# Operations Research

### Credits

6 ECTS, CTD 36h, TP 18h

### Instructor

Nadia Brauner, Jérôme Malick

### Description

Operations Research offers scientific methods for better decisions. The idea is to develop and use mathematics and informatics tools to solve complex organization problems. Historical applications are in the management of large systems of humans, machines, materials in industry, service, humanitarian aid, environment…

At the end of this course, students should be able to propose a modelization and implement practical solutions (dedicated or industrial tools) to solve a decision or optimization problem. Interested students can continue in master 2 Operations Research, Combinatorics and Optimization (ORCO).

This course is divided into two parts : an introduction to operations Research modelling and solving methods (common with M1 Mosig) and a complementary part for M1 AM students only.

## Part 1: introduction to OR (common with M1 Mosig)

### Skills

- Recognize a situation where Operations Research is relevant.
- Know the main tools of Operations Research.
- Have the methodological elements to choose the solution methods and the tools the most adapted for a given practical problem.
- Know how to manipulate the software tools to solve a discrete optimization problem.

### The course covers various topics:

- Linear Programming (modelling, solving, duality)
- Mixed Integer Linear Programming (modelling techniques, solving with Branch and Bound)
- Dynamic Programming
- Bonus (riddles, elsewhere on the web, OR News)

### Prerequisites

- Classical algorithms (sort, divide and conquer)
- Algorithms complexity calculation
- Programming: basic notions (variables, fonctions, if, for, while, tables)
- Language Python or Java
- Basic notions on graphs (basic definitions, graph search, trees, shortest paths)
- Basic notions on linear algebra and matrix analysis (matrix multiplication, invertible matrix definition)
- Basics of statistics and probability

More details for the first part : https://moodle.caseine.org/course/view.php?id=42

## Part 2: OR Complementary for M1 AM students

In this part, we will investigate in more details some mathematical notions related to operations research. We will focus on three aspects: Spectral graph theory, Game theory, and Numerical Optimal transport. For each of these themes, we will see how these theoretical results relate to practical operations research problem and finally illustrate them numerically in Python.