IE 234 (Spring 24) • Optimization Methods I • Final

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

Degeneracy

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

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

General Procedure

Changing Coefficients of a Non-Basic Variable

Example 1

Example 2

Introducing a New Variable

Example 3

Example 4

Changing Right-Hand-Side of a Constraint

Example 5

Example 6

Changing Coefficients of a Basic Variable

Example 7

Example 8

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

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

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

Sensitivity Analysis