IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v229y2013i2p345-352.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713001975
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.02.048?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Hamilton Emmons, 1969. "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Operations Research, INFORMS, vol. 17(4), pages 701-715, August.
    11. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    3. 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.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    3. Louis-Philippe Bigras & Michel Gamache & Gilles Savard, 2008. "Time-Indexed Formulations and the Total Weighted Tardiness Problem," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 133-142, February.
    4. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
    5. Yagiura, Mutsunori & Ibaraki, Toshihide, 1996. "The use of dynamic programming in genetic algorithms for permutation problems," European Journal of Operational Research, Elsevier, vol. 92(2), pages 387-401, July.
    6. Chengbin Chu, 1992. "A branch‐and‐bound algorithm to minimize total tardiness with different release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 265-283, March.
    7. Sen, Tapan & Sulek, Joanne M. & Dileepan, Parthasarati, 2003. "Static scheduling research to minimize weighted and unweighted tardiness: A state-of-the-art survey," International Journal of Production Economics, Elsevier, vol. 83(1), pages 1-12, January.
    8. Robbert Fokkink & Thomas Lidbetter & László A. Végh, 2019. "On Submodular Search and Machine Scheduling," Management Science, INFORMS, vol. 44(4), pages 1431-1449, November.
    9. Christoph Ambühl & Monaldo Mastrolilli & Nikolaus Mutsanas & Ola Svensson, 2011. "On the Approximability of Single-Machine Scheduling with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 653-669, November.
    10. John J. Kanet, 2014. "One-Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons," Operations Research, INFORMS, vol. 62(2), pages 345-347, April.
    11. Haiyan Wang & Chung‐Yee Lee, 2005. "Production and transport logistics scheduling with two transport mode choices," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 796-809, December.
    12. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    13. Felix Happach & Lisa Hellerstein & Thomas Lidbetter, 2022. "A General Framework for Approximating Min Sum Ordering Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1437-1452, May.
    14. 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.
    15. J. J. Kanet, 2007. "New Precedence Theorems for One-Machine Weighted Tardiness," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 579-588, August.
    16. Yunpeng Pan & Zhe Liang, 2017. "Dual relaxations of the time-indexed ILP formulation for min–sum scheduling problems," Annals of Operations Research, Springer, vol. 249(1), pages 197-213, February.
    17. Koulamas, Christos & Kyparisis, George J., 2019. "New results for single-machine scheduling with past-sequence-dependent setup times and due date-related objectives," European Journal of Operational Research, Elsevier, vol. 278(1), pages 149-159.
    18. Valente, Jorge M.S., 2007. "Improving the performance of the ATC dispatch rule by using workload data to determine the lookahead parameter value," International Journal of Production Economics, Elsevier, vol. 106(2), pages 563-573, April.
    19. Bilge, Umit & Kurtulan, Mujde & Kirac, Furkan, 2007. "A tabu search algorithm for the single machine total weighted tardiness problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1423-1435, February.
    20. P. Detti & D. Pacciarelli, 2001. "A branch and bound algorithm for the minimum storage‐time sequencing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(4), pages 313-331, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:229:y:2013:i:2:p:345-352. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.