Cranium Inc purchases term papers from an overseas supplier

Cranium, Inc., purchases term papers from an overseas supplier under a continuous review system. The average demand for a popular mode is 300 units a day with a standard deviation of 30 units a day. It costs $60 to process each order and there is a fiveday leadtime. The holding cost for a paper is $0.25 per year and the company policy is to maintain a 98% service level. Cranium operates 200 days per year.

What is the reorder point R to satisfy a 98% cycleminusservice level?

A. greater than 1,700 units

B. greater than 1,600 units but less than or equal to 1,700 units

C. greater than 1,500 units but less than or equal to 1,600 units

D. less than or equal to 1,500 units

Solution

Standard deviation of daily demand = 30 units

Lead time = 5 days

Therefore ,

Standard deviation demand during lead time

= Standard deviation of daily demand x Square root ( Lead time )

= 30 x Square root ( 5 )

= 30 x 2.236

= 67.08

Required service level = 98%,

i.e In service probability = 0.98

Corresponding Z value = NORMSINV ( 0.98) = 2.0537

Therefore,

Required safety stock = Z value x Standard deviation of demand during lead time = 2.0537 x 67.08 = 137.76 ( 138 rounded to nearest whole number)

Thus,

Reorder point = Average daily demand x Lead time + safety stock = 300 x 5 + 138 = 1500 + 138 = 1638

Reorder point is 1638 units which is” greater than 1600 units but less than or equal to 1700 units “

ANSWER : b) GREATER THAN 1600 UNITS BUT LESS THAN OR EQUAL TO 1700 UNITS