Question 12.13: Finding the Optimal Stocking Level When Demand Is Normally D...
Finding the Optimal Stocking Level When Demand Is Normally Distributed
Cindy’s Cider Bar also sells a blend of cherry juice and apple cider. Demand for the blend is approximately normal, with a mean of 200 liters per week and a standard deviation of 10 liters per week. C_s = $2.40 per liter, and C_e = $.80 per liter. Find the optimal stocking level for the apple-cherry blend.
SL = SL = \frac{C_s}{C_s + C_e}=\frac{\$2.40}{\$2.40 +\$.80}=.75
This indicates that 75 percent of the area under the normal curve must be to the left of the stocking level. Appendix B, Table B, shows that for a value of z between +.67 and +.68, use the value of z that has a probability nearest to .75. In this case, it is .67. The optimal stocking level is So = mean + zσ. Thus,
So = 200 liters + .67(10 liters) = 206.7 liters
