Evaluation of optimality in the fuzzy single machine scheduling problem including discounted costs

  • Toufik BentrciaEmail author
  • Leila-Hayet Mouss
  • Nadia-Kinza Mouss
  • Farouk Yalaoui
  • Lyes Benyoucef


The single machine scheduling problem has been often regarded as a simplified representation that contains many polynomial solvable cases. However, in real-world applications, the imprecision of data at the level of each job can be critical for the implementation of scheduling strategies. Therefore, the single machine scheduling problem with the weighted discounted sum of completion times is treated in this paper, where we assume that the processing times, weighting coefficients and discount factor are all described using trapezoidal fuzzy numbers. Our aim in this study is to elaborate adequate measures in the context of possibility theory for the assessment of the optimality of a fixed schedule. Two optimization approaches namely genetic algorithm and pattern search are proposed as computational tools for the validation of the obtained properties and results. The proposed approaches are experimented on the benchmark problem instances and a sensitivity analysis with respect to some configuration parameters is conducted. Modeling and resolution frameworks considered in this research offer promise to deal with optimality in the wide class of fuzzy scheduling problems, which is recognized to be a difficult task by both researchers and practitioners.


Single machine scheduling Discounted costs Possibility theory Augmented Lagrangian method Genetic algorithm Pattern search 


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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Toufik Bentrcia
    • 1
    Email author
  • Leila-Hayet Mouss
    • 1
  • Nadia-Kinza Mouss
    • 1
  • Farouk Yalaoui
    • 2
  • Lyes Benyoucef
    • 3
  1. 1.LAP, Industrial Engineering DepartmentUniversity of BatnaBatnaAlgeria
  2. 2.Charles Delaunay Institute, LOSI, UMR STMR 6279University of Technology of TroyesTroyesFrance
  3. 3.Aix-Marseille University, LSIS UMR 7296Marseille Cedex 20France

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