Decision Methods and Models
A.Y. 2024/2025
Learning objectives
This course aims to
- discuss the aspects that characterise a complex decision
- present practical case studies, in particular concerning public works
- present mathematical methods to deal with complexity
- present the resulting mathematical models
- discuss limitations and errors typical of those methods and models
- discuss the aspects that characterise a complex decision
- present practical case studies, in particular concerning public works
- present mathematical methods to deal with complexity
- present the resulting mathematical models
- discuss limitations and errors typical of those methods and models
Expected learning outcomes
The student will learn to set up the solution of complex decision problems, recognising the basic aspects of their complexity, or to identify the strong and weak points of the solution approaches applied by other subjects. The student will learn to know the models adopted in the solution of such problems, to solve them with the most appropriate methods and to be conscious of the intrinsic limitations of such models and methods.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
The teaching aims to
- discuss the aspects that characterise a complex decision
- present practical case studies, in particular concerning public works
- present mathematical methods to deal with complexity
- present the resulting mathematical models
- discuss limitations and errors typical of those methods and models
Introduction to complex decision problems
Case studies
Formal definition of complex decision problems
Mathematical Programming: Karush-Kuhn-Tucker conditions
Multi-objective Programming:
* the Pareto case
* multi-attribute utility theory
* Analytic Hierarchy Process and ELECTRE methods
Uncertain Programming:
* decision making under ignorance
* decision making under risk
* decision theory
Game theory:
* generalities
* zero-sum games
* symmetric games
Group decision theory
Descriptive models:
* transportation system models
* queueing theory models
* discrete-event simulation models
* system dynamics
- discuss the aspects that characterise a complex decision
- present practical case studies, in particular concerning public works
- present mathematical methods to deal with complexity
- present the resulting mathematical models
- discuss limitations and errors typical of those methods and models
Introduction to complex decision problems
Case studies
Formal definition of complex decision problems
Mathematical Programming: Karush-Kuhn-Tucker conditions
Multi-objective Programming:
* the Pareto case
* multi-attribute utility theory
* Analytic Hierarchy Process and ELECTRE methods
Uncertain Programming:
* decision making under ignorance
* decision making under risk
* decision theory
Game theory:
* generalities
* zero-sum games
* symmetric games
Group decision theory
Descriptive models:
* transportation system models
* queueing theory models
* discrete-event simulation models
* system dynamics
Prerequisites for admission
Knowing the main mathematical functions and the concepts of limit, derivative,
representation of lines on the Cartesian plane.
Knowing the fundamental operations of matrix calculus and the concepts of
eigenvalue and eigenvector.
Knowing the foundations of probability calculus.
It is strongly recommended to have passed the exams of Continuous mathematics,
Statistics, Operations Research.
representation of lines on the Cartesian plane.
Knowing the fundamental operations of matrix calculus and the concepts of
eigenvalue and eigenvector.
Knowing the foundations of probability calculus.
It is strongly recommended to have passed the exams of Continuous mathematics,
Statistics, Operations Research.
Teaching methods
The teaching consists of classroom-taught lectures and numerical exercise sessions.
Teaching Resources
Slides, lecture notes and survey papers on the web site
https://rcordonedmm.ariel.ctu.unimi.it
https://rcordonedmm.ariel.ctu.unimi.it
Assessment methods and Criteria
The exam is written, and its length ranges between two and three hours.
It requires to answer open questions on the topics of the teaching
and to solve numerical exercises applying the techniques presented in the teaching.
The evaluation of the exam is expressed on a scale of 30 points, keeping into account
the following aspects: knowledge of the topics, capacity of applying knowledge to the
solution of practical problems, capacity of critical reasoning, clarity and correct use of language.
It requires to answer open questions on the topics of the teaching
and to solve numerical exercises applying the techniques presented in the teaching.
The evaluation of the exam is expressed on a scale of 30 points, keeping into account
the following aspects: knowledge of the topics, capacity of applying knowledge to the
solution of practical problems, capacity of critical reasoning, clarity and correct use of language.
MAT/09 - OPERATIONS RESEARCH - University credits: 6
Lessons: 48 hours
Professor:
Cordone Roberto
Shifts:
Turno
Professor:
Cordone RobertoProfessor(s)