IE 303 • Midterm • Modeling and Methods in Optimization

What is Integer Programming?

Constraints with Binary Variables

Special Constraints

Fixed Charge Problems

Example 1

Exam Like Question 1

Assignment Problems

Example 2

Set Covering Problems

Example 3

Non-Linear Objectives

Piecewise Linear Example

Absolute Value Example

Max-Min Example

If-then --> Either-or

Example 1

Example 2

Integer Programming 1

Integer Programming 2

Integer Programming 3

Integer Programming 4

Integer Programming 5

Introduction

Example 1

Example 2

An Important Question

Knapsack Problem and Branch&Bound

Knapsack Problemi B&B Example

Method

Example 1

Example 2

Example 3

Valid Inequalities

Example 1

Chvàtal Gomory Rounding Procedure

Cutting Plane and Ideal Formulation

Gomory Fractional Cutting Plane

Cutting Plane Algorithm

Example 2

Example 3

Branch and Bound Technique

Branch and Bound Technique

Branch and Bound Technique

Valid Inequality

Ideal Formulation

Gomory Fractional Cutting Plane

Cutting Plane Algorithm

Definition

Cover and Cover Inequality

Example 1

Minimal and Extended Cover

Example 2

What is it?

LP Solution

Assignment Problem

Example 1

Shortest Path Problem

Example 2

Integer Programming 1

Integer Programming 2

Integer Programming 3

Integer Programming 4

Integer Programming 5

Integer Programming 6

Integer Programming 7

Integer Programming 8

Integer Programming 9

Integer Programming 10

Integer Programming 11

Implicit Enumeration 1

Implicit Enumeration 2

Implicit Enumeration 3

Branch and Bound 1

Branch and Bound 2

Branch and Bound 3

Cutting Plane Algorithm

Cover Inequality and Knapsack Problem 1

Cover Inequality and Knapsack Problem 2

Cover Inequality and Knapsack Problem 3

Cover Inequality and Knapsack Problem 4

Cover Inequality and Knapsack Problem 5

Cover Inequality and Knapsack Problem 6

Shortest Path Problem (Sadece part a)

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