IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v53y2005i1p170-176.html
   My bibliography  Save this article

The Single-Product Lot-Sizing Problem with Constant Parameters and Backlogging: Exact Results, a New Solution, and All Parameter Stability Regions

Author

Listed:
  • Ioannis Ganas

    (Department of Accounting, Technological Educational Institute of Epirus, Ioanninon Avenue 210, 481 00 Preveza, Greece)

  • Sotirios Papachristos

    (Department of Mathematics, Probability, Statistics, and Operations Research Section, University of Ioannina, 451 10 Ioannina, Greece)

Abstract

We consider the single-product lot-sizing problem over a finite planning horizon. Demand at each period is constant, and excess demand is completely backlogged. Holding and backlogging costs are proportional to the amount of inventory stocked or backlogged, while ordering cost is fixed, independent of the quantity ordered. The optimal policy targets to minimize the total relevant costs over the planning horizon. The key results of this paper are: (1) an explicit formula for the optimal total cost as a function of the model parameters and the number of cycles of the policy; (2) a new, polynomial-time algorithm which determines the overall optimal policy; and (3) stability regions for any solution considering simultaneous variations on all cost and demand parameters. The proposed algorithm is easy to implement and therefore is suitable for practical use.

Suggested Citation

  • Ioannis Ganas & Sotirios Papachristos, 2005. "The Single-Product Lot-Sizing Problem with Constant Parameters and Backlogging: Exact Results, a New Solution, and All Parameter Stability Regions," Operations Research, INFORMS, vol. 53(1), pages 170-176, February.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:1:p:170-176
    DOI: 10.1287/opre.1040.0163
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1040.0163
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1040.0163?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
    ---><---

    References listed on IDEAS

    as
    1. van Hoesel, Stan & Wagelmans, Albert, 1991. "A note on `Stability of the constant cost dynamic lot size model' by K. Richter," European Journal of Operational Research, Elsevier, vol. 55(1), pages 112-114, November.
    2. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
    3. Richter, Knut, 1994. "Sequential stability of the constant cost dynamic lot size model," International Journal of Production Economics, Elsevier, vol. 35(1-3), pages 359-363, June.
    4. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    5. Joseph D. Blackburn & Howard Kunreuther, 1974. "Planning Horizons for the Dynamic Lot Size Model with Backlogging," Management Science, INFORMS, vol. 21(3), pages 251-255, November.
    6. Thomas E. Morton, 1978. "Note--An Improved Algorithm for the Stationary Cost Dynamic Lot Size Model with Backlogging," Management Science, INFORMS, vol. 24(8), pages 869-873, April.
    7. 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.
    8. Hoesel, C. P. M. Van & Wagelmans, A. P. M., 2000. "Parametric analysis of setup cost in the economic lot-sizing model without speculative motives," International Journal of Production Economics, Elsevier, vol. 66(1), pages 13-22, June.
    9. Richter, Knut, 1987. "Stability of the constant cost dynamic lot size model," European Journal of Operational Research, Elsevier, vol. 31(1), pages 61-65, July.
    10. Awi Federgruen & Michal Tzur, 1993. "The dynamic lot‐sizing model with backlogging: A simple o(n log n) algorithm and minimal forecast horizon procedure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 459-478, June.
    11. Chand, Suresh & Voros, Jozsef, 1992. "Setup cost stability region for the dynamic lot sizing problem with backlogging," European Journal of Operational Research, Elsevier, vol. 58(1), pages 68-77, April.
    12. Alok Aggarwal & James K. Park, 1993. "Improved Algorithms for Economic Lot Size Problems," Operations Research, INFORMS, vol. 41(3), pages 549-571, 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


    Cited by:

    1. Wu, Tao & Shi, Leyuan & Geunes, Joseph & AkartunalI, Kerem, 2011. "An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging," European Journal of Operational Research, Elsevier, vol. 214(2), pages 428-441, October.
    2. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    3. Konstantaras, I. & Papachristos, S., 2007. "Optimal policy and holding cost stability regions in a periodic review inventory system with manufacturing and remanufacturing options," European Journal of Operational Research, Elsevier, vol. 178(2), pages 433-448, April.

    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. Hoesel, C. P. M. Van & Wagelmans, A. P. M., 2000. "Parametric analysis of setup cost in the economic lot-sizing model without speculative motives," International Journal of Production Economics, Elsevier, vol. 66(1), pages 13-22, June.
    2. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    3. Vernon Ning Hsu, 2000. "Dynamic Economic Lot Size Model with Perishable Inventory," Management Science, INFORMS, vol. 46(8), pages 1159-1169, August.
    4. 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.
    5. Kian, Ramez & Gürler, Ülkü & Berk, Emre, 2014. "The dynamic lot-sizing problem with convex economic production costs and setups," International Journal of Production Economics, Elsevier, vol. 155(C), pages 361-379.
    6. Hwang, Hark-Chin & Jaruphongsa, Wikrom, 2008. "Dynamic lot-sizing model for major and minor demands," European Journal of Operational Research, Elsevier, vol. 184(2), pages 711-724, January.
    7. 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.
    8. 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.
    9. Hark‐Chin Hwang & Wilco van den Heuvel, 2012. "Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 244-253, April.
    10. Kerkkamp, R.B.O. & van den Heuvel, W. & Wagelmans, A.P.M., 2019. "Two-echelon lot-sizing with asymmetric information and continuous type space," Omega, Elsevier, vol. 87(C), pages 158-176.
    11. Hark-Chin Hwang, 2010. "Economic Lot-Sizing for Integrated Production and Transportation," Operations Research, INFORMS, vol. 58(2), pages 428-444, April.
    12. Hark-Chin Hwang & Hyun-Soo Ahn & Philip Kaminsky, 2013. "Basis Paths and a Polynomial Algorithm for the Multistage Production-Capacitated Lot-Sizing Problem," Operations Research, INFORMS, vol. 61(2), pages 469-482, April.
    13. Yale T. Herer & Michal Tzur, 2001. "The dynamic transshipment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 386-408, August.
    14. Hark-Chin Hwang, 2009. "Inventory Replenishment and Inbound Shipment Scheduling Under a Minimum Replenishment Policy," Transportation Science, INFORMS, vol. 43(2), pages 244-264, May.
    15. Voros, Jozsef, 1995. "Setup cost stability region for the multi-level dynamic lot sizing problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 132-141, November.
    16. Hark-Chin Hwang & Wilco van den Heuvel & Albert P. M. Wagelmans, 2023. "Multilevel Lot-Sizing with Inventory Bounds," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1470-1490, November.
    17. 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.
    18. 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.
    19. Alper Atamtürk & Dorit S. Hochbaum, 2001. "Capacity Acquisition, Subcontracting, and Lot Sizing," Management Science, INFORMS, vol. 47(8), pages 1081-1100, August.
    20. Geunes, Joseph & Romeijn, H. Edwin & van den Heuvel, Wilco, 2016. "Improving the efficiency of decentralized supply chains with fixed ordering costs," European Journal of Operational Research, Elsevier, vol. 252(3), pages 815-828.

    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:inm:oropre:v:53:y:2005:i:1:p:170-176. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.