Stage Two Incorporated produces a popular item at its Paducah, KY plant and ships this item to its national distribution center (DC) in Columbus, OH. The item has an annual demand of 20,000 units, which transpires at a relatively steady rate throughout the year. The fixed cost of replenishing the finished goods inventory at the Paducah plant is $200, and the fixed replenishment cost at the Columbus DC is $50. Annual holding costs at Paducah are $20 per unit. Annual holding costs at the Columbus DC at $30 per unit. (For the purposes of this problem, you can assume that replenishment of finished goods at the Paducah plant is sufficiently close to instantaneous to allow you to ignore the effects of changes in the average inventory level as production proceeds.)

(a) Use the methods developed in Section 3.6 to compute the optimal order quantity at the plant and at the DC assuming decentralized inventory control.

(b) Use the methods developed in Section 3.6 to compute the optimal order quantity at the plant and at the DC assuming centralized inventory control.

(c) What is the difference in total annual cost of the decentralized and centralized systems?