Art of modeling and elements of decision models, Linear programming, Transportation problem, Integer linear programming, Introduction to graphs theory, Nonlinear programming, Dynamic programming, Monte Carlo simulation, Project management (CPM, PERT)
General topics for lectures:
General topics:
Solve the dual problem to following primal problem:
MAX (4x + 6y + 5z)
3x + 7y + 6z <= 500
5x + 5y + 4z <= 480
6y + 6z <= 330
x,y,z, => 0
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The project of constructing a small bridge consist of 8 major activities. Information pertaining to the project is given below:
|
Acivity |
Previous activity |
Optilistic (a) [week] |
Most likely (m) [week] |
Pessimistic (b) [week] |
|
A |
- |
2 |
5 |
8 |
|
B |
A |
4 |
7 |
10 |
|
C |
A |
4 |
9 |
14 |
|
D |
B |
6 |
10 |
20 |
|
E |
C |
1 |
3 |
5 |
|
F |
C |
3 |
6 |
9 |
|
G |
D,F |
4 |
5 |
12 |
|
H |
E |
6 |
8 |
10 |
Subtasks:
1. Develop a PERT network for this project.
2. Find the critical path.
3. Compute the probability of completing the project in 36 weeks.
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Using inverse transformation method generate random number from continuous distribution defined by the probability density function.
f (x) = a*cos(x)
x is from interval <-π/2; + π/2>
a is constant
You have random number from uniform distribution Ro (0,1), r=0.247.
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Find the practical application of any optimization method with which you are familiar in the subject and solve the problem. Regirements for seminar work:
1. Detailed description of the problem formulation and including all figures, their size and how they are getting
2. Own mathematical model
3. The solution of the mathematical model, including any sensitivity analysis (you can use any available software - specify)
4. A detailed analysis of the solution results
Scope of your work (approximately 8 pages in pdf format) upload in the desired deadline. Presentation of the project is required!