Operations research

Course objectives

The course gives an introduction on the basic tools for mathematical modeling and solving decision and optimization problems using quantitative methods. At the end of the course, students should be able to recognize such problems, build mathematical models for them, and solve them using a number of modeling techniques and solution algorithms, also by means of specific software tools. Expected learning outcomes (Dublin Descriptors): 1. Understand all basic mathematical aspects of solving linear, linear integer, and nonlinear convex optimization problems. Understand main modeling techniques in mathematical programming. 2. Be able to develop an optimization model from a decision problem with quantitative data. Be able to select and use suitable software to solve such model. 3. Be able to identify weaknesses of optimization models and limits of numerical solvers (students develop these abilities also during any practical test of the course when they practically solve relevant decision problems). 4. Be able to describe any aspect of a mathematical program and of the main algorithms for the solution of linear, linear integer, and nonlinear programs (students develop these abilities also during any practical test of the course when they practically solve relevant decision problems by working in groups). 5. Get mathematical basis to self-study solution techniques for complex mathematical programs such as nonconvex and multi-objective programming.

Channel 1
Gianluca Priori Lecturers' profile

Program - Frequency - Exams

Course program
Part 1: Model Formulation (20 hours) - Linear Programming (LP) models: optimal resource allocation, blending, transportation; - Integer Linear Programming (ILP) models: binary knapsack, assignment, capital budgeting, fixed cost, lot sizing, facility location, use of indicator variables. Part 2: Model Analysis (20 hours) - Elements of geometry in R^n; - Fundamental theorem of linear programming; - Algebraic characterization of the vertices of a polyhedron in general/standard form; - Duality theory in LP: weak duality, strong duality, complementarity. Part 3: Numerical Solution (20 hours) - Simplex algorithm: structure, optimality and unboundedness criteria, construction of a new feasible basis, Phase I of the simplex.
Prerequisites
Basic linear algebra.
Books
Lecture notes provided by Proff. Massimo Roma e Stefano Lucidi: https://drive.google.com/file/d/15LzLhnk5-HZJkZ6zlTjkYud6Gnscmus6/view
Teaching mode
Module 0: Mathematical Programming: lectures Module 1: LP practical aspects: class exercises Module 2: LP theoretical aspects: lectures Module 3: ILP practical aspects: class exercises Module 4: ILP theoretical aspects: lectures Module 5: NLP: class exercises and lectures
Frequency
Attendance is optional but strongly recommended.
Exam mode
The assessment of the examination is based on the following criteria: 1. the logical reasoning adopted by the student in solving the exercises in the written test; 2. the correctness of the procedure identified to solve the problem; 3. the adequacy of the proposed solution with respect to the skills the student is expected to have acquired by the end of the course; 4. the student’s knowledge of the theoretical results presented during the course, including the appropriate use of terminology and formalism in their exposition. Meeting criteria 1 and 4 is a necessary condition for obtaining a grade of 20. Grades above 24 will be awarded only to students whose work satisfies all four of the criteria listed above.
Lesson mode
In-person lectures and online exercises in agreement with the class.
Gianluca Priori Lecturers' profile

Program - Frequency - Exams

Course program
Part 1: Model Formulation (20 hours) - Linear Programming (LP) models: optimal resource allocation, blending, transportation; - Integer Linear Programming (ILP) models: binary knapsack, assignment, capital budgeting, fixed cost, lot sizing, facility location, use of indicator variables. Part 2: Model Analysis (20 hours) - Elements of geometry in R^n; - Fundamental theorem of linear programming; - Algebraic characterization of the vertices of a polyhedron in general/standard form; - Duality theory in LP: weak duality, strong duality, complementarity. Part 3: Numerical Solution (20 hours) - Simplex algorithm: structure, optimality and unboundedness criteria, construction of a new feasible basis, Phase I of the simplex.
Prerequisites
Basic linear algebra.
Books
Lecture notes provided by Proff. Massimo Roma e Stefano Lucidi: https://drive.google.com/file/d/15LzLhnk5-HZJkZ6zlTjkYud6Gnscmus6/view
Teaching mode
Module 0: Mathematical Programming: lectures Module 1: LP practical aspects: class exercises Module 2: LP theoretical aspects: lectures Module 3: ILP practical aspects: class exercises Module 4: ILP theoretical aspects: lectures Module 5: NLP: class exercises and lectures
Frequency
Attendance is optional but strongly recommended.
Exam mode
The assessment of the examination is based on the following criteria: 1. the logical reasoning adopted by the student in solving the exercises in the written test; 2. the correctness of the procedure identified to solve the problem; 3. the adequacy of the proposed solution with respect to the skills the student is expected to have acquired by the end of the course; 4. the student’s knowledge of the theoretical results presented during the course, including the appropriate use of terminology and formalism in their exposition. Meeting criteria 1 and 4 is a necessary condition for obtaining a grade of 20. Grades above 24 will be awarded only to students whose work satisfies all four of the criteria listed above.
Lesson mode
In-person lectures and online exercises in agreement with the class.
  • Lesson code1002027
  • Academic year2025/2026
  • CourseInformation Engineering
  • CurriculumGestionale
  • Year2nd year
  • Semester1st semester
  • SSDMAT/09
  • CFU6