TY - JOUR

T1 - A mirror-image lead time inventory model

AU - Hayya, Jack

AU - Harrison, Terry P.

N1 - Funding Information:
The authors acknowledge with thanks the support of the Center for Supply Chain Research (CSCR) and the invaluable help rendered us by Eduardo Santiago of Minitab Inc. in the design of experiments. The authors also thank two anonymous referees who have made invaluable suggestions toward making this a better paper.
Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010/1

Y1 - 2010/1

N2 - The production-operations literature is rife with the inventory model where the demand rate, D, is iid, but where the lead time, L, is deterministic. Here we present a mirror-image lead time model where the reverse is true; that is, where D is deterministic and L is iid. This lead time model is interesting: first, it is subject to order crossover; second, because of order crossover, the optimal order cycle and order quantity could be smaller; and third, the optimal cost incurs inventory savings due to the reduction in the variance of the lead times in crossover situations. We perform this analysis in the context of three inventory reorder point, order quantity models that differ only in the characterisation of the shortage cost. These are Model 1 that uses the shortage cost per stockout occasion; Model 2 with the shortage cost per unit short; and Model 3, where the shortage cost is per unit short per unit time. Also, we develop response surfaces (for the normal approximation) for the optimal cost, C, the optimal order quantity, Q, and the optimal safety stock factor, [image omitted], in terms of the problem parameters (ordering cost per order, holding cost per unit per unit time, the particular shortage cost, and the standard deviation of the parent lead time). However, we find that the normal approximation is good in Model 1 and adequate for Model 3. For Model 2, the normal approximation understates the cost, because of the large penalties associated with the long right tail of the distribution of the demand during the effective lead time when the parent lead time is exponentially distributed. Nevertheless, the normal approximation could serve to provide a bound for the total cost and could be more convenient, albeit biased slightly upward in the case of Model 3 and significantly downward in the case of Model 2 than a straightforward simulation of the problem.

AB - The production-operations literature is rife with the inventory model where the demand rate, D, is iid, but where the lead time, L, is deterministic. Here we present a mirror-image lead time model where the reverse is true; that is, where D is deterministic and L is iid. This lead time model is interesting: first, it is subject to order crossover; second, because of order crossover, the optimal order cycle and order quantity could be smaller; and third, the optimal cost incurs inventory savings due to the reduction in the variance of the lead times in crossover situations. We perform this analysis in the context of three inventory reorder point, order quantity models that differ only in the characterisation of the shortage cost. These are Model 1 that uses the shortage cost per stockout occasion; Model 2 with the shortage cost per unit short; and Model 3, where the shortage cost is per unit short per unit time. Also, we develop response surfaces (for the normal approximation) for the optimal cost, C, the optimal order quantity, Q, and the optimal safety stock factor, [image omitted], in terms of the problem parameters (ordering cost per order, holding cost per unit per unit time, the particular shortage cost, and the standard deviation of the parent lead time). However, we find that the normal approximation is good in Model 1 and adequate for Model 3. For Model 2, the normal approximation understates the cost, because of the large penalties associated with the long right tail of the distribution of the demand during the effective lead time when the parent lead time is exponentially distributed. Nevertheless, the normal approximation could serve to provide a bound for the total cost and could be more convenient, albeit biased slightly upward in the case of Model 3 and significantly downward in the case of Model 2 than a straightforward simulation of the problem.

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U2 - 10.1080/00207540802616843

DO - 10.1080/00207540802616843

M3 - Article

AN - SCOPUS:77953624026

SN - 0020-7543

VL - 48

SP - 4483

EP - 4499

JO - International Journal of Production Research

JF - International Journal of Production Research

IS - 15

ER -