National Auto parts uses a 4-week periodic review system to reorder parts for its inventory stock. A one week lead time is required to fill the order. Demand for one particular part during the five week replenishment period is normally distributed with a mean of 18 units and a standard deviation of 6 units. 1.At a particular periodic review, 8 units are in inventory. The parts manager places an order for 16 units. What is the probability that this part will have a stockout before an order that is placed at the next 4-week review period arrives? 2. Assume that the company is willing to tolerate a 2.5% chance of stockout associated with a replenishment decision. What is the replenishment level for the 4-week periodic review system? 3.How many parts should the manager have ordered in part (1)?

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A health and nutrition store stocks a multivitamin with an annual demand of 1,000 bottles has  Co = $26.50 and Ch = $7. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with ? = 25 and ? = 5. (a) What is the recommended order quantity? (Round your answer to the nearest integer.):________   (b) What are the reorder point and safety stock if the store desires at most a 6% probability of stock-out on any given order cycle? (Round your answers to the nearest integer.) reorder point:________ safety stock:________ (c) If a manager sets the reorder point at 30, what is the probability of a stock-out on any given order cycle? (Round your answer to four decimal places.):________   How many times would you expect a stock-out during the year if this reorder point were used? (Round your answer to the nearest integer.):________

Nationwide Auto Parts uses a periodic review inventory control system for one of its stock items. The review interval is 6 weeks, and the lead time for receiving the materials ordered from its wholesaler is 3 weeks. Weekly demand is normally distributed, with a mean of 100 units and a standard deviation of 20 units.a. What is the average and the standard deviation of demand during the protection interval?b. What should be the target inventory level if the firm desires 97.5 percent stockout protection?c. If 350 units were in stock at the time of a periodic review, how many units should be ordered?