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Яндекс.Метрика

Презентация на тему Parametric Linear Programming

Systematic Changes in cjObjective function is replaced by Find the optimal solution as a function of θ
Parametric Linear Programming Systematic Changes in cjObjective function Example: Wyndor Glass ProblemZ(θ) = (3 + 2θ) x1+(5 - θ) x2 Example: Wyndor Glass Problem0 ≤ θ ≤ 9/7 Example: Wyndor Glass Problem9/7 ≤ θ ≤ 5 Example: Wyndor Glass Problemθ ≥ 5 Procedure Summary for Systematic Changes in cj1.	Solve the problem with θ = Systematic Changes in biConstraints Example: Wyndor Glass Problemy1    + 3y3 ≥ 3 + Example: Wyndor Glass Problem0 ≤ θ ≤ 9/7 Example: Wyndor Glass Problem9/7 ≤ θ ≤ 5 Example: Wyndor Glass Problemθ ≥ 5 Procedure Summary for Systematic Changes in bi1.	Solve the problem with θ =
Слайды презентации

Слайд 2 Systematic Changes in cj
Objective function

Systematic Changes in cjObjective function      is

is

replaced by



Find the optimal solution as a function of θ


Слайд 3 Example: Wyndor Glass Problem
Z(θ) = (3 + 2θ)

Example: Wyndor Glass ProblemZ(θ) = (3 + 2θ) x1+(5 - θ) x2

x1+(5 - θ) x2


Слайд 4
Example: Wyndor Glass Problem

0 ≤ θ ≤ 9/7

Example: Wyndor Glass Problem0 ≤ θ ≤ 9/7

Слайд 5

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

Example: Wyndor Glass Problem9/7 ≤ θ ≤ 5

Слайд 6 Example: Wyndor Glass Problem
θ ≥ 5

Example: Wyndor Glass Problemθ ≥ 5

Слайд 7 Procedure Summary for Systematic Changes in cj
1. Solve the

Procedure Summary for Systematic Changes in cj1.	Solve the problem with θ

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

Systematic Changes in biConstraints

are replaced by



Find the optimal solution as a function of θ


Слайд 9 Example: Wyndor Glass Problem
y1 +

Example: Wyndor Glass Problemy1  + 3y3 ≥ 3 + 2θ

3y3 ≥ 3 + 2θ
2y2 + 2y3

≥ 5 - θ


Слайд 10
Example: Wyndor Glass Problem

0 ≤ θ ≤ 9/7

Example: Wyndor Glass Problem0 ≤ θ ≤ 9/7

Слайд 11
Example: Wyndor Glass Problem

9/7 ≤ θ ≤ 5

Example: Wyndor Glass Problem9/7 ≤ θ ≤ 5

Слайд 12 Example: Wyndor Glass Problem
θ ≥ 5

Example: Wyndor Glass Problemθ ≥ 5

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