Parametric Linear Programming презентация

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

Слайд 1Parametric Linear Programming


Слайд 2Systematic Changes in cj
Objective function

is replaced by



Find the optimal solution as a function of θ


Слайд 3Example: 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 6Example: Wyndor Glass Problem
θ ≥ 5


Слайд 7Procedure 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 8Systematic Changes in bi
Constraints

are replaced by



Find the optimal solution as a function of θ


Слайд 9Example: 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 12Example: Wyndor Glass Problem
θ ≥ 5


Слайд 13Procedure Summary for Systematic Changes in bi
1. Solve the problem with θ

= 0 by the simplex method.
Use the sensitivity analysis procedure to introduce the Δbi = αiθ changes to the right side column.
Increase θ until one of the basic variables has its value in the right side column go negative (or until θ has been increased as far as desired).
Use this variable as the leaving basic variable for an iteration of the dual simplex method to find the new optimal solution. Return to Step 3.

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