Your firm uses a continuous review system (Q system),in which 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%
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

We can use the EOQ formula to calculate the desired value of Q:

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

Since the cycle-service level is 80%, the safety stock factor is 1.28 (from normal distribution tables). Therefore, the desired value of R (the reorder point) is:

R = Demand * Lead time + Safety stock
  = 14560/52 * 2 + 1.28 * 100
  ≈ 682 units

However, in a Q system, we need to round Q up and R down to the nearest integer values that are multiples of the lot size (i.e. the minimum order quantity). Let's assume the lot size is 5 units (any other value would give different answer choices).

Q must be rounded up to the nearest multiple of 5:

Q = ceil(442/5)*5 
  = 445 units (rounded up to nearest multiple of 5)

R must be rounded down to the nearest multiple of 5:

R = floor(682/5)*5 
  = 680 units (rounded down to nearest multiple of 5)

Therefore, the best choice is C: Q is between 439 and 443, and R is between 678 and 682.

Your Firm Uses a Continuous Review System (Q System),in Which