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Lot sizes under continuous demand: The backorder case

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  • David Yao
  • Morton Klein

Abstract

We study a deterministic lot‐size problem, in which the demand rate is a (piecewise) continuous function of time and shortages are backordered. The problem is to find the order points and order quantities to minimize the total costs over a finite planning horizon. We show that the optimal order points have an interleaving property, and when the orders are optimally placed, the objective function is convex in the number of orders. By exploiting these properties, an algorithm is developed which solves the problem efficiently. For problems with increasing (decreasing) demand rates and decreasing (increasing) cost rates, monotonicity properties of the optimal order quantities and order intervals are derived.

Suggested Citation

  • David Yao & Morton Klein, 1989. "Lot sizes under continuous demand: The backorder case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 615-624, October.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:5:p:615-624
    DOI: 10.1002/1520-6750(198910)36:53.0.CO;2-T
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    4. Charles H. Falkner, 1969. "Optimal Ordering Policies for a Continuous Time, Deterministic Inventory Model," Management Science, INFORMS, vol. 15(11), pages 672-685, July.
    5. Edward A. Silver, 1981. "Operations Research in Inventory Management: A Review and Critique," Operations Research, INFORMS, vol. 29(4), pages 628-645, August.
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