Your firm uses a continuous review system (Q system),where the inventory position is updated after every transaction.The firm operates 52 weeks per year.One of the items has the following characteristics:
Demand = 14,560 units per year
Ordering cost = $40 per order
Holding cost = $6 per unit per year
Lead time = 2 weeks
Standard deviation in weekly demand = 100 units
Cycle-service level = 80 percent
If Q is made equal to the EOQ,what are the desired values for Q and R?
A) Q is between 65 and 69, and R is between 398 and 402.
B) Q is between 65 and 69, and R is between 362 and 366.
C) Q is between 439 and 443, and R is between 678 and 682.
D) Q is between 439 and 443, and R is between 559 and 563.

Question

Quizplus · Accepted Answer

First, we need to calculate the EOQ:

EOQ = sqrt[(2*Demand*Ordering cost)/Holding cost] 
    = sqrt[(2*14560*40)/6]
    ≈ 442

Then, we need to calculate the safety stock using the standard deviation in weekly demand:

Safety stock = Z*sqrt(Lead time*Variance in weekly demand)
            = 1.28*sqrt(2*100^2)
            ≈ 181

Next, we can calculate the reorder point (R) as follows:

R = Demand/52*Lead time + Safety stock
  = 14560/52*2 + 181
  ≈ 682

Finally, we need to round Q and R to the nearest order interval, which we'll assume is 1.

Therefore, the desired values for Q and R are between 439 and 443, and 678 and 682, respectively.

The only answer choice that includes these intervals is C.

Your Firm Uses a Continuous Review System (Q System),where the Inventory