# OPERATIONS RESEARCH

**Academic Year 2018/2019**- 3° Year

**Teaching Staff:**

**Patrizia DANIELE**

**Credit Value:**9

**Scientific field:**MAT/09 - Operational research

**Taught classes:**49 hours

**Exercise:**24 hours

**Term / Semester:**1°

## Learning Objectives

The student will acquire the ability to formulate, in mathematical terms, problems related to profit maximization and cost minimization, optimization of resources, traffic network equilibria and games between two players.

In particular, the course of Operations Research has the following objectives:

- formulating a management problem in mathematical terms;
- solving linear optimization problems using numerical algorithms;
- formulate linear programming and binary programming problems;
- finding the equilibrium distribution in a traffic network by means of the solution to a variational inequality;
- finding the solution to a game between two players.

## Course Structure

The course will be taught through lectures and exercises in the classroom and at the computer labs.

## Detailed Course Content

**Linear Programming: **the simplex method, duality, sensitivity analysis (about 26 hours).

**Linear Integer Programming:** the Branch & Bound method (about 4 hours).

**Linear Integer Programming 0-1:** the knapsack problem (about 4 hours).

**Variational Inequalities: **the projection on a convex closed set, existence and uniqueness results for the solution to a variational inequality (about 8 hours).

**Traffic networks:** Wardrop's principle, characterization by means of variational ineqaulities, direct method for the computation of the equilibrium solution, projection method (about 14 hours).

**Game theory:** pure and mixed strategies, Von Neumann Theorem (about 8 hours).

**Elements of Nonlinear Optimization:** Lagrange theory and KKT multipliers (about 9 hours).

## Textbook Information

- F.S. Hillier, G.J. Lieberman, "Introduction to Operations Research", McGraw-Hill, 2001.
- Papers on STUDIUM