IE 335 • Midterm • Optimization Methods II

Magic of Linear Algebra

Matrices of LP

Forming a Table

Example 1

One Formula to Rule Them All

Example 2

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

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

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 1

Example 2

Example 3

Definition / LP Solution

Assumptions of the Problem

Hungarian Method

Hungarian Method: Trouble in Paradise

Example 1

Example 2

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Duality 7

Duality 8

Duality 9

Duality 10

Duality 11

Dual Simplex 1

Dual Simplex 2

Dual Simplex 3

Dual Simplex 4

Dual Simplex 5

Sensitivity Analysis 1

Sensitivity Analysis 2

Sensitivity Analysis 3

Sensitivity Analysis 4

Sensitivity Analysis 5

Sensitivity Analysis 6

Sensitivity Analysis 7

Transportation Problem 1

Transportation Problem 2

Hungarian Method 1

Hungarian Method 2

Hungarian Method 3

Hungarian Method 4