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A Dynamic Lot-Sizing Model with Demand Time Windows


Author Info

  • Chung-Yee Lee

    (Texas A&M University)

  • Sila Çetinkaya

    (Texas A&M University)

  • Albert P.M. Wagelmans

    (Econometric Institute, RIBES, Erasmus University)

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    One of the basic assumptions of the classical dynamic lot-sizing model is that theaggregate demand of a given period must be satisfied in that period. Under thisassumption, if backlogging is not allowed then the demand of a given period cannotbe delivered earlier or later than the period. If backlogging is allowed, the demandof a given period cannot be delivered earlier than the period, but can be deliveredlater at the expense of a backordering cost. Like most mathematical models, theclassical dynamic lot-sizing model is a simplified paraphrase of what might actuallyhappen in real life. In most real life applications, the customer offers a graceperiod - we call it a demand time window - during which a particular demand can besatisfied with no penalty. That is, in association with each demand, the customerspecifies an earliest and a latest delivery time. The time interval characterizedby the earliest and latest delivery dates of a demand represents the correspondingtime window.This paper studies the dynamic lot-sizing problem with demand time windows andprovides polynomial time algorithms for computing its solution. If shortages arenot allowed, the complexity of the proposed algorithm is order T square. Whenbacklogging is allowed, the complexity of the proposed algorithm is order T cube.

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    Bibliographic Info

    Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 99-095/4.

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    Date of creation: 22 Dec 1999
    Date of revision:
    Handle: RePEc:dgr:uvatin:19990095

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    Related research

    Keywords: lot-sizing; dynamic programming; time windows;

    This paper has been announced in the following NEP Reports:


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    1. 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.
    2. van Hoesel, C.P.M. & Wagelmans, A.P.M., 1997. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Econometric Institute Research Papers EI 9735/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Hoesel,C.P.M.,van & Wagelmans,A.P.M., 1997. "Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
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