Question: A distributor of printer copier spare parts maintains four regional warehouses in the United States. Each warehouse faces a fairly constant demand that can be modeled by a constant demand rate of 200 units per day. The distributor can place replenishment orders with the manufacturer for any order size. Orders can be delivered immediately. There is a fixed shipment cost of $1000 regardless of order size. The cost of carrying inventory in stock is $0.1 per unit per day.
a) What is the optimal order quantity at each warehouse? What is the corresponding total cost (ordering + holding cost) in the system?
b) The distributor is considering consolidating the four warehouses into a single one. What is the optimal order quantity if all demand is satisfied from a single warehouse? What is the corresponding total cost?
c) With the centralized warehouse, the fixed shipping cost is likely to increase since deliveries would likely travel longer distances. What is the maximum increase in the fixed shipping cost that would be acceptable to the distributor?