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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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    1. Hanif D. Sherali & Churlzu Lim, 2007. "Enhancing Lagrangian Dual Optimization for Linear Programs by Obviating Nondifferentiability," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 3-13, February.
    2. Kenneth R. Baker & Linus E. Schrage, 1978. "Finding an Optimal Sequence by Dynamic Programming: An Extension to Precedence-Related Tasks," Operations Research, INFORMS, vol. 26(1), pages 111-120, February.
    3. Chris N. Potts & Luk N. Van Wassenhove, 1985. "A Branch and Bound Algorithm for the Total Weighted Tardiness Problem," Operations Research, INFORMS, vol. 33(2), pages 363-377, April.
    4. José R. Correa & Andreas S. Schulz, 2005. "Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1005-1021, November.
    5. François Margot & Maurice Queyranne & Yaoguang Wang, 2003. "Decompositions, Network Flows, and a Precedence Constrained Single-Machine Scheduling Problem," Operations Research, INFORMS, vol. 51(6), pages 981-992, December.
    6. Richard K. Congram & Chris N. Potts & Steef L. van de Velde, 2002. "An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 52-67, February.
    7. Jeffrey B. Sidney, 1975. "Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs," Operations Research, INFORMS, vol. 23(2), pages 283-298, April.
    8. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    9. Ibaraki, Toshihide & Nakamura, Yuichi, 1994. "A dynamic programming method for single machine scheduling," European Journal of Operational Research, Elsevier, vol. 76(1), pages 72-82, July.
    10. Andreas S. Schulz & Nelson A. Uhan, 2011. "Near-Optimal Solutions and Large Integrality Gaps for Almost All Instances of Single-Machine Precedence-Constrained Scheduling," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 14-23, February.
    11. Linus Schrage & Kenneth R. Baker, 1978. "Dynamic Programming Solution of Sequencing Problems with Precedence Constraints," Operations Research, INFORMS, vol. 26(3), pages 444-449, June.
    12. C. N. Potts, 1985. "A Lagrangean Based Branch and Bound Algorithm for Single Machine Sequencing with Precedence Constraints to Minimize Total Weighted Completion Time," Management Science, INFORMS, vol. 31(10), pages 1300-1311, October.
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    Cited by:

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    2. Zhang, Hanxiao & Li, Yan-Fu, 2022. "Integrated optimization of test case selection and sequencing for reliability testing of the mainboard of Internet backbone routers," European Journal of Operational Research, Elsevier, vol. 299(1), pages 183-194.
    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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