IE 335 • Tüm Sınavlar • 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

What is a network?

Shortest Path Problems

Dijkstra's Algorithm

Example 1

Example 2

Example 3

Example 4

Example 5

Maximum Flow Problems

Minimum Cut (Eğer İşlendiyse)

Ford Fulkerson Algorithm (Eğer İşlendiyse)

Example 1 (Eğer İşlendiyse)

Example 2 (Eğer İşlendiyse)

Boss of Network Problems

Example 1

Example 2

Step 1: Finding Initial BFS

Step 2: Finding Entering Variable

Step 3: Finding Leaving Variable & Pivoting

Let's Continue with Iterations

What is Integer Programming?

Fixed Cost Problems

Example 1

Example 2

Constraints with Binary Variables

Special Constraints

Assignment Problems

Example 3

Set Covering Problems

Example 4

Non-Linear Objectives

Piecewise Linear Example

Absolute Value Example

Max-Min Example

If-then --> Either-or

Example 1

Example 2

Dijkstra's Algorithm 1

Shortest Path Problem 1

Shortest Path Problem 2

Shortest Path Problem 3

Shortest Path Problem 4

Shortest Path Problems True/False 1

Shortest Path Problems True/False 2

Maximum Flow Problem 1

Maximum Flow Problem / Ford Fulkerson Algorithm 1

Ford Fulkerson Algorithm 1

MCNFP 1

Network Simplex

IP Modeling 1

IP Modeling 2

IP Modeling 3

IP Modeling 4

IP Modeling 5

IP Modeling 6

IP Modeling 7

IP Modeling 8

IP Modeling 9

IP Modeling 10

IP Modeling 11

IP Modeling 12