IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v186y2011i1p175-19810.1007-s10479-010-0832-9.html
   My bibliography  Save this article

A time-indexed LP-based approach for min-sum job-shop problems

Author

Listed:
  • Giuseppe Lancia
  • Franca Rinaldi
  • Paolo Serafini

Abstract

In this paper we propose two time-indexed IP formulations for job-shop scheduling problems with a min-sum objective. The first model has variables associated to job scheduling patterns. The exponential number of variables calls for a column generation scheme which is carried out by a dynamic programming procedure. The second model is of network flow type with side constraints. This model can be strengthened by adding cutting inequalities of clique type. It turns out that the two models are equivalent, since the dual of the second formulation is equivalent to the compact dual of the first model. However, they require significantly different solution approaches and may behave differently in terms of computing time and memory usage. Good upper bounds are found by a heuristic procedure that randomly generates schedules from fractional solutions. These features allow for an effective pruning of the branch-and-bound tree and narrowing the gap between lower and upper bounds. However, the size of both models is critically affected by the time-indexed formulation which may heavily slow down the computation. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Giuseppe Lancia & Franca Rinaldi & Paolo Serafini, 2011. "A time-indexed LP-based approach for min-sum job-shop problems," Annals of Operations Research, Springer, vol. 186(1), pages 175-198, June.
    • Handle: RePEc:spr:annopr:v:186:y:2011:i:1:p:175-198:10.1007/s10479-010-0832-9
    DOI: 10.1007/s10479-010-0832-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0832-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0832-9?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. DYER, Martin E. & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 878, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Brailsford, Sally C. & Potts, Chris N. & Smith, Barbara M., 1999. "Constraint satisfaction problems: Algorithms and applications," European Journal of Operational Research, Elsevier, vol. 119(3), pages 557-581, December.
    3. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    4. E. DYER, Martin & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 917, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Ulrich Dorndorf & Erwin Pesch & Toàn Phan-Huy, 2002. "Constraint Propagation and Problem Decomposition: A Preprocessing Procedure for the Job Shop Problem," Annals of Operations Research, Springer, vol. 115(1), pages 125-145, September.
    6. J.M. van den Akker & C.A.J. Hurkens & M.W.P. Savelsbergh, 2000. "Time-Indexed Formulations for Machine Scheduling Problems: Column Generation," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 111-124, May.
    7. R. J. M. Vaessens & E. H. L. Aarts & J. K. Lenstra, 1996. "Job Shop Scheduling by Local Search," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 302-317, August.
    8. Chen, Haoxun & Luh, Peter B., 2003. "An alternative framework to Lagrangian relaxation approach for job shop scheduling," European Journal of Operational Research, Elsevier, vol. 149(3), pages 499-512, September.
    9. B. J. Lageweg & J. K. Lenstra & A. H. G. Rinnooy Kan, 1977. "Job-Shop Scheduling by Implicit Enumeration," Management Science, INFORMS, vol. 24(4), pages 441-450, December.
    10. J. Christopher Beck & T. K. Feng & Jean-Paul Watson, 2011. "Combining Constraint Programming and Local Search for Job-Shop Scheduling," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 1-14, February.
    11. 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.
    12. Martin W. P. Savelsbergh & R. N. Uma & Joel Wein, 2005. "An Experimental Study of LP-Based Approximation Algorithms for Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 123-136, February.
    13. Della Croce, F. & Ghirardi, M. & Tadei, R., 2002. "An improved branch-and-bound algorithm for the two machine total completion time flow shop problem," European Journal of Operational Research, Elsevier, vol. 139(2), pages 293-301, June.
    14. Joseph Adams & Egon Balas & Daniel Zawack, 1988. "The Shifting Bottleneck Procedure for Job Shop Scheduling," Management Science, INFORMS, vol. 34(3), pages 391-401, March.
    15. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.
    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. Giuseppe Lancia & Paolo Serafini, 2016. "Deriving compact extended formulations via LP-based separation techniques," Annals of Operations Research, Springer, vol. 240(1), pages 321-350, May.
    2. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    3. Clautiaux, François & Hanafi, Saïd & Macedo, Rita & Voge, Marie-Émilie & Alves, Cláudio, 2017. "Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints," European Journal of Operational Research, Elsevier, vol. 258(2), pages 467-477.
    4. Kartak, Vadim M. & Ripatti, Artem V., 2018. "The minimum raster set problem and its application to the d-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 33-39.
    5. T. C. E. Cheng & Bo Peng & Zhipeng Lü, 2016. "A hybrid evolutionary algorithm to solve the job shop scheduling problem," Annals of Operations Research, Springer, vol. 242(2), pages 223-237, July.

    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. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.
    2. Kurowski, Krzysztof & Pecyna, Tomasz & Slysz, Mateusz & Różycki, Rafał & Waligóra, Grzegorz & Wȩglarz, Jan, 2023. "Application of quantum approximate optimization algorithm to job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 310(2), pages 518-528.
    3. Bürgy, Reinhard & Bülbül, Kerem, 2018. "The job shop scheduling problem with convex costs," European Journal of Operational Research, Elsevier, vol. 268(1), pages 82-100.
    4. Natashia Boland & Riley Clement & Hamish Waterer, 2016. "A Bucket Indexed Formulation for Nonpreemptive Single Machine Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 14-30, February.
    5. Murovec, Boštjan, 2015. "Job-shop local-search move evaluation without direct consideration of the criterion’s value," European Journal of Operational Research, Elsevier, vol. 241(2), pages 320-329.
    6. Christian Artigues & Dominique Feillet, 2008. "A branch and bound method for the job-shop problem with sequence-dependent setup times," Annals of Operations Research, Springer, vol. 159(1), pages 135-159, March.
    7. Sels, Veronique & Craeymeersch, Kjeld & Vanhoucke, Mario, 2011. "A hybrid single and dual population search procedure for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 215(3), pages 512-523, December.
    8. 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.
    9. Artur Alves Pessoa & Teobaldo Bulhões & Vitor Nesello & Anand Subramanian, 2022. "Exact Approaches for Single Machine Total Weighted Tardiness Batch Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1512-1530, May.
    10. Chatterjee A K & Mukherjee, Saral, 2006. "Unified Concept of Bottleneck," IIMA Working Papers WP2006-05-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    11. 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.
    12. Francis Sourd, 2009. "New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 167-175, February.
    13. Pasquale Avella & Maurizio Boccia & Bernardo D’Auria, 2005. "Near-Optimal Solutions of Large-Scale Single-Machine Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 183-191, May.
    14. Lotte Berghman & Roel Leus & Frits Spieksma, 2014. "Optimal solutions for a dock assignment problem with trailer transportation," Annals of Operations Research, Springer, vol. 213(1), pages 3-25, February.
    15. Martin W. P. Savelsbergh & R. N. Uma & Joel Wein, 2005. "An Experimental Study of LP-Based Approximation Algorithms for Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 123-136, February.
    16. El-Bouri, A. & Azizi, N. & Zolfaghari, S., 2007. "A comparative study of a new heuristic based on adaptive memory programming and simulated annealing: The case of job shop scheduling," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1894-1910, March.
    17. F. Guerriero, 2008. "Hybrid Rollout Approaches for the Job Shop Scheduling Problem," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 419-438, November.
    18. Pisut Pongchairerks, 2019. "A Two-Level Metaheuristic Algorithm for the Job-Shop Scheduling Problem," Complexity, Hindawi, vol. 2019, pages 1-11, March.
    19. I. Ece Içyüz & Jean-Philippe P. Richard & Erdem Eskigun & Dharma Acharya, 2016. "A Two-Model Solution Approach for the Monthly Coal Train Reservations Planning Problem," Transportation Science, INFORMS, vol. 50(3), pages 926-946, August.
    20. Pannee Suanpang & Pitchaya Jamjuntr & Kittisak Jermsittiparsert & Phuripoj Kaewyong, 2022. "Tourism Service Scheduling in Smart City Based on Hybrid Genetic Algorithm Simulated Annealing Algorithm," Sustainability, MDPI, vol. 14(23), pages 1-21, December.

    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:spr:annopr:v:186:y:2011:i:1:p:175-198:10.1007/s10479-010-0832-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.