Table 1
Peterson Enterprises uses a fixed order quantity inventory control system. The firm operates 50 weeks per year and has the following characteristics for an item:
Demand $= 50,000$ units/year
Ordering cost $= \$ 35 /$ order
Inventory-carrying cost as a percent of item value $= 25 \%$
Item (Unit) value $= \$ 8$
Lead time $= 3$ weeks
Standard deviation in weekly demand $= 125$ units
-Using the information in Table 1, if Peterson wishes to provide a 97 percent cycle service level, what is the reorder point?
A) Less than or equal to 2,800 units
B) Greater than 2,800 but less than or equal to 3,200 units
C) Greater than 3,200 but less than or equal to 3,600 units
D) Greater than 3,600 units

Question

Quizplus · Accepted Answer

The reorder point (ROP) is calculated as the sum of the product of lead time and average demand plus the safety stock. Average weekly demand is $50,000 \ units/year \div 50 \ weeks/year = 1,000 \ units/week$. For a 97% service level, using the standard normal distribution, the Z-score is approximately 1.88. Safety stock is calculated as Z-score $\times$ standard deviation in weekly demand $\times$ square root of lead time, which is $1.88 \times 125 \times \sqrt{3} \approx 408$ units. Therefore, ROP = $3 \ weeks \times 1,000 \ units/week + 408 \ units \approx 3,408$ units, which is greater than 3,200 but less than or equal to 3,600 units.

Table 1 Peterson Enterprises Uses a Fixed Order Quantity Inventory =50,000= 50,000=50,000

Table 1
Peterson Enterprises Uses a Fixed Order Quantity Inventory $= 50,000$