Question

The annual demand for a product is 15,300 units. The weekly demand is 294 units with a standard deviation of 90 units. The cost to place an order is $28.50, and the time from ordering to receipt is ten weeks. The annual inventory carrying cost is $0.20 per unit. Find the reorder point necessary to provide a 98% service probability. Suppose the production manager is asked to reduce the safety stock of this item by 50%. If she does so, what will the new service probability be?

Answer 1

Reorder point = (weekly demand * lead time) + (Z * standard deviation * √lead time) = (294 * 10) + (2.326 * 90 * √10) = 2,940 + 661.99 = 3,602 units

Old safety stock = Z * standard deviation * √lead time = 662 units

new safety stock = 331

331 = Z * 90 * √10

Z = 331 / 284.60 = 1.163

Using Normal distribution function, the new confidence interval is 87.76%