OPERATIONS PLANNING & CONTROL
HOMEWORK
Q1) (Project Management) The following information has been gathered for a project:
|
Activity
|
Activity Time
(weeks)
|
Immediate
Predecessor(s)
|
|
A
|
4
|
None
|
|
B
|
7
|
A
|
|
C
|
9
|
B
|
|
D
|
3
|
B
|
|
E
|
14
|
D
|
|
F
|
10
|
C, D
|
|
G
|
11
|
F, E
|
a) Draw the network diagram.
b) Calculate the slack for each activity.
c) Determine the critical path.
d) How long will the project take?
Q2) (Project Management) Table given below contains information about an environmental clean-up project. Shorten the project three weeks by finding the minimum-cost schedule. Assume that project indirect costs and penalty costs are negligible. Identify activities to crash while minimizing the additional crash costs.
|
Activity
|
Normal Time (weeks)
|
Crash Time (weeks)
|
Cost to Crash ($ per week)
|
Immediate Predecessor(s)
|
|
A
|
7
|
6
|
200
|
None
|
|
B
|
12
|
9
|
250
|
None
|
|
C
|
7
|
6
|
250
|
A
|
|
D
|
6
|
5
|
300
|
A
|
|
F
|
1
|
1
|
|
B
|
|
F
|
1
|
1
|
|
C, D
|
|
G
|
3
|
1
|
200
|
D, E
|
|
H
|
3
|
2
|
350
|
F, E
|
|
I
|
2
|
2
|
|
G
|
Q3) (Sourcing Decisions in a Supply Chain) A publisher sells books to Barnes & Noble at $12 each. The marginal production cost for the publisher is $1 per book. Barnes & Noble prices the book to its customers at $24 and expects demand over the next two months to be normally distributed, with a mean of 20,000 and a standard deviation of 5,000. Barnes & Noble places a single order with the publisher for delivery at the beginning of the two-month period. Currently, Barnes & Noble discounts any unsold books at the end of the two-months down to $3 and any books that did not sell at full price sell at this price.
(a) How many books should Barnes & Noble order? What is their expected profit? How many books do they expect to sell at a discount?
(b) What is the profit that the publisher makes given Barnes & Noble's actions?
(c) A plan under discussion is for the publisher to refund Barnes & Noble $5 per book that does not sell during the two-month period. As before Barnes & Noble will discount them to $3 and sell any that remain.
• Under this plan, how many books will Barnes & Noble order?
• What is the expected profit for Barnes & Noble?
• How many books are expected to be unsold?
• What is the expected profit for the publisher?
• What should the publisher do?