IE 201 • Final • Introduction to Optimization

Standard Form of LP

Example 1

Basic Solutions - Basic Feasible Solutions

Example 2

What is Simplex Method?

Example 3

Example 4

Example 5

Example 6 (Minimization)

Example 7 (Minimization)

Example 8 (Reverse)

Infeasible LP

Alternative Optimal Solutions

Unbounded LP

Direction of Unboundedness

Degeneracy

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

What is duality anyway?

Example 1

Example 2

Example 3

Meaning of Dual Varibles and Complementary Slackness

Example 4

Example 5

Idea Behind Dual Simplex

Comparing Primal/Dual Simplex

Example 1

Example 2

Combining with Primal Simplex

Example 3

Example 4

Example 5

General Procedure

Optimal Basis v Optimal Solution

Changing Objective Function Coefficient of a NBV

Example

Changing Objective Function Coefficient of a BV

Example

Changing RHS of a Constraint

Example

Changing Column of a NBV

Example

Adding a New Variable

Example

Adding a New Constraint

Example

Simplex Method 1

Simplex Method 2

Simplex Method 3

Simplex Method 4

Simplex Method 5

Simplex Method 6

Simplex Method 7

Simplex Method 8

Big M and Two-Phase Methods 1

Big M and Two-Phase Methods 2

Big M and Two-Phase Methods 3

Big M and Two-Phase Methods 4

Big M and Two-Phase Methods 5

Big M and Two-Phase Methods 6

Big M and Two-Phase Methods 7

Big M and Two-Phase Methods 8

Duality 1

Duality 2

Duality 3

Duality 4

Dual Simplex 1

Dual Simplex 2

Dual Simplex 3

Dual Simplex 4

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3

Sensitivity Analysis 4

Sensitivity Analysis 5

Simplex Method 1

Simplex Method 2

Simplex Method 3

Big M and Two-Phase Methods 1

Big M and Two-Phase Methods 2

Big M and Two-Phase Methods 3

Duality 1

Duality 2

Dual Simplex 1

Dual Simplex 2

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3