IDEAS home Printed from https://ideas.repec.org/p/cdl/uctcwp/qt6zz2g0z4.html
   My bibliography  Save this paper

A Study of the Lot-Sizing Polytope

Author

Listed:
  • Atamturk, Alper
  • Munoz, Juan Carlos

Abstract

The lot-sizing polytope is a fundamental structure contained in many practical production planning problems. Here we study this polytope and identify fact-defining inequalities that cut of all fractional extreme points of its linear programming relaxation, as well as liftings from those facets. We give a polynomial-time combinatorial separation algorithm for the inequalities when capacities are constant. We also report on an extensive computational study on solving the lot-sizing problem for instances up to 365 time periods with varying cost and capacity characteristics.

Suggested Citation

  • 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.
    • Handle: RePEc:cdl:uctcwp:qt6zz2g0z4
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/6zz2g0z4.pdf;origin=repeccitec
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. C. P. M. van Hoesel & A. P. M. Wagelmans, 1996. "An O(T 3 ) Algorithm for the Economic Lot-Sizing Problem with Constant Capacities," Management Science, INFORMS, vol. 42(1), pages 142-150, January.
    2. 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.
    3. Laurence A. Wolsey, 2002. "Solving Multi-Item Lot-Sizing Problems with an MIP Solver Using Classification and Reformulation," Management Science, INFORMS, vol. 48(12), pages 1587-1602, December.
    4. WOLSEY, Laurence A., 2002. "Solving multi-item lot-sizing problems with an MIP solver using classification and reformulation," LIDAM Reprints CORE 1605, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Michael Florian & Morton Klein, 1971. "Deterministic Production Planning with Concave Costs and Capacity Constraints," Management Science, INFORMS, vol. 18(1), pages 12-20, September.
    6. POCHET, Yves & WOLSEY, Laurence A., 1993. "Lot-sizing with constant batches: formulation and valid inequalities," LIDAM Reprints CORE 1066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    8. Yves Pochet & Laurence A. Wolsey, 1991. "Solving Multi-Item Lot-Sizing Problems Using Strong Cutting Planes," Management Science, INFORMS, vol. 37(1), pages 53-67, January.
    9. 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.
    10. 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.
    11. BELVAUX, Gaetan & WOLSEY, Laurence A., 2001. "Modelling practical lot-sizing problems as mixed-integer programs," LIDAM Reprints CORE 1516, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Zonghao Gu & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Sequence Independent Lifting in Mixed Integer Programming," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 109-129, March.
    13. 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.
    14. 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. Atamturk, Alper & Munoz, Juan Carlos, 2002. "A Study of the Lot-Sizing Polytope," University of California Transportation Center, Working Papers qt9gx170tx, University of California Transportation Center.
    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. 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.
    4. AkartunalI, Kerem & Miller, Andrew J., 2009. "A heuristic approach for big bucket multi-level production planning problems," European Journal of Operational Research, Elsevier, vol. 193(2), pages 396-411, March.
    5. Alper Atamtürk & Simge Küçükyavuz, 2005. "Lot Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation," Operations Research, INFORMS, vol. 53(4), pages 711-730, August.
    6. Laurence A. Wolsey, 2002. "Solving Multi-Item Lot-Sizing Problems with an MIP Solver Using Classification and Reformulation," Management Science, INFORMS, vol. 48(12), pages 1587-1602, December.
    7. 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.
    8. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    9. Francesco Gaglioppa & Lisa A. Miller & Saif Benjaafar, 2008. "Multitask and Multistage Production Planning and Scheduling for Process Industries," Operations Research, INFORMS, vol. 56(4), pages 1010-1025, August.
    10. 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.
    11. 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.
    12. Alper Atamtürk & Dorit S. Hochbaum, 2001. "Capacity Acquisition, Subcontracting, and Lot Sizing," Management Science, INFORMS, vol. 47(8), pages 1081-1100, August.
    13. Yongpei Guan & Andrew J. Miller, 2008. "Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 56(5), pages 1172-1183, October.
    14. Eksioglu, Sandra Duni, 2009. "A primal-dual algorithm for the economic lot-sizing problem with multi-mode replenishment," European Journal of Operational Research, Elsevier, vol. 197(1), pages 93-101, August.
    15. Mathieu Van Vyve, 2007. "Algorithms for Single-Item Lot-Sizing Problems with Constant Batch Size," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 594-613, August.
    16. Ming Zhao & Minjiao Zhang, 2020. "Multiechelon Lot Sizing: New Complexities and Inequalities," Operations Research, INFORMS, vol. 68(2), pages 534-551, March.
    17. 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.
    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. van Hoesel, C.P.M. & Romeijn, H.E. & Romero Morales, M.D. & Wagelmans, A., 2002. "Polynomial time algorithms for some multi-level lot-sizing problems with production capacities," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    More about this item

    Keywords

    Social and Behavioral Sciences;

    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:cdl:uctcwp:qt6zz2g0z4. 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: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/itucbus.html .

    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.