Program Overview

OPERATIONS RESEARCH

Course Description

The teaching unit in Operations Research provides students with skills related to the construction of mathematical models and the use of algorithms to solve decision-making problems formulated as optimization problems.

Aims and Content

Learning Outcomes

The course provides the basic knowledge of optimization methods to solve decision-making problems. In particular, the course will provide knowledge to model from the mathematical viewpoint a decision problem, and solve it through linear programming, linear integer programming, nonlinear programming, and optimization over graphs.

Aims and Learning Outcomes

This teaching unit introduces fundamental concepts and methods in optimization for solving decision problems. In particular, students will acquire the ability to mathematically model decision-making situations and solve them using linear programming, integer linear programming, nonlinear programming, and graph-based optimization techniques.

Prerequisites

• Basic knowledge of Mathematical Analysis
• Geometry
• Computer Science

Teaching Methods

• Lectures delivered in class

Syllabus/Content

• Basic concepts in computational complexity theory
• Introduction to mathematical programming and decision problems
• Linear programming with continuous variables: problem formulation, the simplex algorithm, post-optimality analysis, duality theory, and the dual simplex method
• Integer linear programming: binary variables, problem formulation, total unimodularity, cutting planes method, and branch-and-bound algorithm
• Graph optimization: fundamental definitions, the minimum spanning tree problem (Kruskal's and Prim's algorithms); the shortest path problem (Dijkstra, Bellman-Ford, and Floyd-Warshall algorithms)
• Network flows: example formulations, the max-flow min-cut problem and the augmenting path algorithm; the minimum-cost flow problem, cycle-canceling algorithms, and the network simplex algorithm
• Practical examples of modeling and solving linear and mixed-integer programming problems using IBM's CPLEX solver

Recommended Reading/Bibliography

• Handouts provided by the lecturer
• Books for possible further study:
  • Hillier, Lieberman Introduction to operations research. McGraw-Hill, 2004
  • D. Bertsimas, J.N. Tsitsiklis Introduction to linear optimization. Athena Scientific, 1999

Teachers and Exam Board

• MASSIMO PAOLUCCI
• Exam Board:
  • MASSIMO PAOLUCCI (President)
  • SILVIA SIRI

Lessons

• The timetable for this course is available on the Portale EasyAcademy

Exams

Exam Description

• Written exam, potentially including questions that require solving exercises (applying algorithms) related to the classes of problems covered in the teaching unit
• The exam may also include short theoretical questions on the concepts taught, as well as tasks requiring the formulation of simple combinatorial decision problems

Assessment Methods

• By the end of the teaching unit, students are expected to:
  • Demonstrate an understanding of the concepts covered in lectures and explain them using appropriate academic language
  • Be able to select and apply the most suitable algorithm for solving decision problems presented in the course
  • Formulate linear programming models to solve decision problems of a combinatorial nature

Exam Schedule

• Data appello | Orario | Luogo | Degree type | Note
  • 09/01/2026 | 14:30 | GENOVA | Scritto |
  • 04/02/2026 | 14:30 | GENOVA | Scritto |
  • 03/06/2026 | 14:30 | GENOVA | Scritto |
  • 02/07/2026 | 09:00 | GENOVA | Scritto |
  • 17/09/2026 | 14:30 | GENOVA | Scritto |

Agenda 2030 - Sustainable Development Goals

• Quality education