IE 232 • Midterm II + Final • Mathematical Modeling and 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

Alternative Optimal Solutions Example 1

Alternative Optimal Solutions Example 2

Introducing Artifical Variables

Big M Method

Example 1

Example 2

What is duality anyway?

Example 1

Example 2

Example 3

Meaning of Dual Varibles and Complementary Slackness

Example 4

Example 5

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

Big M Method 5

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Idea Behind Dual Simplex

Comparing Primal/Dual Simplex

Example 1

Example 2

Matrices of LP

Example 1

Forming a Table with Given BV

Example 2

Simplex Method in Matrix Form

Example 3

Example 4

Constraint Slopes

Objective Function Slope

Range of Objective Function Coefficients

Shadow Price

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

Introducing a New Constraint

Example 7

Example 8

Changing Coefficients of a Basic Variable

Example 9

Example 10

Definition / LP Solution

Assumptions of the Problem

Least Cost Method

Example 1

Example 2

Northwest Corner Method

Example 3

Example 4

Vogel's Method

Example 5

Transportation Simplex Method

Example 6

Example 7

Transshipment Problem Definition/LP Solution

Example 8

Definition / LP Solution

Assumptions of the Problem

Hungarian Method

Hungarian Method: Trouble in Paradise

Example 1

Example 2

Representation of LP with Linear Algebra 1

Representation of LP with Linear Algebra 2

Dual Simplex 1

Dual Simplex 2

Dual Simplex 3

Graphical Sensitivity Analysis 1

Graphical Sensitivity Analysis 2

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3

Transportation Problem 1

Transportation Problem 2

Transportation Problem 3

Transportation Problem 4

Transshipment Problem 1

Assignment Problem 1

Assignment Problem 2

Assignment Problem 3

Assignment Problem 4

Assignment Problem 5