who can solve this problem?

Question

The purchasing manager for a firm is trying to determine what the safety stock should be for a particular product. She has developed the following table, which gives the distribution of demand during the lead-time and the probabilities:

Demand during lead time / probability
40/ 0.2
50/ 0.25
60/ 0.25
70/ 0.2
80/ 0.1
The carrying cost is $5 per unit per year, the ordering cost is $30 per order, and the stockout cost is $40 per unit. The reorder point is 60 units, and 6 orders are placed each year. What level of safety stock should be maintained?
ROP (reroder point)=d (daily demand) x L (order lead time) +SS (safety stock)
I don't know how to solve it.

Answer 1

Since you have a demand during lead time with its probability (note that the total probability adds up to 1), multiply each demand with its probability, then add them all up.
Based on your final formula that value should be d.

Answer 2

The straightforward approach is to find the probability-weighted average demand (57.5) and subtract it form 60, yielding a safety stock of 2.5. You have other weighting factors to consider, though: carrying cost, and stockout cost, and the problem seems to want you to minimize the cost. This is easiest done with a "what-if" spreadsheet, subtracting an estimated SS, weighting the "over" by $5 and the "under" by $40, summing the cost, and changing the SS until you have minimum cost. You can do it by hand, or with a calculator, but it gets really tedious quickly. I arrived at a minimum cost at a SS of 10 (which you will note is much higher than the average SS)