Read both Appendices A and B attached, and then, solve the following problem:
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
Immediate predecessors
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-
|
-
|
A
|
A
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B
|
B
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C. E
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D. F
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The 21st Century Studios is about to begin the production of its most important (and most expensive) movie of the year. The movie's producer, Dusty Hoffmer, has decided to use PERT/CPM to help plan and control this key project. He has identified the eight major activities (labeled A, B, . . . ,H) required to produce the movie. Their precedence relationships are shown in the table below.
Dusty now has learned that another studio also will be coming out with a blockbuster movie during the middle of the upcoming summer, just when his movie was to be released. This would be very unfortunate timing. Therefore, he and the top management of 21st Century Studios have concluded that they must accelerate production of their movie and bring it out at the beginning of the summer (14 weeks from now) to establish it as THE movie of the year. Although this will require substantially increasing an already huge budget, management feels that this will pay off in much larger box office earnings both nationally and internationally. Dusty now wants to determine the least costly way of meeting the new deadline 14 weeks hence. Using the CPM method of timecost trade-offs, he has obtained the following data.
| Activity |
Normal
Time
|
Crash
Time
|
Normal
Cost
|
Crash
Cost
|
| A |
5 weeks
|
3 weeks
|
$24 million
|
$36 million
|
| B |
3 weeks
|
2 weeks
|
$13 million
|
$25 million
|
| C |
4 weeks
|
2 weeks
|
$21 million
|
$29 million
|
| D |
6 weeks
|
3 weeks
|
$30 million
|
$50 million
|
| E |
5 weeks
|
4 weeks
|
$26 million
|
$36 million
|
| F |
7 weeks
|
4 weeks
|
$35 million
|
$57 million
|
| G |
9 weeks
|
5 weeks
|
$30 million
|
$53 million
|
| H |
8 weeks
|
6 weeks
|
$35 million
|
$51 million
|
(a) Formulate a linear programming model to find the least costly way of meeting the new deadline:
(b) Solve the problem using LINGO (or other LP solver) and describe the optimal solution briefly in "plain English"