METODI DI OTTIMIZZAZIONE PER L'INGEGNERIA A - L
Academic Year 2025/2026 - Teacher: Arturo BUSCARINOExpected Learning Outcomes
This course aims to introduce students to the fundamental concepts of linear programming and stochastic programming in the context of engineering and business applications, where these techniques are employed for process optimization. The course covers both the theoretical foundations and methodological tools required to formulate and solve optimization problems, as well as their practical application to engineering challenges.
Knowledge and Understanding
Upon completion of the course, students will have acquired a solid understanding of the principles underlying the formulation and solution of linear, binary, and integer optimization problems, as well as sensitivity analysis. Additionally, students will gain foundational knowledge in statistics and probability, serving as an introduction to stochastic optimization problems.
Applied Knowledge and Understanding
Students will be capable of defining and solving constrained optimization problems, with particular emphasis on engineering applications. They will also be able to evaluate the optimality of the solutions obtained.
Judgement and Decision-Making
Students will develop the ability to select appropriate modeling and solution strategies for optimization problems, taking into account the complexity and feasibility of the methods employed.
Communication Skills
Students will be able to clearly communicate the costs, benefits, and rationale behind different optimization techniques. They will also be able to rigorously describe the characteristics of optimization problems and justify the decisions made during problem formulation, particularly in engineering processes constrained by limited resources.
Learning Skills
Students will be able to identify and consult relevant books and scientific publications that provide deeper insights and specialized knowledge on the optimization techniques covered in the course.
Course Structure
Required Prerequisites
Attendance of Lessons
Detailed Course Content
Introduction to Constrained Optimization Problems
Overview of optimization problems, including the definition of objective functions and constraints, mathematical formulation, and illustrative examples from engineering applications.
Deterministic vs. Stochastic Models
Problem definition and data collection; formulation of mathematical models; introduction to statistics and probability; stochastic distributions (normal, exponential, weibull, ecc).
Linear Programming
Classical examples and fundamental assumptions; standard and augmented forms; simplex method theory; artificial variables and equality constraints; Big-M method; duality; sensitivity analysis; brief overview of alternative linear programming solution methods.
Integer and Binary Programming
Binary variables; branch-and-bound method; introduction to mixed-integer programming.
Introduction to Stochastic Optimization
Evolutionary algorithms; simulation; introduction to statistical learning.
Textbook Information
(1) F. S. Hillier, G. J. Lieberman, "Introduction to operation research", McGraw Hill, 2021
(2) G. James, D. Witten, T. Hastie, R. Tibshirani, "An introduction to statistical learning", Springer, 2020
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Introduction to optimization problems with engineering examples | Book (1) - chapter 1; Lecture notes |
| 2 | Deterministic models | Book (1) - chapter 2 |
| 3 | Stochastic models | Book (1) - chapter 2 |
| 4 | Basic concepts on statistics and probability | Lecture notes |
| 5 | Linear programming: classic examples | Book (1) - chapter 3 |
| 6 | Linear programming: standard and augmented forms | Book (1) - chapter 3 |
| 7 | Linear programming: the simplex method | Book (1) - chapter 4 |
| 8 | Linear programming: the big-M method | Book (1) - chapter 5 |
| 9 | Duality and sensitivity analysis | Book (1) - chapter 6-7 |
| 10 | Integer programming | Book (1) - chapter 12 |
| 11 | Binary programming | Book (1) - chapter 12 |
| 12 | Mixed-integer programming | Book (1) - chapter 12 |
| 13 | Stochastic optimization | Book (1) - chapter 14; Book (1) - chapter 20 |
| 14 | Statistical learning | Book (2) |
Learning Assessment
Learning Assessment Procedures
Examples of frequently asked questions and / or exercises
Example of Written Test:
- Given a problem in verbal form, determine the decision variables, their domain, the objective function, and the constraints.
- Determine the optimal solution using an appropriate method.
- Perform a sensitivity analysis of the solution.
Examples of Oral Test Questions:
- Fundamental theorem of linear programming;
- Duality;
- Branch-and-bound method;
- Weibull distribution.