Assignment
1. Epson produces printers for sale in Europe in its Taiwan factory. Currently, Epson assembles and packs printers for sale in individual countries. The weekly demand in different countries is normally distributed, with means and standard deviations given below:
|
Country
|
Mean
demand
|
Standard
deviation
|
|
A
|
3,000
|
2,000
|
|
B
|
4,000
|
2,200
|
|
C
|
2,000
|
1,400
|
|
D
|
2,500
|
1,600
|
|
E
|
1,000
|
800
|
|
F
|
4,000
|
2,400
|
(a) Given that the lead time from the Taiwan factory is 8 weeks, how much safety stock does Epson require in Europe if it targets a CSL of 95%?
(b) Epson decides to build a central DC in Europe. How much will safety stock reduce?
2. A publisher sells books to Borders at $12 each. The marginal production cost for the publisher is $1 per book. Borders prices the book to its customers at $24. Borders places a single order with the publisher for delivery at the beginning of the season. Currently, Borders discounts any unsold books at the end of the season down to $3. Borders has the following forecast for its demand:
|
Demand
|
Probability
|
|
1,000
|
11%
|
|
1,500
|
20%
|
|
2,000
|
28%
|
|
2,500
|
26%
|
|
3,000
|
15%
|
(a) How many books should Borders order? What is its expected profit? How many books does it expect to sell at a discount?
(b) What is the profit that the publisher makes given Border's actions?
(c) If the publisher buys back any unsold books from Borders at a price of $5 per book, and sells them at the discount price of $3. Under this arrangement, how many books will Border order? What is the expected profit for Borders? How many books are expected to be returned to the publisher? What is the expected profit for the publisher?
3. A manufacturer decides to ration a total supply of 100,000 units of its most popular toy to its retailers. The toy is sold at a margin of $4 in the discount retail channel, and at a margin of $6 in the high-service channel. The manufacturer has forecasted that the demand for the toy at the high-service channel is normally distributed with mean 40,000 and standard deviation 15,000. How many toys should the manufacturer ration to high- service channel?
4. An airline serving Denver's Stapleton Airport and Steamboat Springs, Colorado is considering overbooking its flights to avoid flying with empty seats. During the past month, the no-show experience has been:
|
# of No-show customers
|
0
|
1
|
2
|
3
|
4
|
|
Probability
|
0.1
|
0.25
|
0.2
|
0.35
|
0.1
|
A round-trip ticket sells for $180. If the reservation cannot be honored, the airline will issue a voucher of $150 to the customer. How many reservations should the airline accept, if the plane has 100 seats?