A pharmacy considers selling graduation congratulation cards with 2017 printed o
ID: 3239128 • Letter: A
Question
A pharmacy considers selling graduation congratulation cards with 2017 printed on the cards. These cards are typically released in April and need to be sold before end of June for full value. After June, the remaining cards would be marked down to get sold. For each card, the item cost is exist1.39, the selling price from April to June is exist4.99, and marked down price after June is exist0.98. The pharmacy's historical demand is normally distributed with a mean of 1.6 million cards and a standard deviation of 0.23 million cards. You would need to show equations, steps, and the final results with units for full credits. Answers are in millions using 5 decimals, e.g. 1.76384 million cards. You should not round up the numbers! For simplicity, all taxes and other costs are not considered. All parts below are based on the optimal order quantity decision in part (a). (a) To maximize expected profit, how many cards should the pharmacy carry this year? (b) Sketch the normal demand distribution with details to illustrate the business decision. (c) What is the expected inventory? (in millions with 5 decimals) (d) What are the expected sales? (in millions with 5 decimals) (e) What is the expected profit? (in millions of dollars with 5 decimals) (f) What is the in-stock probability? (5 decimals) (g) What is the stock out probability? (5 decimals)Explanation / Answer
This problem will be solved as per Newsvendor Model of problem solving.
Given the data,
Selling price of item card = P = $ 4.99
Cost price of each item = C = $ 1.29
Salvage price ( marked down price ) of the card = S = $0.98
Thus,
Cost of underordering = Cu = P – C = $ 4.99 - $1.29 = $3.7
Cost of overordering = Co = C – S = $1.29 - $0.98 = $0.31
Hence,
Critical ratio = Cu / ( Cu + Co) = 3.7 / ( 3.7 + 0.31) = 3.7/ 4.01 = 0.92269
In order to maximize profit, one must choose the order quantity in such a way so that the probability of the order quantity getting sold is equal to Critical ratio which is 0.92269
Answer to Question a:
Since the pharmacy’s demand is uniformly distributed between 1.1 million and 1.8 million cards ( i.e. equal probability of having any number of cards between 1.1 million and 1.8 million cards ) ,
Thus demand corresponding to Critical ratio
= 1.1 million + Critical ratio x ( 1.8 million – 1.1 million)
= 1.1 million + 0.92269 x 0.7 million
= 1.1 million + 0.64588 million
= 1.74588 million
THE PHARMCY SHOULD CARRY 1.74588 MILLION CARDS THIS YEAR
Answer to Question b:
As per table, Z value corresponding to Critical ratio of 0.92269 is 1.42342
Therefore,
Number of cards pharmacy should carry this year
= Mean demand + Z value x Standard deviation of demand
= 1.6 million + 1.42342 x 0.17 million
= 1.6 million + 0.24198 million
= 1.84198 million
THE PHARMACY SHOULD CARRY 1.84198 MILLION CARDS THIS YEAR
THE PHARMCY SHOULD CARRY 1.74588 MILLION CARDS THIS YEAR
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