IE 312 • Midterm I • Operations Research II

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

If-then --> Either-or

Example 5

Example 6

Problem Definition

MTZ Subtour Elimination

DFJ Subtour Elimination

Example

Branch

Bound

Example 1

Example 2

Example 3

What is Knapsack Problem?

B & B Solution of Knapsack Problem

Example 4

Valid Inequalities

Example 1

Chvàtal Gomory Rounding Procedure

Cutting Plane and Ideal Formulation

Gomory Fractional Cutting Plane

Cutting Plane Algorithm

Example 2

Example 3

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

Branch and Bound

Cutting Plane

gurobipy

Modeling

Modeling

Branch and Bound

Cutting Plane

gurobipy

Modeling

Modeling

Branch and Bound

Branch and Bound

Cutting Plane

Modeling

Modeling

Branch and Bound

Cutting Plane

gurobipy

Modeling

Modeling

Branch and Bound

Cutting Plane

gurobipy

What is a network?

Shortest Path Problems

Dijkstra's Algorithm

Example 1

Example 2

Example 3

Shortest Path Problem

Shortest Path Problem

Shortest Path Problem

Shortest Path Problem