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A mail-order firm has four regional warehouses. Demand at each warehouse for a particular item is normally distributed with a mean of 10,000 per week and a standard deviation of 2,000. Annualized cost of capital is 25%, and each unit of product costs the company $10. Each order incurs an ordering cost of $1000 (primarily from fixed transportation costs), and lead time from the supplier is 1 week. The company wants a 95% service level. Assume 50 working weeks in a year. Inventories can be monitored and managed in continuous time.
1. Assume that each warehouse operates independently. What should be the ordering policy at each warehouse?
2. Given the policy, you computed in part (a.), how much inventory does each warehouse hold on average?
3. Now assume that the firm has centralized all inventories into a single warehouse. What should be the ordering policy for the central warehouse?
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