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A Dynamic Lot-Sizing Model with Demand Time Windows

Author

Listed:
  • Chung-Yee Lee

    (Department of Industrial Engineering, Texas A...M University, College Station, Texas 77843-3131)

  • Sila Çetinkaya

    (Department of Industrial Engineering, Texas A...M University, College Station, Texas 77843-3131)

  • Albert P. M. Wagelmans

    (Econometric Institute and RIBES, Erasmus University Rotterdam, P.O.Box 1738, 3000 DR Rotterdam, The Netherlands)

Abstract

One of the basic assumptions of the classical dynamic lot-sizing model is that the aggregate demand of a given period must be satisfied in that period. Under this assumption, if backlogging is not allowed, then the demand of a given period cannot be delivered earlier or later than the period. If backlogging is allowed, the demand of a given period cannot be delivered earlier than the period, but it can be delivered later at the expense of a backordering cost. Like most mathematical models, the classical dynamic lot-sizing model is a simplified paraphrase of what might actually happen in real life. In most real-life applications, the customer offers a grace period---we call it a demand time window---during which a particular demand can be satisfied with no penalty. That is, in association with each demand, the customer specifies an acceptable earliest and a latest delivery time. The time interval characterized by the earliest and latest delivery dates of a demand represents the corresponding time window. This paper studies the dynamic lot-sizing problem with demand time windows and provides polynomial time algorithms for computing its solution. If backlogging is not allowed, the complexity of the proposed algorithm is O(T 2 ) where T is the length of the planning horizon. When backlogging is allowed, the complexity of the proposed algorithm is O(T 3 ).

Suggested Citation

  • Chung-Yee Lee & Sila Çetinkaya & Albert P. M. Wagelmans, 2001. "A Dynamic Lot-Sizing Model with Demand Time Windows," Management Science, INFORMS, vol. 47(10), pages 1384-1395, October.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:10:p:1384-1395
    DOI: 10.1287/mnsc.47.10.1384
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    4. 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.
    5. Guiffrida, Alfred L. & Nagi, Rakesh, 2006. "Cost characterizations of supply chain delivery performance," International Journal of Production Economics, Elsevier, vol. 102(1), pages 22-36, July.
    6. 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.
    7. 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.
    8. Yiyong Xiao & Meng You & Xiaorong Zuo & Shenghan Zhou & Xing Pan, 2018. "The Uncapacitatied Dynamic Single-Level Lot-Sizing Problem under a Time-Varying Environment and an Exact Solution Approach," Sustainability, MDPI, vol. 10(11), pages 1-14, October.
    9. Jaruphongsa, Wikrom & Cetinkaya, Sila & Lee, Chung-Yee, 2004. "Warehouse space capacity and delivery time window considerations in dynamic lot-sizing for a simple supply chain," International Journal of Production Economics, Elsevier, vol. 92(2), pages 169-180, November.
    10. Guan, Yongpei & Liu, Tieming, 2010. "Stochastic lot-sizing problem with inventory-bounds and constant order-capacities," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1398-1409, December.
    11. 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.
    12. 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.
    13. WOLSEY, Laurence A., 2005. "Lot-sizing with production and delivery time windows," LIDAM Discussion Papers CORE 2005043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. 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.
    15. Yongpei Guan, 2011. "Stochastic lot-sizing with backlogging: computational complexity analysis," Journal of Global Optimization, Springer, vol. 49(4), pages 651-678, April.
    16. Bakker, Hannah & Bindewald, Viktor & Dunke, Fabian & Nickel, Stefan, 2023. "Logistics for diagnostic testing: An adaptive decision-support framework," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1120-1133.
    17. Hark‐Chin Hwang, 2007. "Dynamic lot‐sizing model with production time windows," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 692-701, September.
    18. Darvish, Maryam & Coelho, Leandro C., 2018. "Sequential versus integrated optimization: Production, location, inventory control, and distribution," European Journal of Operational Research, Elsevier, vol. 268(1), pages 203-214.
    19. Andrew Lim & Zhaowei Miao & Brian Rodrigues & Zhou Xu, 2005. "Transshipment through crossdocks with inventory and time windows," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 724-733, December.
    20. Merzifonluoglu, Yasemin & Geunes, Joseph, 2006. "Uncapacitated production and location planning models with demand fulfillment flexibility," International Journal of Production Economics, Elsevier, vol. 102(2), pages 199-216, August.
    21. 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.

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