Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self-Destruction, an expose on a famous politician's lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book's retail price is $20 and the wholesale price is $ 12. The publisher will buy back the retailer's leftover copies at a full refund, but McClure Books incurs $4 in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a norn1al distribution with mean 200 and standard deviation 80.
a. Dan will consider this book to be a blockbuster for him if it sells more than 400 units. What is the probability Power and Self-Destruction will be a blockbuster?
b. Dan considers a book a "dog" if it sells less than 50 percent of his mean forecast. What is the probability this expose is a "dog"?
c. What is the probability demand for this book will be within 20 percent of the mean forecast?
d. What order quantity maximizes Dan's expected profit?
e. Dan prides himself on good customer service. In fact, his motto is "McClure's got what you want to rcad." What order quantity should he choose to satisfy a 95 percent fill rate?
f. How many books should Dan order if he wants to achieve a 95 percent in-stock probability?
g. If Dan orders the quantity chosen in part to achieve a 95 percent in-stock probability, then what is the probability that "Dan won't have what some customer wants to read" (i.e., what is the probability some customer won't be able to purchase a copy of the book)?
h. Suppose Dan orders 300 copies of the book. What would Dan's expected profit be in this case?
i. Suppose Dan orders 1 50 copies of the book. What would Dan's fill rate be in this case?
j. Being an introspective chap, Dan decided to evaluate his forecasting skills in his spare time. He collected the following data on recent books he felt matched the characteristics of Power and Self-Destruction. If Dan used these data to construct an empirical distribution function, then what would be his optimal order quantity?
|
Book
|
Actual Demand
|
Forecast
|
A/F Ratio
|
|
Book
|
Actual Demand
|
Forecast
|
A/F Ratio
|
|
1
|
27
|
100
|
0.27
|
|
9
|
88
|
100
|
0.88
|
|
2
|
209
|
170
|
1.23
|
|
10
|
57
|
70
|
0.81
|
|
3
|
83
|
160
|
0.52
|
|
11
|
188
|
140
|
1.34
|
|
4
|
77
|
100
|
0.77
|
|
12
|
157
|
130
|
1.21
|
|
5
|
205
|
150
|
1.37
|
|
13
|
65
|
110
|
0.59
|
|
6
|
228
|
190
|
1.20
|
|
14
|
135
|
170
|
0.79
|
|
7
|
12
|
60
|
0.20
|
|
15
|
155
|
160
|
0.97
|
|
8
|
88
|
60
|
1.47
|
|
16
|
82
|
90
|
0.91
|