IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v68y2017icp76-84.html
   My bibliography  Save this article

Maximum lateness minimization in one-dimensional bin packing

Author

Listed:
  • Arbib, Claudio
  • Marinelli, Fabrizio

Abstract

In the One-dimensional Bin Packing problem (1-BP) items of different lengths must be assigned to a minimum number of bins of unit length. Regarding each item as a job that requires unit time and some resource amount, and each bin as the total (discrete) resource available per time unit, the 1-BP objective is the minimization of the makespan Cmax=maxj{Cj}. We here generalize the problem to the case in which each item j is due by some date dj: our objective is to minimize a convex combination of Cmax and Lmax=maxj{Cj−dj}. For this problem we propose a time-indexed Mixed Integer Linear Programming formulation. The formulation can be decomposed and solved by column generation relegating single-bin packing to a pricing problem to be solved dynamically. We use bounds to (individual terms of) the objective function to address the oddity of activation constraints. In this way, we get very good gaps for instances that are considered difficult for the 1-BP.

Suggested Citation

  • Arbib, Claudio & Marinelli, Fabrizio, 2017. "Maximum lateness minimization in one-dimensional bin packing," Omega, Elsevier, vol. 68(C), pages 76-84.
    • Handle: RePEc:eee:jomega:v:68:y:2017:i:c:p:76-84
    DOI: 10.1016/j.omega.2016.06.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030504831630305X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2016.06.003?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. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    2. Gleb Belov & Guntram Scheithauer, 2007. "Setup and Open-Stacks Minimization in One-Dimensional Stock Cutting," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 27-35, February.
    3. François Clautiaux & Cláudio Alves & José Valério de Carvalho, 2010. "A survey of dual-feasible and superadditive functions," Annals of Operations Research, Springer, vol. 179(1), pages 317-342, September.
    4. 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.
    5. Bennell, Julia A. & Soon Lee, Lai & Potts, Chris N., 2013. "A genetic algorithm for two-dimensional bin packing with due dates," International Journal of Production Economics, Elsevier, vol. 145(2), pages 547-560.
    6. 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.
    7. J.M. Valério de Carvalho, 1999. "Exact solution of bin‐packing problems using column generation and branch‐and‐bound," Annals of Operations Research, Springer, vol. 86(0), pages 629-659, January.
    8. Marjan Akker & Han Hoogeveen & Steef Velde, 2005. "Applying Column Generation to Machine Scheduling," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 303-330, Springer.
    9. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.
    10. Reinertsen, Harald & Vossen, Thomas W.M., 2010. "The one-dimensional cutting stock problem with due dates," European Journal of Operational Research, Elsevier, vol. 201(3), pages 701-711, 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. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).
    2. Polyakovskiy, Sergey & M’Hallah, Rym, 2018. "A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates," European Journal of Operational Research, Elsevier, vol. 266(3), pages 819-839.
    3. Arbib, Claudio & Felici, Giovanni & Servilio, Mara, 2019. "Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs," Omega, Elsevier, vol. 84(C), pages 18-30.
    4. Polyakovskiy, Sergey & M’Hallah, Rym, 2021. "Just-in-time two-dimensional bin packing," Omega, Elsevier, vol. 102(C).

    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. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    2. Keehoon Kwon & Doyeong Kim & Sunkuk Kim, 2021. "Cutting Waste Minimization of Rebar for Sustainable Structural Work: A Systematic Literature Review," Sustainability, MDPI, vol. 13(11), pages 1-21, May.
    3. Arbib, Claudio & Felici, Giovanni & Servilio, Mara, 2019. "Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs," Omega, Elsevier, vol. 84(C), pages 18-30.
    4. Arbib, Claudio & Marinelli, Fabrizio & Pizzuti, Andrea, 2021. "Number of bins and maximum lateness minimization in two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 291(1), pages 101-113.
    5. Park, Jongyoon & Han, Jinil & Lee, Kyungsik, 2022. "Integer Optimization Model and Algorithm for the Stem Cell Culturing Problem," Omega, Elsevier, vol. 108(C).
    6. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    7. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    8. 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.
    9. 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.
    10. Roberto Cordone & Pierre Hosteins & Giovanni Righini, 2018. "A Branch-and-Bound Algorithm for the Prize-Collecting Single-Machine Scheduling Problem with Deadlines and Total Tardiness Minimization," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 168-180, February.
    11. Cui, Yaodong & Zhao, Zhigang, 2013. "Heuristic for the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns," European Journal of Operational Research, Elsevier, vol. 231(2), pages 288-298.
    12. Fırat, M. & Briskorn, D. & Laugier, A., 2016. "A Branch-and-Price algorithm for stable workforce assignments with hierarchical skills," European Journal of Operational Research, Elsevier, vol. 251(2), pages 676-685.
    13. Polyakovskiy, Sergey & M’Hallah, Rym, 2018. "A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates," European Journal of Operational Research, Elsevier, vol. 266(3), pages 819-839.
    14. 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.
    15. Sung, Inkyung & Lee, Taesik, 2016. "Optimal allocation of emergency medical resources in a mass casualty incident: Patient prioritization by column generation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 623-634.
    16. 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.
    17. 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.
    18. Kelly Cristina Poldi & Silvio Alexandre Araujo, 2016. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem," Annals of Operations Research, Springer, vol. 238(1), pages 497-520, March.
    19. Timo Gschwind & Stefan Irnich & Christian Tilk & Simon Emde, 2020. "Branch-cut-and-price for scheduling deliveries with time windows in a direct shipping network," Journal of Scheduling, Springer, vol. 23(3), pages 363-377, June.
    20. Krzysztof C. Kiwiel, 2010. "An Inexact Bundle Approach to Cutting-Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 131-143, February.

    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:jomega:v:68:y:2017:i:c:p:76-84. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.