Question

A restaurant uses 5,000 quart bottles of ketchup each year. The ketchup costs $3.00 per bottle and is served only in whole bottles because its taste quickly deteriorates. The restaurant figures that it costs $10.00 each time an order is placed, and holding costs are 20 percent of the purchase price. It takes 3 weeks for an order to arrive. The restaurant operates 50 weeks per year. The restaurant would like to use an inventory system that minimizes inventory cost. Suppose that things have become uncertain and that customer demand is no more constant. Customer demand is now normally distributed with mean being the same as given in the problem description and standard deviation = 30 units per week. The supply source is still very reliable and as a result the lead time is constant.
Find out the safety stock needed to achieve 95% customer service level.
a. 55
b. 65
c. 75
d. 85
e. None of the above

Answer 1

Answer:

d. 85

Explanation:

safety stock = z-score x standard deviation of demand x √lead time

z-score for 95% confidence level (using a table) = 1.644

standard deviation of demand = 30

√lead time = √3 = 1.732

safety stock = 1.644 x 30 x 1.732 = 85.42 ≈ 85 bottles of ketchup