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

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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%.

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Authors and Affiliations

  1. Department of Industrial Engineering, Faculty of Engineering, Meybod University, Meybod, Iran

    Abbasali Jafari-Nodoushan

  2. Department of Industrial Engineering, Faculty of Engineering, Yazd University, Yazd, Iran

    Hassan Khademi Zare & M. M. Lotfi

  3. School of Industrial Engineering and Engineering Optimization Research Group, College of Engineering, University of Tehran, Tehran, Iran

    R. Tavakkoli-Moghaddam

Authors
  1. Abbasali Jafari-Nodoushan
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  2. Hassan Khademi Zare
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  3. M. M. Lotfi
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  4. R. Tavakkoli-Moghaddam
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Correspondence to Abbasali Jafari-Nodoushan.

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Jafari-Nodoushan, A., Zare, H.K., Lotfi, M. et al. Scheduling Piecewise Linear Deteriorating Jobs to Minimize Makespan in a Two-Machine Flowshop. Oper. Res. Forum 2, 49 (2021). https://doi.org/10.1007/s43069-021-00096-7

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  • DOI: https://doi.org/10.1007/s43069-021-00096-7

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