Advanced Search
MyIDEAS: Login

The capacitated lot sizing problem: a review of models and algorithms

Contents:

Author Info

  • Karimi, B.
  • Fatemi Ghomi, S. M. T.
  • Wilson, J. M.
Registered author(s):

    Abstract

    Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/B6VC4-48TM9NN-2/2/07f9b62f4aaf7dff2c8225d2a521fd86
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Omega.

    Volume (Year): 31 (2003)
    Issue (Month): 5 (October)
    Pages: 365-378

    as in new window
    Handle: RePEc:eee:jomega:v:31:y:2003:i:5:p:365-378

    Contact details of provider:
    Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description

    Order Information:
    Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/order?id=375&ref=375_01_ooc_1&version=01

    Related research

    Keywords: Capacitated lot sizing problem Heuristics Integer programming Production planning;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Selen, W. J. & Heuts, R. M., 1989. "A modified priority index for Gunther's lot-sizing heuristic under capacitated single stage production," European Journal of Operational Research, Elsevier, vol. 41(2), pages 181-185, July.
    2. Cattrysse, Dirk & Maes, Johan & Van Wassenhove, Luk N., 1990. "Set partitioning and column generation heuristics for capacitated dynamic lotsizing," European Journal of Operational Research, Elsevier, vol. 46(1), pages 38-47, May.
    3. Ganas, Ioannis S. & Papachristos, Sotirios, 1997. "Analytical evaluation of heuristics performance for the single-level lot-sizing problem for products with constant demand," International Journal of Production Economics, Elsevier, vol. 48(2), pages 129-139, January.
    4. Alan S. Manne, 1957. "Programming of Economic Lot Sizes," Cowles Foundation Discussion Papers 23, Cowles Foundation for Research in Economics, Yale University.
    5. Gaetan Belvaux & Laurence A. Wolsey, 2001. "Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs," Management Science, INFORMS, vol. 47(7), pages 993-1007, July.
    6. Wolsey, Laurence A., 1995. "Progress with single-item lot-sizing," European Journal of Operational Research, Elsevier, vol. 86(3), pages 395-401, November.
    7. Stadtler, Hartmut, 1997. "Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 7096, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    8. William W. Trigeiro & L. Joseph Thomas & John O. McClain, 1989. "Capacitated Lot Sizing with Setup Times," Management Science, INFORMS, vol. 35(3), pages 353-366, March.
    9. Chung, Chia-Shin & Flynn, James & Lin, Chien-Hua Mike, 1994. "An effective algorithm for the capacitated single item lot size problem," European Journal of Operational Research, Elsevier, vol. 75(2), pages 427-440, June.
    10. 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.
    11. Fleischmann, B. & Meyr, H., 1997. "The General Lotsizing and Scheduling Problem," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 36068, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    12. Millar, Harvey H. & Yang, Minzhu, 1994. "Lagrangian heuristics for the capacitated multi-item lot-sizing problem with backordering," International Journal of Production Economics, Elsevier, vol. 34(1), pages 1-15, February.
    13. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    14. Hartmut Stadtler, 2000. "Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem," Management Science, INFORMS, vol. 46(2), pages 318-326, February.
    15. Maes, Johan & McClain, John O. & Van Wassenhove, Luk N., 1991. "Multilevel capacitated lotsizing complexity and LP-based heuristics," European Journal of Operational Research, Elsevier, vol. 53(2), pages 131-148, July.
    16. Dong X. Shaw & Albert P. M. Wagelmans, 1998. "An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Management Science, INFORMS, vol. 44(6), pages 831-838, June.
    17. Drexl, Andreas & Haase, Knut, 1995. "Proportional lotsizing and scheduling," International Journal of Production Economics, Elsevier, vol. 40(1), pages 73-87, June.
    18. Imre Barany & Tony J. Van Roy & Laurence A. Wolsey, 1984. "Strong Formulations for Multi-Item Capacitated Lot Sizing," Management Science, INFORMS, vol. 30(10), pages 1255-1261, October.
    19. Tempelmeier, Horst & Helber, Stefan, 1994. "A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures," European Journal of Operational Research, Elsevier, vol. 75(2), pages 296-311, June.
    20. 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.
    21. Kirca, Omer & Kokten, Melih, 1994. "A new heuristic approach for the multi-item dynamic lot sizing problem," European Journal of Operational Research, Elsevier, vol. 75(2), pages 332-341, June.
    22. Chand, Suresh, 1982. "Lot sizing for products with finite demand horizon and periodic review inventory policy," European Journal of Operational Research, Elsevier, vol. 11(2), pages 145-148, October.
    23. Wee, Hui-Ming, 1999. "Deteriorating inventory model with quantity discount, pricing and partial backordering," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 511-518, March.
    24. Armentano, Vinícius A. & França, Paulo M. & de Toledo, Franklina M. B., 1999. "A network flow model for the capacitated lot-sizing problem," Omega, Elsevier, vol. 27(2), pages 275-284, April.
    25. 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.
    26. Gelders, Ludo F. & Van Wassenhove, Luk N., 1981. "Production planning: a review," European Journal of Operational Research, Elsevier, vol. 7(2), pages 101-110, June.
    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 in new window

    Cited by:
    1. Helber, Stefan & Sahling, Florian, 2008. "A Fix-and-Optimize Approach for the Multi-Level Capacitated Lot Sizing Problems," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-393, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    2. Süral, Haldun & Denizel, Meltem & Van Wassenhove, Luk N., 2009. "Lagrangean relaxation based heuristics for lot sizing with setup times," European Journal of Operational Research, Elsevier, vol. 194(1), pages 51-63, April.
    3. Tiacci, Lorenzo & Saetta, Stefano, 2012. "Demand forecasting, lot sizing and scheduling on a rolling horizon basis," International Journal of Production Economics, Elsevier, vol. 140(2), pages 803-814.
    4. LAMAS, ALEJANDRO & CHEVALIER, Philippe, 2013. "Jumping the hurdles for collaboration: fairness in operations pooling in the absence of transfer payments," CORE Discussion Papers 2013073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Mocquillon, Cédric & Lenté, Christophe & T'Kindt, Vincent, 2011. "An efficient heuristic for medium-term planning in shampoo production," International Journal of Production Economics, Elsevier, vol. 129(1), pages 178-185, January.
    6. Bredström, David & Rönnqvist, Mikael, 2006. "Supply Chain Optimization in Pulp Distribution using a Rolling Horizon Solution Approach," Discussion Papers 2006/17, Department of Business and Management Science, Norwegian School of Economics.
    7. Sahling, Florian & Buschkühl, Lisbeth & Tempelmeier, Horst & Helber, Stefan, 2008. "Solving a Multi-Level Capacitated Lot Sizing Problem with Multi-Period Setup Carry-Over via a Fix-and-Optimize Heuristic," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-400, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    8. Kovcs, Andrs & Brown, Kenneth N. & Tarim, S. Armagan, 2009. "An efficient MIP model for the capacitated lot-sizing and scheduling problem with sequence-dependent setups," International Journal of Production Economics, Elsevier, vol. 118(1), pages 282-291, March.
    9. Wolter, Anja & Helber, Stefan, 2013. "Simultaneous Production and Maintenance Planning for a Single Capacitated Resource facing both a Dynamic Demand and Intensive Wear and Tear," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-522, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    10. Gamberi, M. & Gamberini, R. & Manzini, R. & Regattieri, A., 2008. "An analytical model to evaluating the implementation of a batch-production-oriented line," International Journal of Production Economics, Elsevier, vol. 111(2), pages 729-740, February.
    11. Ferreira, Deisemara & Clark, Alistair R. & Almada-Lobo, Bernardo & Morabito, Reinaldo, 2012. "Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production," International Journal of Production Economics, Elsevier, vol. 136(2), pages 255-265.
    12. Azaron, Amir & Tang, Ou & Tavakkoli-Moghaddam, Reza, 2009. "Dynamic lot sizing problem with continuous-time Markovian production cost," International Journal of Production Economics, Elsevier, vol. 120(2), pages 607-612, August.
    13. Ferreira, Deisemara & Morabito, Reinaldo & Rangel, Socorro, 2009. "Solution approaches for the soft drink integrated production lot sizing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 196(2), pages 697-706, July.
    14. Tiacci, Lorenzo & Saetta, Stefano, 2009. "An approach to evaluate the impact of interaction between demand forecasting method and stock control policy on the inventory system performances," International Journal of Production Economics, Elsevier, vol. 118(1), pages 63-71, March.
    15. Rezaei, Jafar & Davoodi, Mansoor, 2011. "Multi-objective models for lot-sizing with supplier selection," International Journal of Production Economics, Elsevier, vol. 130(1), pages 77-86, March.
    16. Florian Sahling, 2013. "A Column-Generation Approach for a Short-Term Production Planning Problem in Closed-Loop Supply Chains," BuR - Business Research, German Academic Association for Business Research, vol. 6(1), pages 55-75, May.
    17. Ibarra-Rojas, Omar J. & Ríos-Mercado, Roger Z. & Rios-Solis, Yasmin A. & Saucedo-Espinosa, Mario A., 2011. "A decomposition approach for the piece-mold-machine manufacturing problem," International Journal of Production Economics, Elsevier, vol. 134(1), pages 255-261, November.
    18. Tempelmeier, Horst, 2011. "A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint," Omega, Elsevier, vol. 39(6), pages 627-633, December.
    19. 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.
    20. Meyr, Herbert & Mann, Matthias, 2013. "A decomposition approach for the General Lotsizing and Scheduling Problem for Parallel production Lines," European Journal of Operational Research, Elsevier, vol. 229(3), pages 718-731.
    21. Almada-Lobo, Bernardo & Oliveira, José F. & Carravilla, Maria Antónia, 2008. "Production planning and scheduling in the glass container industry: A VNS approach," International Journal of Production Economics, Elsevier, vol. 114(1), pages 363-375, July.
    22. Vidal-Carreras, Pilar I. & Garcia-Sabater, Jose P. & Coronado-Hernandez, Jairo R., 2012. "Economic lot scheduling with deliberated and controlled coproduction," European Journal of Operational Research, Elsevier, vol. 219(2), pages 396-404.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:jomega:v:31:y:2003:i:5:p:365-378. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.