Program Overview

OPERATIONS RESEARCH

Overview

Operations Research (OR) consists of a set of mathematical models and methods for solving decision problems in a wide range of application sectors. The purpose of this course is to provide 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

This module aims to provide students with knowledge about a set of models and methods of Operations Research that will enable them to deal with decision problems. In particular, students will learn how to use mathematical linear programming models with continuous variables to formulate certain classes of decision problems, and they will learn how to find the optimal solution using the Simplex algorithm; in addition, students will learn how to perform sensitivity analysis and apply duality theory. A very important type of model that will be explained is the integer programming model that allows facing discrete decision problems; the branch and bound and cutting planes methods will be explained for this model. Finally, graph theory and network flow models will be presented; these classes of models are very important as they can model practical decision problems in telecommunications.

Aims and Learning Outcomes

The main objective is to provide students with the skills to define mathematical programming models to solve a series of decision problems by formulating them as optimization problems. Students will be able to solve continuous and mixed integer programming problems using appropriate methods and algorithms. Students will be able to solve problems using networks flow models and graphs. The presented models and algorithms are fundamental tools for optimization in telecommunications.

Teaching Methods

The course consists of classroom lectures. Students with valid certifications for Specific Learning Disorders (SLDs), disabilities, or other educational needs are invited to contact the teacher and the School's contact person for disability at the beginning of teaching to agree on possible teaching arrangements that, while respecting the teaching objectives, take into account individual learning patterns.

Syllabus/Content

• Introduction to decisional problems and models. The process of problem formulation by means of quantitative models.
• 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. Network simplex algorithm.
  • Introduction to TSP and routing problems.
• Basic concepts of the theory of complexity.
• Examples of heuristic algorithms for combinatorial problems
• Basic concepts of multi-criteria decision making

Recommended Reading/Bibliography

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

Teachers and Exam Board

• MASSIMO PAOLUCCI
• Exam Board:
  • SEBASTIANO SERPICO (President)
  • ABDUL BASIT
  • GABRIELE MOSER (President Substitute)
  • MASSIMO PAOLUCCI (President Substitute)
  • MARTINA PASTORINO (President Substitute)

Lessons

The timetable for this course is available.

Exams

Exam Description

Written exam text.

Assessment Methods

Written examination, potentially including:

• Exercises requiring the application of algorithms to the problem classes presented in the course
• Short theoretical questions
• Formulation of simple combinatorial decision-making problems

Exam Schedule

• 09/01/2026, 09:00, GENOVA
• 04/02/2026, 08:30, GENOVA
• 04/06/2026, 08:30, GENOVA
• 01/07/2026, 09:00, GENOVA
• 17/09/2026, 08:30, GENOVA

Further Information

Students who have a valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework, and exams should speak with the instructor.