Question

A newsvendor orders the quantity that maximizes expected profit for two products, X and Y. The critical ratio for both products is 0.8. The demand forecast for both products is 9,000 units and both are normally distributed. Product X has more uncertain demand in the sense that it has the larger standard deviation. Of which of the two products does the newsvendor order more

A. Product A, because it has less certain demand.
B. Product B, because it has more certain demand.
C. The order quantities are the same because they have the same critical ratio.
D. More information is needed to determine which has the higher order quantity.

Answer 1

Answer:

A. Product A, because it has less certain demand.

Explanation:

According to the statement, the product X (A) is the one with the highest proportion of standard deviation, that is, it has a more uncertain demand. Taking into account this condition, it is expected that the number of optimal products will be greater because it has an average and critical relationship. For this reason, it is expected that the news seller will lean towards the first product, since it will generate higher income as explained at the beginning.

Answer 2

Following are the calculation to the standard deviation:

$Cr = 0.8,$ which is the critical ratio.

The value of Z corresponding to the critical ratio of 0.8 from the standard normal distribution tables is $0.8416$.

Unless the quantity ordered by the newsvendor is Q, then

$Q = \text{Mean value of demand + Z} \times \text{Standard deviation of demand}$

Below are the specifications of the two products:

The mean requirement for both X and Y is 900O units.

Z value for both X and Y = 0.8416

Let,

$Sd_1 =$Demand Standard Deviation for Product X

$Sd_2$ = Demand Standard Deviation for Product Y

Assuming that $Sd_1 > Sd_2$ (Product X does have a higher standard deviation than Product Y),

quantities for $\text{X = Mean value of demand + Z} \times \text{Standard deviation of demand}$

$= 9000 + 0.8416.Sd_1$

Order amount for $\text{Y = demand mean + Z } \times \text{ demand standard deviation}$

$= 9000 + 0.8416.Sd_2$

$X_1 > X_2$ because

As a result, $9000 + 0.8416.Sd_1 > 9000 + 0.8416.Sd_2$

OR

The quantity ordered for X is > the quantity ordered for Y. As a result, Newsvendor orders Product X more frequently because it has a higher level of certainty.

In this question, all the estimates are wrong so, the correct answer is "Product X because it has less certain demand".

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