IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v5y2024i3d10.1007_s43069-024-00350-8.html
   My bibliography  Save this article

A Modeling and Hybridized Decomposition Approach for the Multi-level Capacitated Lot-Sizing Problem with Setup Carryover, Backlogging, and Emission Control

Author

Listed:
  • Nusrat T. Chowdhury

    (Bemidji State University
    University of Windsor)

  • Mohammed F. Baki

    (University of Windsor)

  • Ahmed Azab

    (University of Windsor)

Abstract

The goal of the production planning problem is to determine the optimum quantity to produce in order to satisfy demand over a predetermined planning horizon with the least amount of money spent. Making the appropriate choices in production planning will impact a manufacturing company’s performance and productivity, which is crucial to remain competitive in the market. Therefore, developing and enhancing techniques for solving production planning problems is very significant. This paper proposes a mixed-integer linear programming model for this extension of the dynamic multi-level capacitated lot-sizing under study, where setup carryover, backlogging, and emission control are considered. An item Dantzig-Wolfe decomposition-based heuristic procedure is developed, and a dynamic programming and column generation approach is used to solve the problem. We also propose a multi-step iterative capacity allocation heuristic procedure to handle any infeasibilities that arise when solving the problem. We evaluate the performance of the developed solution approach using a test data set available in the literature. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable timeframe.

Suggested Citation

  • Nusrat T. Chowdhury & Mohammed F. Baki & Ahmed Azab, 2024. "A Modeling and Hybridized Decomposition Approach for the Multi-level Capacitated Lot-Sizing Problem with Setup Carryover, Backlogging, and Emission Control," SN Operations Research Forum, Springer, vol. 5(3), pages 1-32, September.
    • Handle: RePEc:spr:snopef:v:5:y:2024:i:3:d:10.1007_s43069-024-00350-8
    DOI: 10.1007/s43069-024-00350-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-024-00350-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s43069-024-00350-8?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. François Vanderbeck, 2000. "On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm," Operations Research, INFORMS, vol. 48(1), pages 111-128, February.
    2. Peter J. Billington & John O. McClain & L. Joseph Thomas, 1983. "Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction," Management Science, INFORMS, vol. 29(10), pages 1126-1141, October.
    3. Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
    4. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
    5. Diego Jacinto Fiorotto & Jackeline del Carmen Huaccha Neyra & Silvio Alexandre de Araujo, 2020. "Impact analysis of setup carryover and crossover on lot sizing problems," International Journal of Production Research, Taylor & Francis Journals, vol. 58(20), pages 6350-6369, October.
    6. Retel Helmrich, Mathijn J. & Jans, Raf & van den Heuvel, Wilco & Wagelmans, Albert P.M., 2015. "The economic lot-sizing problem with an emission capacity constraint," European Journal of Operational Research, Elsevier, vol. 241(1), pages 50-62.
    7. Ioannis Fragkos & Zeger Degraeve & Bert De Reyck, 2016. "A Horizon Decomposition Approach for the Capacitated Lot-Sizing Problem with Setup Times," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 465-482, August.
    8. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    9. Horst Tempelmeier & Matthias Derstroff, 1996. "A Lagrangean-Based Heuristic for Dynamic Multilevel Multiitem Constrained Lotsizing with Setup Times," Management Science, INFORMS, vol. 42(5), pages 738-757, May.
    10. Zeger Degraeve & Raf Jans, 2007. "A New Dantzig-Wolfe Reformulation and Branch-and-Price Algorithm for the Capacitated Lot-Sizing Problem with Setup Times," Operations Research, INFORMS, vol. 55(5), pages 909-920, October.
    11. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
    12. M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
    Full references (including those not matched with items on IDEAS)

    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. Kerem Akartunalı & Andrew Miller, 2012. "A computational analysis of lower bounds for big bucket production planning problems," Computational Optimization and Applications, Springer, vol. 53(3), pages 729-753, December.
    2. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.
    3. Brahimi, Nadjib & Dauzere-Peres, Stephane & Najid, Najib M. & Nordli, Atle, 2006. "Single item lot sizing problems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 1-16, January.
    4. Kerem Akartunalı & Ioannis Fragkos & Andrew J. Miller & Tao Wu, 2016. "Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 766-780, November.
    5. Zhang, Zhi-Hai & Jiang, Hai & Pan, Xunzhang, 2012. "A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain," International Journal of Production Economics, Elsevier, vol. 140(1), pages 249-255.
    6. Dziuba, Daryna & Almeder, Christian, 2023. "New construction heuristic for capacitated lot sizing problems," European Journal of Operational Research, Elsevier, vol. 311(3), pages 906-920.
    7. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
    8. Ming Zhao & Minjiao Zhang, 2020. "Multiechelon Lot Sizing: New Complexities and Inequalities," Operations Research, INFORMS, vol. 68(2), pages 534-551, March.
    9. Drexl, A. & Kimms, A., 1997. "Lot sizing and scheduling -- Survey and extensions," European Journal of Operational Research, Elsevier, vol. 99(2), pages 221-235, June.
    10. Tao Wu, 2022. "Predictive Search for Capacitated Multi-Item Lot Sizing Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 385-406, January.
    11. Farhat, Mlouka & Akbalik, Ayse & Hadj-Alouane, Atidel B. & Sauer, Nathalie, 2019. "Lot sizing problem with batch ordering under periodic buyback contract and lost sales," International Journal of Production Economics, Elsevier, vol. 208(C), pages 500-511.
    12. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2005. "Integrated Lot Sizing in Serial Supply Chains with Production Capacities," Management Science, INFORMS, vol. 51(11), pages 1706-1719, November.
    13. Atamturk, Alper & Munoz, Juan Carlos, 2002. "A Study of the Lot-Sizing Polytope," University of California Transportation Center, Working Papers qt6zz2g0z4, University of California Transportation Center.
    14. Vernon Ning Hsu, 2000. "Dynamic Economic Lot Size Model with Perishable Inventory," Management Science, INFORMS, vol. 46(8), pages 1159-1169, August.
    15. Nadjib Brahimi & Stéphane Dauzère-Pérès & Najib M. Najid, 2006. "Capacitated Multi-Item Lot-Sizing Problems with Time Windows," Operations Research, INFORMS, vol. 54(5), pages 951-967, October.
    16. Chung-Lun Li & Qingying Li, 2016. "Polynomial-Time Solvability of Dynamic Lot Size Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-20, June.
    17. Fink, Jiří & Hurink, Johann L., 2015. "Minimizing costs is easier than minimizing peaks when supplying the heat demand of a group of houses," European Journal of Operational Research, Elsevier, vol. 242(2), pages 644-650.
    18. Goisque, Guillaume & Rapine, Christophe, 2017. "An efficient algorithm for the 2-level capacitated lot-sizing problem with identical capacities at both levels," European Journal of Operational Research, Elsevier, vol. 261(3), pages 918-928.
    19. Almeder, Christian & Klabjan, Diego & Traxler, Renate & Almada-Lobo, Bernardo, 2015. "Lead time considerations for the multi-level capacitated lot-sizing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 727-738.
    20. Okhrin, Irena & Richter, Knut, 2011. "The linear dynamic lot size problem with minimum order quantity," International Journal of Production Economics, Elsevier, vol. 133(2), pages 688-693, 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:spr:snopef:v:5:y:2024:i:3:d:10.1007_s43069-024-00350-8. 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.