What order-up-to point maximizes the net profit on Great White?

(Ans-v)

Plotting a graph between Order up to points and Net Profits:

It is clear that the net profit $1,516.36 is maximum at the Order up to point 57

Q# b)

i) Evaluate Brown's proposal that he should use the holding cost of one unit for the two-week period as the cost of overage in the newsvendor model. Calculate this overage cost for the Great White SKU.

(Ans-i)

The holding cost of one unit = cost of overage

Annual Holding Cost =0. 25*20 (Holding cost is 25%, and $20 is the cost per unit)

Annual Holding Cost = $5

This is the annual holding cost per unit holding cost for two weeks it would be (25 Bi weeks in a year)

Co= 5/25 = $0.2

ii) Evaluate Brown's proposal that he should use the margin on one unit (= retail price -wholesale price) as the cost of underage.

(Ans-ii)

Cost of underage = margin on one unit

=21 - 20 (21 is the retail price, and 20 is wholesale price)

With = $1

iii) Calculate the critical fractile based on the underage and overage costs given (i) and (ii) above. This gives the optimal in-stock rate for those costs. The corresponding optimal order-up-to the point is the smallest order-up-to point that has an in-stock rate equal to or higher than the critical fractile. Use your table of order-up-to points and in-stock rates to find the optimal order-up-to point based on your calculated critical fractile.

(Ans-iii)

Critical fractile = Cu/(Co+Cu)

=1/1.2

CF= 0.8333

This is the "Optimal In Stock rate" for this in stock rate; the order up to the point will be 60.

4. The number calculated from 3 does not match the order-up-to point determined in #1 (a-v). Brown wonders if his cost of underage depends on his order-up-to point. Evaluate Brown's thought that if his order-up-to point is high enough, the cost of underage is close to his margin minus the holding cost, but as his order-up-to point gets lower and lower the cost of underage should get closer to just the margin.

5. Based on 4, the margin calculated in 2 is the maximum value of the cost of underage. Calculate the minimum value of the cost of underage and the corresponding order-up-to point. What is the maximum difference in net profits over the range of order-up-to points from the order point calculated in 3 to the order-up-to point calculated here?