IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v6y2025i2d10.1007_s43069-025-00441-0.html
   My bibliography  Save this article

An Efficient Algorithm to Check Feasibility for Two-Level Discrete Lot-Sizing and Scheduling

Author

Listed:
  • Murat Güngör

    (Istanbul Medeniyet University)

  • Ali Tamer Ünal

    (Boğaziçi University)

Abstract

In general, discrete lot-sizing and scheduling problem (DLSP) is NP-hard in single level, all the more so in multiple levels. We investigate the computational complexity of conceivably the simplest yet nontrivial multi-level DLSP. Namely, we ignore setups and examine the feasibility problem that asks whether all demand can be met on time. As it turns out, an answer can be provided by an algorithm that is polynomial in the planning horizon.

Suggested Citation

  • Murat Güngör & Ali Tamer Ünal, 2025. "An Efficient Algorithm to Check Feasibility for Two-Level Discrete Lot-Sizing and Scheduling," SN Operations Research Forum, Springer, vol. 6(2), pages 1-8, June.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00441-0
    DOI: 10.1007/s43069-025-00441-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-025-00441-0
    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/s43069-025-00441-0?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Marc Salomon & Leo G. Kroon & Roelof Kuik & Luk N. Van Wassenhove, 1991. "Some Extensions of the Discrete Lotsizing and Scheduling Problem," Management Science, INFORMS, vol. 37(7), pages 801-812, July.
    2. Gothe-Lundgren, Maud & T. Lundgren, Jan & A. Persson, Jan, 2002. "An optimization model for refinery production scheduling," International Journal of Production Economics, Elsevier, vol. 78(3), pages 255-270, August.
    3. Irvin J. Lustig & Jean-François Puget, 2001. "Program Does Not Equal Program: Constraint Programming and Its Relationship to Mathematical Programming," Interfaces, INFORMS, vol. 31(6), pages 29-53, December.
    4. Bruggemann, Wolfgang & Jahnke, Hermann, 2000. "The discrete lot-sizing and scheduling problem: Complexity and modification for batch availability," European Journal of Operational Research, Elsevier, vol. 124(3), pages 511-528, August.
    5. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    6. Lee, Younsoo & Lee, Kyungsik, 2020. "Lot-sizing and scheduling in flat-panel display manufacturing process," Omega, Elsevier, vol. 93(C).
    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. Rohaninejad, Mohammad & Hanzálek, Zdeněk, 2023. "Multi-level lot-sizing and job shop scheduling with lot-streaming: Reformulation and solution approaches," International Journal of Production Economics, Elsevier, vol. 263(C).
    2. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Melega, Gislaine Mara & Xu, Chi & Jans, Raf & Paquette, Julie, 2025. "An integrated approach for lot-sizing and storage assignment," Omega, Elsevier, vol. 131(C).
    4. Lee, Younsoo & Lee, Kyungsik, 2023. "Valid inequalities and extended formulations for lot-sizing and scheduling problem with sequence-dependent setups," European Journal of Operational Research, Elsevier, vol. 310(1), pages 201-216.
    5. 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.
    6. Lee, Younsoo & Lee, Kyungsik, 2020. "Lot-sizing and scheduling in flat-panel display manufacturing process," Omega, Elsevier, vol. 93(C).
    7. Lee, Younsoo & Lee, Kyungsik, 2022. "New integer optimization models and an approximate dynamic programming algorithm for the lot-sizing and scheduling problem with sequence-dependent setups," European Journal of Operational Research, Elsevier, vol. 302(1), pages 230-243.
    8. Martin Wörbelauer & Herbert Meyr & Bernardo Almada-Lobo, 2019. "Simultaneous lotsizing and scheduling considering secondary resources: a general model, literature review and classification," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 1-43, March.
    9. Jing Wu & Lijie Su & Gongshu Wang & Yang Yang, 2024. "Approximated Dynamic Programming for Production and Inventory Planning Problem in Cold Rolling Process of Steel Production," Mathematics, MDPI, vol. 12(24), pages 1-17, December.
    10. Theresa M. Roeder & Robert M. Saltzman, 2014. "Schedule-Based Group Assignment Using Constraint Programming," INFORMS Transactions on Education, INFORMS, vol. 14(2), pages 63-72, February.
    11. Sungmin Kang & Kavindra Malik & L. Joseph Thomas, 1999. "Lotsizing and Scheduling on Parallel Machines with Sequence-Dependent Setup Costs," Management Science, INFORMS, vol. 45(2), pages 273-289, February.
    12. 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.
    13. Farahani, Mohsen & Rahmani, Donya, 2017. "Production and distribution planning in petroleum supply chains regarding the impacts of gas injection and swap," Energy, Elsevier, vol. 141(C), pages 991-1003.
    14. Schirmer, Andreas, 1995. "A guide to complexity theory in operations research," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 381, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    15. 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.
    16. Alfieri, A. & Bianco, A. & Brandimarte, P. & Chiasserini, C.F., 2007. "Maximizing system lifetime in wireless sensor networks," European Journal of Operational Research, Elsevier, vol. 181(1), pages 390-402, August.
    17. Yavuz, Mesut & Tufekci, Suleyman, 2006. "A bounded dynamic programming solution to the batching problem in mixed-model just-in-time manufacturing systems," International Journal of Production Economics, Elsevier, vol. 103(2), pages 841-862, October.
    18. Madjid Tavana & Kaveh Khalili-Damghani & Francisco J. Santos Arteaga & Arousha Hashemi, 2020. "A Malmquist productivity index for network production systems in the energy sector," Annals of Operations Research, Springer, vol. 284(1), pages 415-445, January.
    19. van Hoesel, C.P.M. & Wagelmans, A., 1997. "Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    20. Yannis Pavlis & Will Recker, 2009. "A Mathematical Logic Approach for the Transformation of the Linear Conditional Piecewise Functions of Dispersion-and-Store and Cell Transmission Traffic Flow Models into Linear Mixed-Integer Form," Transportation Science, INFORMS, vol. 43(1), pages 98-116, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00441-0. 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.