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. Let us consider the case when both demand and lead times are variable. We make the following assumptions: The inventory system is reviewed periodically with a review period of T days. The inventory system involves a single item. Demand for the item is variable but the distribution governing the demand is known or can be estimated. We assume the demand is normally distributed with a known mean and standard deviation. Lead time, L, is variable but the distribution governing the lead time is known or can be estimated. We assume the lead time is normally distributed with a known mean and standard deviation. An order of size is placed on completion of review. The size of the order is such that it brings the inventory on hand, 1, up to a maximum level, S. specified by the management. Q will, therefore, vary from period to period. In this scenario, the order quantity Q can be given by Q = d( TL) +2 27 [(T +L)ca] +do- (6.12) where h45 z is the standard normal variate; . and ou are the standard deviations of the demand and lead time, respectively; . I is the on-hand inventory including inventory on order. Safety stock and maximum inventory level for this condition are as follows: (6.12a) SS = V[(T + L) o] + do? S = (T+L) +2V [T + Lyo] +4d (6.12b) Solved Problem 6.16 A retail shop uses a periodic review inventory system. The annual demand for a consumer product sold by the shop is 5500 units, the ordering cost is $43 per order, and the inventory carrying rate is 35% per year. The product costs $100 per unit. The daily demand for the product is normally distributed with a mean of 15 units and a standard deviation of 3 units. If the procurement lead time is normally distributed with a mean of 5 days and a standard deviation of 1 day, compute the safety stock if the retailer wishes a 90% probability of not stocking out during lead time