Scenario 9.7
You are the operations manager of a firm that uses the continuous-review inventory control system.Suppose the firm operates 52 weeks a year,365 days,and has the following characteristics for its primary item:
Demand = 25,000 units/year
Ordering cost = $30/order
Holding cost = $8/unit/year
Lead time = 2 weeks
Standard deviation in weekly demand = 100 units
A normal distribution table is appended to this exam.
-Use the information in Scenario 9.7.What safety stock level provides a 95% cycle-service level?
A)less than or equal to 150 units
B)greater than 150 but less than or equal to 200 units
C)greater than 200 but less than or equal to 250 units
D)greater than 250 units

Question

Quizplus · Accepted Answer

To calculate the safety stock level that provides a 95% cycle-service level, we need to use the formula:

Safety stock = Z × σL

where Z is the number of standard deviations corresponding to the desired cycle-service level and σL is the standard deviation of demand during lead time.

From the normal distribution table, we can find that the value of Z for a 95% cycle-service level is 1.64.

To calculate σL, we need to first convert the standard deviation of weekly demand to a standard deviation of demand during lead time. Since lead time is 2 weeks, we can use the following formula to find the standard deviation of demand during lead time:

σL = σw × √LT

where σw is the standard deviation of weekly demand and LT is the lead time in weeks.

Substituting the given values, we get:

σL = 100 × √2 = 141.42 units

Therefore, the safety stock level that provides a 95% cycle-service level is:

Safety stock = 1.64 × 141.42 = 231.47 units

Since the question asks for the safety stock level rounded to the nearest 50 units, the answer is C) greater than 200 but less than or equal to 250 units.

Scenario 9.7 You Are the Operations Manager of a Firm That Uses