Question

​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 variance of 900 units a day. It costs​ $62 to process each order and there is a​ five-day lead-time. The holding cost for a paper is​ $0.25 per year and the company policy is to maintain a​ 95% service level. Cranium operates 200 days per year.  

A. What is the EOQ for these​ papers? (round up to a whole​ number)

A.

386

B.

7370

C.

315

D.

5456

B. What is the reorder point​ (R) to satisfy a​ 95% cycle-service​ level? (round up to a whole​ number)

A.

111

B.

1500

C.

1611

D.

68

C. What service level does a reorder point of​ 1,530 imply?

A.

​67.36%

B.

​45%

C.

​67.08%

D.

​100%

D. What is just the cost of holding safety​ stock? (do not report total​ cost)

A.

​$16.77

B.

​$110.35

C.

​$27.59

D.

​$251.98

E. What is just the cost of holding cycle​ inventory? (don not report total​ cost)

A.

​$187.50

B.

​$1364.00

C.

​$251.98

D.

​$682.00

Answer 1

A.

EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*300*200*62)/0.25) = 5455.272679 = 5456 (Rounded up to a whole number)

Correct answer is D. 5456

B.

Reorder point to satisfy 95% service level = Daily demand*lead time + z*standard deviation of demand*sqrt(lead time)

as z score for 95% service level is 1.645,

Reorder point = 300*5+1.645*sqrt(900)*sqrt(5) = 1610.349955 = 1611 (Rounded up to a whole number)

Correct answer is C. 1611

C.

Reorder point = Daily demand*lead time + z*standard deviation of demand*sqrt(lead time)

or, 1530 = 300*5+z*sqrt(900)*sqrt(5)

or, 30 = z*30*sqrt(5)

or, z =1/sqrt(5) = 0.447213595 = 0.45

So Required service level = 0.6736 for z = 0.45

So correct answer is A.67.36%

D.

Cost of holding safety stock = 1.645*sqrt(900)*sqrt(5)*0.25 = 27.58748867

So correct answer is C. 27.59

E.

cost of holding cycle​ inventory = (5456/2)*0.25 = 682

So correct answer is D.​$682.00