OPERATIONS RESEARCH

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:

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

Knowledge and understanding: the aim of the course is to be able in transforming real life situations in mathematical problems.

Applying knowledge and understanding: students will be able to suggest optimal solutions to real life problems.

Making judgments: students will be able to analyze the data.

Communication skills: students will be able to communicate their experience and knowledge to other people.

Learning skills: students will have acquired the ability to learn, even autonomously, further knowledge on the problems related to applied mathematics.

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

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).

1. F.S. Hillier, G.J. Lieberman, "Introduction to Operations Research", McGraw-Hill, 2001.
2. Papers on STUDIUM http://studium.unict.it