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An exact algorithm for the precedence-constrained single-machine scheduling problem

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  • Tanaka, Shunji
  • Sato, Shun

Abstract

This study proposes an efficient exact algorithm for the precedence-constrained single-machine scheduling problem to minimize total job completion cost where machine idle time is forbidden. The proposed algorithm is based on the SSDP (Successive Sublimation Dynamic Programming) method and is an extension of the authors’ previous algorithms for the problem without precedence constraints. In this method, a lower bound is computed by solving a Lagrangian relaxation of the original problem via dynamic programming and then it is improved successively by adding constraints to the relaxation until the gap between the lower and upper bounds vanishes. Numerical experiments will show that the algorithm can solve all instances with up to 50 jobs of the precedence-constrained total weighted tardiness and total weighted earliness–tardiness problems, and most instances with 100 jobs of the former problem.

Suggested Citation

  • Tanaka, Shunji & Sato, Shun, 2013. "An exact algorithm for the precedence-constrained single-machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 229(2), pages 345-352.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:2:p:345-352
    DOI: 10.1016/j.ejor.2013.02.048
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    Cited by:

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    3. Li, Yantong & Côté, Jean-François & Coelho, Leandro C. & Zhang, Chuang & Zhang, Shuai, 2023. "Order assignment and scheduling under processing and distribution time uncertainty," European Journal of Operational Research, Elsevier, vol. 305(1), pages 148-163.
    4. Rostami, Salim & Creemers, Stefan & Leus, Roel, 2019. "Precedence theorems and dynamic programming for the single-machine weighted tardiness problem," European Journal of Operational Research, Elsevier, vol. 272(1), pages 43-49.
    5. Yiyo Kuo & Sheng-I Chen & Yen-Hung Yeh, 2020. "Single machine scheduling with sequence-dependent setup times and delayed precedence constraints," Operational Research, Springer, vol. 20(2), pages 927-942, June.

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