An article is to be restocked every three months in a year. The quarterly demand U is random and its law of probability in any of the quarters is as given below.
| U |
Probability Mass Function, PU(u) |
| 0 |
0.2 |
| 1 |
0.3 |
| 2 |
0.4 |
| 3 |
0.1 |
| >3 |
0 |
The cost of stocking an article for a unit of time is 4, and when the stock is exhausted, there is a scarcity charge of 12.
The orders that are not satisfied are lost, in other words, are not carried forward to the next period. Further, the stock cannot exceed three articles, owing to the restrictions on space.
Find the annual policy of restocking the article so as to minimize the expected value of the sum of the cost of stocking and of the scarcity charge