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A Dynamic Lot-Sizing Model with Demand Time Windows


  • 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)


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

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    References listed on IDEAS

    1. 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.
    2. Liman, Surya D. & Panwalkar, Shrikant S. & Thongmee, Sansern, 1996. "Determination of common due window location in a single machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 93(1), pages 68-74, August.
    3. Cary Swoveland, 1975. "A Deterministic Multi-Period Production Planning Model with Piecewise Concave Production and Holding-Backorder Costs," Management Science, INFORMS, vol. 21(9), pages 1007-1013, May.
    4. 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.
    5. Gabriel R. Bitran & Thomas L. Magnanti & Horacio H. Yanasse, 1984. "Approximation Methods for the Uncapacitated Dynamic Lot Size Problem," Management Science, INFORMS, vol. 30(9), pages 1121-1140, September.
    6. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Hark-Chin Hwang, 2010. "Economic Lot-Sizing for Integrated Production and Transportation," Operations Research, INFORMS, vol. 58(2), pages 428-444, April.
    4. WOLSEY, Laurence A., 2005. "Lot-sizing with production and delivery time windows," CORE Discussion Papers 2005043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. repec:eee:ejores:v:263:y:2017:i:3:p:838-863 is not listed on IDEAS
    6. 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.
    7. 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.
    8. 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.
    9. Yongpei Guan, 2011. "Stochastic lot-sizing with backlogging: computational complexity analysis," Journal of Global Optimization, Springer, vol. 49(4), pages 651-678, April.
    10. 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.
    11. repec:gam:jsusta:v:10:y:2018:i:11:p:3867-:d:178012 is not listed on IDEAS
    12. 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.
    13. repec:eee:ejores:v:268:y:2018:i:1:p:203-214 is not listed on IDEAS
    14. 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.
    15. 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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    Lot Sizing; Dynamic Programming; Time Windows;


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