Problem
A mail order ?rm has 4 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 510. Each order incurs an ordering cost of $1,000 (primarily from fixed transportation costs), and lead time is 1 week.
The company wants the probability of stocking out to be no more than 5%. Assume 50 working weeks in a year.
1. What is the annual demand at a single warehouse (unit)?
2. What is the Economic Order Quantity for a single warehouse ($/year)?
3. What z would generate the desired service level?
4. What safety stock would achieve the desired service level (units)?
5. What re-order point would achieve the desired service level (units)?
6. What is the average inventory at each warehouse (units)?
7. What is the annual inventory management cost at a single warehouse ($/year)?
8. What is the total average inventory at all 4 warehouses (units)?
9. What is the annual inventory management cost for all 4 warehouses ($/year)?
10. What is the average flow time at each warehouse (weeks)?