The annual demand for sugar at a local soft drink company is normally distributed with a mean of 800 tons and a standard deviation of 25 tons. The sugar sells for $500 each ton, and the annual inventory holding cost rate is 10%. Ordering costs are $5 per order. The delivery time for sugar is 5 working days. Assume that there are 250 working days in a year.
1. Determine the optimal order quantity.
2. What size of safety stock should the company keep at a service-level of 90%?
3. Suppose they keep 8 extra tons in inventory as a safety stock. What is the service-level obtained?
4. Evaluate the fill rate( B beta )for a safety stock of 5 tons.
5. What is the expected number of units short per year?
6. Compare the level of safety stock for each policy a alpha=B beta=0.95.