OVERVIEW

Operations Research (OR) consists in a set of mathematical models and methods for solving decision problems in a very wide number of application sectors. The purpose of this course is to provide the students with competences in using a set of models for problem solving. In particular, the course mainly considers optimization problems faced by mathematical programming techniques and problems on graph and networks.

AIMS AND CONTENT

LEARNING OUTCOMES

Knowledge of a set of OR models and methods (linear mathematical programming models; linear and integer programming methods; graphs and network models)

Capability of problem solving by a set of OR techniques (formulation of mathematical programming models and use of mathematical programming algorithm; algorithms for problem solving on graph and networks)

LEARNING OUTCOMES (FURTHER INFO)

As regards mathematical programming, the main objective is to provide the students with skills for defining the right model to solve a set of decision problems that can be formulated through optimization. In particular, continuous an mixed integer programming algorithms are presented and applied to simple cases. Graph and network models and algorithms are presented as they represent a fundamental tool for optimization in telecommunication.

TEACHING METHODS

The course consists of classroom lectures.

SYLLABUS/CONTENT

• Introduction to decisional problems and models. The process of problem formulation by means of quantitative models.
• Basic concepts of the theory of complexity.
• Mathematical programming
  • Basic definitions
  • Linear programming.
    • Graphic formulation and solution of linear programs.
    • The simplex algorithm.
    • Duality theory.
    • Sensitivity analysis and economic interpretation.
    • Integer programming and combinatorial optimization.
    • Methods of cutting-planes and branch-and-bound.
• Graph and network theory.
  • Shortest paths problems. Spanning tree problems. Max-flow and min cut problems.
  • Hamiltonian paths and circuits (the traveling salesman problem).
  • The dynamic programming method.

RECOMMENDED READING/BIBLIOGRAPHY

Frederick S Hillier, Gerald J Lieberman, Introduction to Operations Research, 9/e, McGraw-Hill Higher Education, 2010, ISBN: 0073376299

TEACHERS AND EXAM BOARD

Exam Board

ROBERTO CIANCI (President)

MAURO GAGGERO (President)

MASSIMO PAOLUCCI (President)

LESSONS

EXAMS

EXAM DESCRIPTION

The final examination consists of a written test and an optional oral test.

ASSESSMENT METHODS

Learning will be assessed by a number of written test consisting of decision problems requiring the definition of a model and/or the application of a method.