ComputerSensitivityAnalysis_Part2
pdf
keyboard_arrow_up
School
University of Waterloo *
*We aren’t endorsed by this school
Course
331
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
4
Uploaded by BrigadierScorpionMaster4905
Sensitivity Analysis
in Linear Programming
msci 331: intro. to optimization
Elhedhli S.
msci 331: intro. to optimization
Slide 8
Elhedhli S.
Example
Tucker Inc. needs to produce 1000 Tucker cars. The company has four production plants.
Due to differing workforces, technological advances, and so on, the plants differ in the cost of producing each car.
They also use a different amount of labor and raw material at each. This is summarized in the following table:
Plant
Cost (000$/car)
Labor
(hours/car)
Raw material (units/car)
1
15
2
3
2
10
3
4
3
9
4
5
4
7
5
6
The labor contract signed requires at least 400 cars to be produced at plant 3; there are 3300 hours of labor and
4000 units of material that can be allocated to the four plants.
Decision variables:
Xi: # of cars produced at plant i, i=1,2,3,4
This leads to the following LP:
min
15 X1 + 10 X2 + 9 X3 + 7 X4
s.t.
2 X1 + 3 X2 + 4 X3 + 5 X4 ≤ 3300
3 X1 + 4 X2 + 5 X3 + 6 X4
≤
4000
X3
≥
400
X1 + X2 + X3 + X4
=
1000
X1, X2, X3, X4
≥
0
msci 331: intro. to optimization
Slide 2
Elhedhli S.
Sensitivity Report
min
s.t.
2 X1 + 3 X2 + 4 X3 + 5 X4 ≤
3 X1 + 4 X2 + 5 X3 + 6 X4 ≤
X3
≥
X1 + X2 + X3 + X4
=
X1, X2, X3, X4 ≥ 0
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
msci 331: intro. to optimization
Slide 3
Elhedhli S.
1. What are the optimal production quantities? What is the total cost of production?
4. How much are Tucker inc.
willing to pay for an extra labor hour?
3. How would the production plan change if it costs only $8,000 to produce one car at plant 2? For what cost range is the
production plan optimal?
2. How much will it cost to produce one more car? How much is saved by producing one less?
7. By how much can the costs at plant 1 increase before Tucker inc. would not produce there?
6. How much is the
raw material worth (to get one more unit)? How many units is Tucker inc. willing to buy at that price?
5. How much is the union contract costing Tucker inc? What would be the value of reducing the 400 car limit down to 200 cars?
To 0 cars? What would be the cost of increasing it by 100 cars? by 200 cars?
Questions: