IE 234 • Final • Optimization Methods I

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

Matrices of LP

Example 1

Forming a Table with Given BV

Example 2

Simplex Method in Matrix Form

Example 3

Example 4

Revised Simplex

Example 5

Example 6

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

Are we doing anything new?

Soru Tipi: Fixed Cost Problems

Example 1

Example 2

Constraints with Binary Variables

Special Constraints

Soru Tipi: Assignment Problems

Example 3

Soru Tipi: Set Covering Problems

Example 4

Exam Like Question 1

Exam Like Question 2

Exam Like Question 3

Exam Like Question 4

Exam Like Question 5

Introduction

Example 1

Example 2

An Important Question

Knapsack Problem and Branch&Bound

Knapsack Problem B&B Example

Big M Method 1

Big M Method 2

Big M Method 3

Big M Method 4

Two Phase Method 1

Two Phase Method 2

Two Phase Method 3

Two Phase Method 4

Revised Simplex 1

Revised Simplex 2

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3

Sensitivity Analysis 4

Sensitivity Analysis 5

Sensitivity Analysis 6

Sensitivity Analysis 7

Integer Programming 1

Integer Programming 2

Integer Programming 3

Integer Programming 4

Integer Programming 5

Integer Programming 6

Integer Programming 7

Branch and Bound Method 1

Branch and Bound Method 2

Branch and Bound Method 3