Batch Size Depending on Stockout Costs (*)
The carrying costs for a certain article are 2 per unit and year. Stockout costs are 5 per unit. The average annual consumption amounts to 1000 , and the standard deviation of demand during lead time is 10 . No safety stock is intended. Normal distribution is assumed.
a. How large should the batch size be, considering the optimum stockout probability? Can the fill rate target of $99 \%$ be met? What are the carrying costs per year?
b. Assume a batch size of only 250 . What are the values for safety stock and fill rate corresponding to the optimum probability of stockout per order cycle?
c. Now assume a safety stock of 20 units. Again, the batch size is 250 . What are the values for service level and fill rate?