Mr. X operates a camera store in Y City. The expected yearly demand for a partic

Question

Mr. X operates a camera store in Y City. The expected yearly demand for a particular camera is 10400 units. The cost of the camera is $40 and the probability distribution of the weekly demand is N(200,2500). The ordering cost is $10, the inventory carrying percentage is 25%, and the unit shortage cost is $25. Suppose Mr. X order quantity is 1000 units. Furthermore, Lee specifies that the expected number of shortages per year is to be 50 units.

(a) Find the reorder point for Mr. X if the delivery lead time is one week.

(b)Find the reorder point for Mr. X if the delivery lead time is a random variable with mean equal to 1 week and variance equal to four week.

Explanation / Answer

Average weekly demand(D)=200

SD of demand= SQRT(2500)=50

Lead time(L)= 1 week

Service level=950/1000=95% ( 50 shortage is estimated)

a.

Reorder point= average demand during lead time+safety stock

Average demand during 1 week lead time= 200 X SQRT(1)=200

Safety stock =SD during lead time X Z-factor for 95%= 50 X SQRT(1) X 1.6449=

Reorder point= 200+82.245 = 282.3

b. Lead time is variable with mean=1 and SD= SQRT(4)=2 weeks

Safety stock = z-factor for safety level X standard deviation of demand during variable lead time

SD during variable lead time = SQRT(Average lead time X Variance of demand +Average demand Xvariance of lead time)= SQRT(1 X 2500+200 X4)= SQRT(3300)

Reorder point = 1 X200+ 57.45 X1.6449=294.5=294 (approximately)

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