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Mathematical formulations for the parallel machine scheduling problem with a single server

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  • Abdelhak Elidrissi
  • Rachid Benmansour
  • Mohammed Benbrahim
  • David Duvivier

Abstract

This paper addresses the problem of scheduling independent jobs on identical parallel machines with a single server to minimise the makespan. We propose mixed integer programming (MIP) formulations to solve this problem. Each formulation reflects a specific concept on how the decision variables are defined. Moreover, we present inequalities that can be used to improve those formulations. A computational study is performed on benchmark instances from the literature to compare the proposed MIP formulations with other known formulations from the literature. It turns out that our proposed time-indexed variables formulation outperforms by far the other formulations. In addition, we propose a very efficient MIP formulation to solve a particular case of the problem with a regular job set. This formulation is able to solve all regular instances for the case of 500 jobs and 5 machines in less than 5.27 min, where all other formulations are not able to produce a feasible solution within 1 h.

Suggested Citation

  • Abdelhak Elidrissi & Rachid Benmansour & Mohammed Benbrahim & David Duvivier, 2021. "Mathematical formulations for the parallel machine scheduling problem with a single server," International Journal of Production Research, Taylor & Francis Journals, vol. 59(20), pages 6166-6184, October.
    • Handle: RePEc:taf:tprsxx:v:59:y:2021:i:20:p:6166-6184
    DOI: 10.1080/00207543.2020.1807637
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    Cited by:

    1. Victor Fernandez-Viagas & Luis Sanchez-Mediano & Alvaro Angulo-Cortes & David Gomez-Medina & Jose Manuel Molina-Pariente, 2022. "The Permutation Flow Shop Scheduling Problem with Human Resources: MILP Models, Decoding Procedures, NEH-Based Heuristics, and an Iterated Greedy Algorithm," Mathematics, MDPI, vol. 10(19), pages 1-32, September.
    2. Abdelhak Elidrissi & Rachid Benmansour & Nicolas Zufferey & Mohammed Benbrahim & David Duvivier, 2024. "Minimization of maximum lateness on parallel machines with a single server and job release dates," 4OR, Springer, vol. 22(3), pages 351-385, September.

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