Parametric Linear Programming

Сентябрь 7, 2022

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Parametric Linear Programming

Содержание

2. Systematic Changes in cj Objective function is replaced by Find the optimal solution as a function
3. Example: Wyndor Glass Problem Z(θ) = (3 + 2θ) x1+(5 - θ) x2
4. Example: Wyndor Glass Problem 0 ≤ θ ≤ 9/7
5. Example: Wyndor Glass Problem 9/7 ≤ θ ≤ 5
6. Example: Wyndor Glass Problem θ ≥ 5
7. Procedure Summary for Systematic Changes in cj 1. Solve the problem with θ = 0 by
8. Systematic Changes in bi Constraints are replaced by Find the optimal solution as a function of
9. Example: Wyndor Glass Problem y1 + 3y3 ≥ 3 + 2θ 2y2 + 2y3 ≥ 5
10. Example: Wyndor Glass Problem 0 ≤ θ ≤ 9/7
11. Example: Wyndor Glass Problem 9/7 ≤ θ ≤ 5
12. Example: Wyndor Glass Problem θ ≥ 5
14. Скачать презентацию

Слайд 2

Systematic Changes in cj
Objective function is replaced by
Find the optimal

solution as a function of θ

Слайд 3

Example: Wyndor Glass Problem
Z(θ) = (3 + 2θ) x1+(5 - θ)

x2

Слайд 4

Example: Wyndor Glass Problem
0 ≤ θ ≤ 9/7

Слайд 5

Example: Wyndor Glass Problem
9/7 ≤ θ ≤ 5

Слайд 6

Example: Wyndor Glass Problem
θ ≥ 5

Слайд 7

Procedure Summary for Systematic Changes in cj
1. Solve the problem with θ

= 0 by the simplex method.
Use the sensitivity analysis procedure to introduce the Δcj = αjθ changes into Eq.(0).
Increase θ until one of the nonbasic variables has its coefficient in Eq.(0) go negative (or until θ has been increased as far as desired).
Use this variable as the entering basic variable for an iteration of the simplex method to find the new optimal solution. Return to Step 3.

Слайд 8

Systematic Changes in bi
Constraints are replaced by
Find the optimal solution

as a function of θ

Слайд 9

Example: Wyndor Glass Problem
y1 + 3y3 ≥ 3 + 2θ
2y2

+ 2y3 ≥ 5 - θ

Слайд 10

Example: Wyndor Glass Problem
0 ≤ θ ≤ 9/7

Слайд 11

Example: Wyndor Glass Problem
9/7 ≤ θ ≤ 5

Слайд 12

Example: Wyndor Glass Problem
θ ≥ 5