/s43069-021-00096-7
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    References listed on IDEAS

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    1. Jun Pei & Bayi Cheng & Xinbao Liu & Panos M. Pardalos & Min Kong, 2019. "Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time," Annals of Operations Research, Springer, vol. 272(1), pages 217-241, January.
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    5. Wang, Ling & Sun, Lin-Yan & Sun, Lin-Hui & Wang, Ji-Bo, 2010. "On three-machine flow shop scheduling with deteriorating jobs," International Journal of Production Economics, Elsevier, vol. 125(1), pages 185-189, May.
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