IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v201y2010i3p729-736.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00224-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Chen, Zhi-Long & Powell, Warren B., 1999. "A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem," European Journal of Operational Research, Elsevier, vol. 116(1), pages 220-232, July.
    2. Gordon, Valery & Proth, Jean-Marie & Chu, Chengbin, 2002. "A survey of the state-of-the-art of common due date assignment and scheduling research," European Journal of Operational Research, Elsevier, vol. 139(1), pages 1-25, May.
    3. Zhi-Long Chen & Warren B. Powell, 1999. "Solving Parallel Machine Scheduling Problems by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 78-94, February.
    4. Azizoglu, Meral & Kirca, Omer, 1999. "On the minimization of total weighted flow time with identical and uniform parallel machines," European Journal of Operational Research, Elsevier, vol. 113(1), pages 91-100, February.
    5. Kenneth R. Baker & Gary D. Scudder, 1990. "Sequencing with Earliness and Tardiness Penalties: A Review," Operations Research, INFORMS, vol. 38(1), pages 22-36, February.
    6. Marjan van den Akker & Han Hoogeveen & Steef van de Velde, 2002. "Combining Column Generation and Lagrangean Relaxation to Solve a Single-Machine Common Due Date Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 37-51, February.
    7. J. M. van den Akker & J. A. Hoogeveen & S. L. van de Velde, 1999. "Parallel Machine Scheduling by Column Generation," Operations Research, INFORMS, vol. 47(6), pages 862-872, December.
    8. Hamilton Emmons, 1987. "Scheduling to a common due date on parallel uniform processors," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 803-810, December.
    9. Tjark Vredeveld & Cor Hurkens, 2002. "Experimental Comparison of Approximation Algorithms for Scheduling Unrelated Parallel Machines," INFORMS Journal on Computing, INFORMS, vol. 14(2), pages 175-189, May.
    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. 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.
    2. 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.
    3. 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.
    4. Wang, Haibo & Alidaee, Bahram, 2019. "Effective heuristic for large-scale unrelated parallel machines scheduling problems," Omega, Elsevier, vol. 83(C), pages 261-274.

    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. Hoogeveen, Han, 2005. "Multicriteria scheduling," European Journal of Operational Research, Elsevier, vol. 167(3), pages 592-623, December.
    2. Chen, Zhi-Long & Lee, Chung-Yee, 2002. "Parallel machine scheduling with a common due window," European Journal of Operational Research, Elsevier, vol. 136(3), pages 512-527, February.
    3. Kerem Bülbül & Philip Kaminsky & Candace Yano, 2004. "Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 407-445, April.
    4. Halil Şen & Kerem Bülbül, 2015. "A Strong Preemptive Relaxation for Weighted Tardiness and Earliness/Tardiness Problems on Unrelated Parallel Machines," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 135-150, February.
    5. Zhi Pei & Mingzhong Wan & Ziteng Wang, 2020. "A new approximation algorithm for unrelated parallel machine scheduling with release dates," Annals of Operations Research, Springer, vol. 285(1), pages 397-425, February.
    6. Daniel Kowalczyk & Roel Leus, 2018. "A Branch-and-Price Algorithm for Parallel Machine Scheduling Using ZDDs and Generic Branching," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 768-782, November.
    7. Marjan van den Akker & Han Hoogeveen & Steef van de Velde, 2002. "Combining Column Generation and Lagrangean Relaxation to Solve a Single-Machine Common Due Date Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 37-51, February.
    8. 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.
    9. Feng Li & Zhi-Long Chen & Zhi-Long Chen, 2017. "Integrated Production, Inventory and Delivery Problems: Complexity and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 232-250, May.
    10. Pereira Lopes, Manuel J. & de Carvalho, J.M. Valerio, 2007. "A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1508-1527, February.
    11. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    12. Stéphane Dauzère-Pérès & Sigrid Lise Nonås, 2023. "An improved decision support model for scheduling production in an engineer-to-order manufacturer," 4OR, Springer, vol. 21(2), pages 247-300, June.
    13. 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.
    14. 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.
    15. Chung‐Yee Lee & Zhi‐Long Chen, 2000. "Scheduling jobs and maintenance activities on parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 145-165, March.
    16. Kramer, Arthur & Iori, Manuel & Lacomme, Philippe, 2021. "Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization," European Journal of Operational Research, Elsevier, vol. 289(3), pages 825-840.
    17. F. Rodriguez & C. Blum & C. García-Martínez & M. Lozano, 2012. "GRASP with path-relinking for the non-identical parallel machine scheduling problem with minimising total weighted completion times," Annals of Operations Research, Springer, vol. 201(1), pages 383-401, December.
    18. Biskup, Dirk & Herrmann, Jan & Gupta, Jatinder N.D., 2008. "Scheduling identical parallel machines to minimize total tardiness," International Journal of Production Economics, Elsevier, vol. 115(1), pages 134-142, September.
    19. Enrique Gerstl & Gur Mosheiov, 2014. "Single machine just‐in‐time scheduling problems with two competing agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 1-16, February.
    20. Zhi‐Long Chen & Warren B. Powell, 2003. "Exact algorithms for scheduling multiple families of jobs on parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 823-840, October.

    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:201:y:2010:i:3:p:729-736. 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.