James R. Bradley - Publications
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| Improved Base-Stock Policies Under Order
Crossover (Revision submitted to Manufacturing and Service Operations Management, 7/03) |
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James R. Bradley and Lawrence W. Robinson |
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| "Order crossover" occurs whenever replenishment orders do not arrive in the sequence in which they were placed. When order crossover is possible, Robinson et al. (2001) showed that its effect can be correctly taken into account by setting inventory levels using the inventory shortfall rather than the lead-time demand. For convenience, a heuristic base-stock level can be found by assuming that the shortfall is Normally distributed. This calculation, however, depends on the variance of the number of orders outstanding, which is cumbersome to compute and requires more information than may be available in practice. This paper makes the Normal approximation to the shortfall distribution tractable by computing bounds on the variance of the number of orders outstanding. Specifically, we show that the variance of the number of orders outstanding is bounded above by the minimum of the lead-time mean, the lead-time variance, and the standard deviation of the lead time divided by v3. This easily-computed upper bound can be used in Normal approximations of the shortfall distribution to take order crossover into account, and so will improve significantly upon policies set according to the lead-time demand distribution. | |
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