Expected Lead time demand = Sum ( Lead time demand x Probability ) = 5 x 0.05 +

ID: 373563 • Letter: E

Question

Expected Lead time demand

= Sum ( Lead time demand x Probability )

= 5 x 0.05 + 10 x 0.1 + 15 x 0.3 + 20 x 0.35 + 25 x 0.15 + 30 x 0.05

= 0.25 + 1 + 4.5 + 7 + 3.75 + 1.50

= 18

Variance of lead time demand

= ( 18 – 5)^2 + ( 18 – 10)^2 + ( 18 – 15)^2 + ( 20 -18)^2 + ( 25 – 18)^2 + ( 30 – 18)^2

= 13^2 + 8^2 + 3^2 + 2^2 + 7^2 + 12^2

= 169 + 64 + 9 + 4 + 49 + 144

= 439

Therefore, standard deviation of lead time demand = Square root ( 439 ) = 20.95

Z value for service level of 0.95 = NORMSINV ( 0.95) = 1.6448

Therefore,

Safety stock = Zvalue x Standard deviation of lead time demand = 1.6448 x 20.95 = 34.46 ( 35 rounded to next higher whole number)

SAFETY STOCK = 35 UNIT

Annual cost of carrying the safety stock = $50 / unit / year x 35 = $1750

Reorder level = Lead time demand + Safety stock

= 18 + 35

= 53

REORDER LEVEL = 53 UNITS

SAFETY STOCK = 35 UNITS

ANNUAL COST OF CARRYING THE SAFETY STOCK = $1750

REORDER LEVEL = 53 UNITS

SAFETY STOCK = 35 UNITS

ANNUAL COST OF CARRYING THE SAFETY STOCK = $1750

Lead-time demand for a product is uncertain, and has the following probability distribution:

Lead-time demand 5 10 15 20 25 30

Probability 0.05 0.1 0.3 0.35 0.15 0.05

Suppose the desired service level is 0.95.

a. Find the reorder level and safety stock.

b. The inventory holding cost is $50/unit/year. What is the annual cost of carrying the safety stock?

Please show step by step solution to this problem

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