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Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations

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  • Plateau, M.-C.
  • Rios-Solis, Y.A.

Abstract

In this work, we take advantage of the powerful quadratic programming theory to obtain optimal solutions of scheduling problems. We apply a methodology that starts, in contrast to more classical approaches, by formulating three unrelated parallel machine scheduling problems as 0-1 quadratic programs under linear constraints. By construction, these quadratic programs are non-convex. Therefore, before submitting them to a branch-and-bound procedure, we reformulate them in such a way that we can ensure convexity and a high-quality continuous lower bound. Experimental results show that this methodology is interesting by obtaining the best results in literature for two of the three studied scheduling problems.

Suggested Citation

  • Plateau, M.-C. & Rios-Solis, Y.A., 2010. "Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations," European Journal of Operational Research, Elsevier, vol. 201(3), pages 729-736, March.
    • Handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:729-736
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    References listed on IDEAS

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    Cited by:

    1. Ramon Alvarez-Valdes & Enric Crespo & Jose Tamarit & Fulgencia Villa, 2012. "Minimizing weighted earliness–tardiness on a single machine with a common due date using quadratic models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 754-767, October.
    2. Chen, Jianfu & Chu, Chengbin & Sahli, Abderrahim & Li, Kai, 2024. "A branch-and-price algorithm for unrelated parallel machine scheduling with machine usage costs," European Journal of Operational Research, Elsevier, vol. 316(3), pages 856-872.
    3. Kramer, Arthur & Dell’Amico, Mauro & Iori, Manuel, 2019. "Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines," European Journal of Operational Research, Elsevier, vol. 275(1), pages 67-79.
    4. Wang, Haibo & Alidaee, Bahram, 2019. "Effective heuristic for large-scale unrelated parallel machines scheduling problems," Omega, Elsevier, vol. 83(C), pages 261-274.
    5. Kerem Bülbül & Halil Şen, 2017. "An exact extended formulation for the unrelated parallel machine total weighted completion time problem," Journal of Scheduling, Springer, vol. 20(4), pages 373-389, August.

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