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Single Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection Cost

Author

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  • Atefeh Moghaddam

    (University of Technology of Troyes, France)

  • Lionel Amodeo

    (University of Technology of Troyes, France)

  • Farouk Yalaoui

    (University of Technology of Troyes, France)

  • Behrooz Karimi

    (Amirkabir University of Technology, Iran)

Abstract

In this paper, the authors consider a single machine scheduling problem with rejection. In traditional research, it is assumed all jobs must be processed. However, in the real-world situation, certain jobs can be rejected. In this study, the jobs can be either accepted and scheduled or be rejected at the cost of a penalty. Two objective functions are considered simultaneously: (1) minimization of the sum of weighted completion times for the accepted jobs, and (2) minimization of the sum of penalties for the rejected jobs. The authors apply two-phase method (TPM), which is a general technique to solve bi-objective combinatorial optimization problems, to find all supported and non-supported solutions for small-sized problems. The authors present a mathematical model for implementing both phases. On the other hand, three different bi-objective simulated annealing algorithms have also been developed to find a good estimation of Pareto-optimal solutions for large-sized problems. Finally the authors discuss the results obtained from each of these algorithms.

Suggested Citation

  • Atefeh Moghaddam & Lionel Amodeo & Farouk Yalaoui & Behrooz Karimi, 2012. "Single Machine Scheduling with Rejection: Minimizing Total Weighted Completion Time and Rejection Cost," International Journal of Applied Evolutionary Computation (IJAEC), IGI Global, vol. 3(2), pages 42-61, April.
    • Handle: RePEc:igg:jaec00:v:3:y:2012:i:2:p:42-61
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    Cited by:

    1. Hanane Krim & Nicolas Zufferey & Jean-Yves Potvin & Rachid Benmansour & David Duvivier, 2022. "Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times," Journal of Scheduling, Springer, vol. 25(1), pages 89-105, February.
    2. Federico Della Croce, 2016. "MP or not MP: that is the question," Journal of Scheduling, Springer, vol. 19(1), pages 33-42, February.

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