Sizing Inventory When Lead Time and Demand are Correlated

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Abstract

Determining appropriate inventory levels has been a subject of interest for both researchers and practitioners. Standard practice is to treat lead time demand as a random sum of random numbers and rely on established probability theory to calculate both reorder point and safety stock levels. A key assumption in these calculations, however, is that lead time and demand are not correlated. In this paper, we first explore situations where this assumption is untrue and then develop equations to determine the reorder point and the safety stock when lead time and demand are correlated. More specifically, we (1) derive formulas for the average and variance of the demand in a lead time, which can then be used to calculate the reorder point and the safety stock, (2) apply these formulas to two distributions for which there is a closed-form solution: normal and Poisson, and (3) examine the effect of correlation on safety stock requirements under the normal distribution.

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