- Suppose you sell three types of donuts: plain, nut covered andchocolate covered. The daily demand of each type of donuts isnormally distributed and independent of each other. The means andstandard deviations are given in the following table:
| Mean | Standard deviation |
Plain | 16 | 4 |
Nut covered | 20 | 10 |
Chocolate covered | 25 | 5 |
Assume that theproduction lead time of making donuts is zero, and you replenishyour inventory of donuts every morning (i.e. review period is oneday). Besides, you want to achieve a service level of 80% for eachtype of donuts.
- If you make three types of donuts at the beginning of the day,how much safety stock do you needto carry in total to achieve aservice level of 80% for each type of donuts?(Please round itup when the safety stock for anytype of donut is not an integer, such as 1.01?2)
- Instead of making three types of donuts at the beginning of theday, you can only make plain donuts and dip plain donuts in nuts orchocolate on demand (assume for no extra cost). If you follow thisstrategy, how much safety stock do you need to carry in total toachieve a service level of 80% for each type of donuts?(Please roundit upwhenthesafetystockisnotaninteger,suchas1.01?2)
- If you follow the strategy in part b, compared to part a, thetotal safety stock would go down by how much percentage?(Please round it to the closest integer percentage,e.g.10.1%?10%)
