IE 201 • Midterm II + Final • Operations Research I

What is Simplex Method?

Example 1

Example 2

Example 3

Example 4 (Minimization)

Example 5 (Minimization)

Example 6 (Reverse)

Infeasible LP

Alternative Optimal Solutions

Unbounded LP

Direction of Unboundedness

Degeneracy

Example 7

Example 8

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

Magic of Linear Algebra

Matrices of LP

Forming a Table

Example 1

One Formula to Rule Them All

Example 2

Simplex Method 1

Simplex Method 2

Simplex Method 3

Simplex Method 4

Simplex Method 5

Simplex Method 6

Simplex Method 7

Simplex Method 8

Simplex Method 9

Simplex Method 10

Simplex Method 11

Simplex Method 12

Two-Phase Simplex Method 1

Two-Phase Simplex Method 2

Two-Phase Simplex Method 3

Two-Phase Simplex Method 4

Two-Phase Simplex Method 5

Two-Phase Simplex Method 6

Big M Method 1

Big M Method 2

Big M Method 3

Big M Method 4

Big M Method 5

Matrix Form of Simplex 1

Matrix Form of Simplex 2

Matrix Form of Simplex 3

Matrix Form of Simplex 4

Matrix Form of Simplex 5

Dual of an LP

Examples 1-2

Example 3

Weak Duality Theorem

Strong Duality Theorem

Shadow Price

Complementary Slackness

Example 4

Example 5

Dual Solution

Primal/Dual Feasibility and Optimality

Example 6

What is Dual Simplex?

Primal/Dual Simplex Comparison

Example 1

Example 2

An Important Question

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

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Dual Simplex 1

Dual Simplex 2

Dual Simplex 3

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3

Sensitivity Analysis 4

Sensitivity Analysis 5

Sensitivity Analysis 6

Sensitivity Analysis 7