The objective of the course is to endow the students with the key aspects of deterministic optimization, including linear programming and network optimization. Topics include basic theory, modeling, algorithms, and applications.
Curriculum
teacher profile teaching materials
Formulations, the five phases method
Elements of Linear Algebra
2. Formulation of typical optimization problems
Blending
Resource allocation
Lot sizing
Cutting stock
Assignment
Planning
3. Solution of Linear Programming problems
Geometry of LP
The simplex algorithm
The Fourier-Motzkin method
geometrical interpretation of the simplex algorithm
4. Duality theory
The dual problem
Duality theorems
Complementarity theorem
Economic interpretation of the dual problem
Sensitivity analysis
5. The simplex network algorithm
Minimum cost flow problem
Basis and spanning trees
Change of basis
Phase 1 and Phase 2
6. Network optimization
Maximum flow problem
Shortest path problem
Minimum spanning tree problem
Programme
1. Introduction to Operations ResearchFormulations, the five phases method
Elements of Linear Algebra
2. Formulation of typical optimization problems
Blending
Resource allocation
Lot sizing
Cutting stock
Assignment
Planning
3. Solution of Linear Programming problems
Geometry of LP
The simplex algorithm
The Fourier-Motzkin method
geometrical interpretation of the simplex algorithm
4. Duality theory
The dual problem
Duality theorems
Complementarity theorem
Economic interpretation of the dual problem
Sensitivity analysis
5. The simplex network algorithm
Minimum cost flow problem
Basis and spanning trees
Change of basis
Phase 1 and Phase 2
6. Network optimization
Maximum flow problem
Shortest path problem
Minimum spanning tree problem
Core Documentation
Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014Type of delivery of the course
Classroom lectures and exercises.Type of evaluation
The exam consists of two steps. In the written part the student is asked to solve two exercises and answer a theoretical question. The oral part consists of one or more questions on the written part and / or theoretical questions. The exams of the last years are available on the web page of the course (http://pacciarelli.dia.uniroma3.it/CORSI/Ric_Op/Welcome.html ), in many cases with an outline of a solution. teacher profile teaching materials
Formulations, the five phases method
Elements of Linear Algebra
2. Formulation of typical optimization problems
Blending
Resource allocation
Lot sizing
Cutting stock
Assignment
Planning
3. Solution of Linear Programming problems
Geometry of LP
The simplex algorithm
The Fourier-Motzkin method
geometrical interpretation of the simplex algorithm
4. Duality theory
The dual problem
Duality theorems
Complementarity theorem
Economic interpretation of the dual problem
Sensitivity analysis
5. The simplex network algorithm
Minimum cost flow problem
Basis and spanning trees
Change of basis
Phase 1 and Phase 2
6. Network optimization
Maximum flow problem
Shortest path problem
Minimum spanning tree problem
Mutuazione: 20801777 RICERCA OPERATIVA I in Ingegneria informatica L-8 A - Z PACCIARELLI DARIO
Programme
1. Introduction to Operations ResearchFormulations, the five phases method
Elements of Linear Algebra
2. Formulation of typical optimization problems
Blending
Resource allocation
Lot sizing
Cutting stock
Assignment
Planning
3. Solution of Linear Programming problems
Geometry of LP
The simplex algorithm
The Fourier-Motzkin method
geometrical interpretation of the simplex algorithm
4. Duality theory
The dual problem
Duality theorems
Complementarity theorem
Economic interpretation of the dual problem
Sensitivity analysis
5. The simplex network algorithm
Minimum cost flow problem
Basis and spanning trees
Change of basis
Phase 1 and Phase 2
6. Network optimization
Maximum flow problem
Shortest path problem
Minimum spanning tree problem
Core Documentation
Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014Type of delivery of the course
Classroom lectures and exercises.Type of evaluation
The exam consists of two steps. In the written part the student is asked to solve two exercises and answer a theoretical question. The oral part consists of one or more questions on the written part and / or theoretical questions. The exams of the last years are available on the web page of the course (http://pacciarelli.dia.uniroma3.it/CORSI/Ric_Op/Welcome.html ), in many cases with an outline of a solution.