IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v50y2003i3p273-288.html
   My bibliography  Save this article

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

Author

Listed:
  • Stéphane Dauzère‐Pérès
  • Marc Sevaux

Abstract

This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed‐integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003

Suggested Citation

  • Stéphane Dauzère‐Pérès & Marc Sevaux, 2003. "Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(3), pages 273-288, April.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:3:p:273-288
    DOI: 10.1002/nav.10056
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.10056
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.10056?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
    ---><---

    References listed on IDEAS

    as
    1. C. N. Potts & L. N. Van Wassenhove, 1988. "Algorithms for Scheduling a Single Machine to Minimize the Weighted Number of Late Jobs," Management Science, INFORMS, vol. 34(7), pages 843-858, July.
    2. Crauwels, H. A. J. & Potts, C. N. & Van Wassenhove, L. N., 1996. "Local search heuristics for single-machine scheduling with batching to minimize the number of late jobs," European Journal of Operational Research, Elsevier, vol. 90(2), pages 200-213, April.
    3. Hiroshi Kise & Toshihide Ibaraki & Hisashi Mine, 1978. "A Solvable Case of the One-Machine Scheduling Problem with Ready and Due Times," Operations Research, INFORMS, vol. 26(1), pages 121-126, February.
    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. François Clautiaux & Boris Detienne & Henri Lefebvre, 2023. "A two-stage robust approach for minimizing the weighted number of tardy jobs with objective uncertainty," Journal of Scheduling, Springer, vol. 26(2), pages 169-191, April.
    2. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.

    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. M'Hallah, Rym & Bulfin, R.L., 2007. "Minimizing the weighted number of tardy jobs on a single machine with release dates," European Journal of Operational Research, Elsevier, vol. 176(2), pages 727-744, January.
    2. Sevaux, Marc & Dauzere-Peres, Stephane, 2003. "Genetic algorithms to minimize the weighted number of late jobs on a single machine," European Journal of Operational Research, Elsevier, vol. 151(2), pages 296-306, December.
    3. Dauzere-Peres, Stephane, 1995. "Minimizing late jobs in the general one machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 81(1), pages 134-142, February.
    4. Peridy, Laurent & Pinson, Eric & Rivreau, David, 2003. "Using short-term memory to minimize the weighted number of late jobs on a single machine," European Journal of Operational Research, Elsevier, vol. 148(3), pages 591-603, August.
    5. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    6. Kolahan, F. & Liang, M., 1998. "An adaptive TS approach to JIT sequencing with variable processing times and sequence-dependent setups," European Journal of Operational Research, Elsevier, vol. 109(1), pages 142-159, August.
    7. Schaller, Jeffrey, 2007. "Scheduling on a single machine with family setups to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 105(2), pages 329-344, February.
    8. Jinliang Cheng & Hiroshi Kise & Hironori Matsumoto, 1997. "A branch-and-bound algorithm with fuzzy inference for a permutation flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 96(3), pages 578-590, February.
    9. Baptiste, Philippe & Peridy, Laurent & Pinson, Eric, 2003. "A branch and bound to minimize the number of late jobs on a single machine with release time constraints," European Journal of Operational Research, Elsevier, vol. 144(1), pages 1-11, January.
    10. Ulrich Pferschy & Julia Resch & Giovanni Righini, 2023. "Algorithms for rescheduling jobs with a LIFO buffer to minimize the weighted number of late jobs," Journal of Scheduling, Springer, vol. 26(3), pages 267-287, June.
    11. Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy & Julia Resch & Giovanni Righini, 2021. "Optimally rescheduling jobs with a Last-In-First-Out buffer," Journal of Scheduling, Springer, vol. 24(6), pages 663-680, December.
    12. Nicholas G. Hall & Marc E. Posner, 2001. "Generating Experimental Data for Computational Testing with Machine Scheduling Applications," Operations Research, INFORMS, vol. 49(6), pages 854-865, December.
    13. Federico Malucelli & Sara Nicoloso, 2007. "Shiftable intervals," Annals of Operations Research, Springer, vol. 150(1), pages 137-157, March.
    14. Hejl, Lukáš & Šůcha, Přemysl & Novák, Antonín & Hanzálek, Zdeněk, 2022. "Minimizing the weighted number of tardy jobs on a single machine: Strongly correlated instances," European Journal of Operational Research, Elsevier, vol. 298(2), pages 413-424.
    15. Tzafestas, Spyros & Triantafyllakis, Alekos, 1993. "Deterministic scheduling in computing and manufacturing systems: a survey of models and algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(5), pages 397-434.
    16. Koulamas, Christos & Kyparisis, George J., 2001. "Single machine scheduling with release times, deadlines and tardiness objectives," European Journal of Operational Research, Elsevier, vol. 133(2), pages 447-453, January.
    17. Martin, Clarence H, 2009. "A hybrid genetic algorithm/mathematical programming approach to the multi-family flowshop scheduling problem with lot streaming," Omega, Elsevier, vol. 37(1), pages 126-137, February.
    18. Vincent T’kindt & Federico Della Croce & Jean-Louis Bouquard, 2007. "Enumeration of Pareto Optima for a Flowshop Scheduling Problem with Two Criteria," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 64-72, February.
    19. 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.
    20. Xiaoqiang Cai & Sean Zhou, 1999. "Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs," Operations Research, INFORMS, vol. 47(3), pages 422-437, June.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:50:y:2003:i:3:p:273-288. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.