Authentic Thai rattan chairs are delivered to Gary Schwartz's chain of retail stores, called The Kathmandu Shop, once a year. The reorder point, without safety stock, is 200 chairs. Carrying cost is $30 per unit per year, and the cost of a stockout is $80 per chair per year.
Given the following demand probabilities during the lead time, how much safety stock should be carried?
Demand during lead time Probability
0 0.2
100 0.2
200 0.2
300 0.2
400 0.2
The optimal quantity of safety stock which minimizes expected total cost is _ units (enter your response as a whole number).

The optimal quantity of safety stock which minimizes expected total cost is _ units is 100 units.

Explanation:

Incremental Costs would be considered here to evaluate which safety stock level is the best for the company.

The working is as under:

Safety Stock  Carrying Cost      Stock-out Cost                    Total Cost

   0                        0                     (100*0.2 + 200*0.2) * 80         4,800

 100                100*30 = $3000   (100 * 0.2) * 80                        1,600

200               200*30 = $6000   (200 * 0.2) * 80                       3,200

The total cost has started growing as the safety starts growing above the 100 units level. This means that the safety stock must be 100 units as the cost at this level is the lowest to the company.