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Question: Solve the newsvendor problem. What is the optimal order quantity?

Probability

0.2

0.1

0.1

0.2

0.3

0.1

Value

1

2

3

4

5

6

Purchase cost c = 15

Selling price p = 25

Salvage value v =10

Short Answer

Expert verified

The best order amount for a corporation to acquire to reduce inventory expenses such as holding charges, shortfall costs, and order fees is known as the optimal order quantity. Ford W. Harris created this production-scheduling model in 1913, and it has been modified over time. The formula is based on the assumption that demand, ordering, and holding costs are all constant.

Step by step solution

01

Calculation of Critical Ratio and service level:-

Critical ratio =p-cp-v=25-1525-10=1015= 0.666666666666667

02

Calculation of Optimal Order quantity

Probability of demand less than 1 = 0, the quantity (Q) is less than the critical ratio (0.66667)

The probability of demand is less than 2 = 0.2, the quantity (Q) is less than the critical ratio (0.66667)

Probability of demand less than 3 = 0.3 (0.2+0.1), the quantity (Q) is less than critical ratio (0.66667)

Probability of demand less than 4 = 0.4 (0.2+0.1+0.1), the quantity (Q) is less than critical ratio (0.66667)

Probability of demand less than 5 = 0.6 (0.2+0.1+0.1+0.2), the quantity (Q) is less than critical ratio (0.66667)

Probability of demand less than 6 = 0.9 (0.2+0.1+0.1+0.2+0.3), the quantity (Q) is more than critical ratio (0.66667)

Thus, the Optimal order quantity is 5.

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