IE 311 • Tüm Sınavlar • Operations Research I

What is Linear Programming?

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

What is different?

Piecewise Linear Example

Absolute Value Example

Max-Min Example

Using Mathematical Notation

Example 1

Example 2

Example 3

Example 4

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

Solving LP with 2 variables

Example 1

Example 2

Example 3

Alternative Optimal Solutions

Example 4

What is Gurobi?

Constructing Model

Defining Input Parameters

Adding Variables

Adding Constraints - Part I

quicksum

Adding Constraints - Part II

Defining Objective Function

Solving Model

Printing Output

Modeling

Modeling

Modeling

Gurobi Solution of Previous Question

Modeling

Modeling

Modeling

Modeling

Modeling

Gurobi Solution of Previous Question

Modeling

Modeling

Graphical Solution

Modeling

Modeling

Modeling

Modeling

Modeling

Modeling

Gurobi Solution of Previous Question

Modeling

Modeling

Modeling

Graphical Solution

Modeling

Modeling

Modeling

Coding

Graphical Solution

Modeling

Modeling

Modeling

Coding

Graphical Solution

Modeling

Modeling

Modeling

Coding

Graphical Solution

Modeling

Modeling

Modeling

Coding

Graphical Solution

Modeling

Modeling

Modeling

Coding

Graphical Solution

Linear Programming

Graphical Solution

Linear Programming

Integer Programming

Standard Form of LP

Example 1

Basic Solutions - Basic Feasible Solutions

Example 2

Convex Functions

Example 3 & 4

Convex Sets

Hyperplane/Half-Space/Polyhedron

Extreme Points and Directions

Example 5

Minkowski's Theorem

What is Simplex Method?

Example 1

Example 2

Example 3

Example 4 (Minimization)

Example 5 (Minimization)

Example 6 (Reverse)

Infeasible LP

Alternative Optimal Solutions

Unbounded LP

Direction of Unboundedness

Degeneracy

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

Dual of an LP

Examples 1-2

Example 3

Weak Duality Theorem

Strong Duality Theorem

Shadow Price

Complementary Slackness

Example 4

Example 5

Simplex Method

Big M Method

Big M Method Example

Two Phase Method

Two Phase Method Example

Magic of Linear Algebra

Matrices of LP

Forming a Table

Example 1

One Formula to Rule Them All

Example 2

Dual Solution

Primal/Dual Feasibility and Optimality

Example 3

Revised Simplex

Example 1

Example 2

Modeling

Preliminaries

Simplex Method

Simplex Method

Big-M Simplex Method

Two-Phase Simplex Method

Python - Simplex Method

Matrix Form of Simplex

Duality

Duality

Modeling

Preliminaries

Simplex Method

Simplex Method

Big-M Simplex Method

Two-Phase Simplex Method

Python - Simplex Method

Matrix Form of Simplex

Revised Simplex - Final Konusu

Duality

Modeling

Preliminaries

Simplex Method

Simplex Method

Big-M Simplex Method

Two-Phase Simplex Method

Python - Simplex Method

Matrix Form of Simplex

Duality

Duality

Modeling

Preliminaries

Simplex Method

Simplex Method

Big-M Simplex Method

Two-Phase Simplex Method

Python - Simplex Method

Matrix Form of Simplex

Revised Simplex - Final Konusu

Duality

Modeling

Preliminaries

Simplex Method

Simplex Method

Big-M Simplex Method

Two-Phase Simplex Method

Python - Simplex Method

Matrix Form of Simplex

Duality

Duality

Modeling

Preliminaries

Simplex Method

Simplex Method

Big-M Simplex Method

Two-Phase Simplex Method

Python - Simplex Method

Matrix Form of Simplex

Duality

Duality

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

Simplex Method

Big-M Simplex Method

Duality

Dual Simplex Method

Sensitivity Analysis

Modeling + Coding

Simplex Method

Dual Simplex Method

Duality

Sensitivity Analysis

Simplex Method

Duality

Dual Simplex Method

Dual Simplex Method

Sensitivity Analysis

Simplex Method

Two-Phase Simplex Method

Duality

Dual Simplex Method

Sensitivity Analysis

Simplex Method

Big-M Simplex Method

Duality

Dual Simplex Method

Sensitivity Analysis + Coding

Modeling

Simplex Method

Duality

Dual Simplex Method

Sensitivity Analysis + Coding