A mail- order firm has four regional warehouses. Demand at each warehouse is normally distributed with a mean of 10,000 per week and a standard deviation of 2,000. Annual holding cost is 25%, and each unit of product costs the company $ 10. Each order incurs an ordering cost of $ 1,000 (primarily from fixed transportation costs), and lead time is 1 week. The company wants the probability of stocking out in a flow to be no more than 5%. Assume 50 working weeks in a year.
a. Assuming that each warehouse operates independently, what should be the ordering policy at each warehouse? How much safety stock does each warehouse hold? How much average inventory is held (at all four warehouses combined) and at what annual cost? On average, how long does a unit of product spend in the warehouse before being sold?
b. Assume that the firm has centralized all inventories in a single warehouse and that the probability of stocking out in a cycle can still be no more than 5%. Ideally, how much average inventory can the company now expect to hold and at what cost? In this case, how long will a unit spend in the ware-house before being sold?