The objective of the course is to endow the students with the key aspects of deterministic optimization, including linear programming and integer programming. Topics include basic theory, modeling, algorithms, and applications. The lessons and practical exercises carried out during the course will allow the student to acquire analysis and problem-solving skills in typical applications.
Curriculum
teacher profile teaching materials
Convex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
5. Introduction to Integer Optimization Problems
Integer Linear Programming (ILP)
Relationship between ILP and ILP
Equivalent Formulations
Relaxations
Standard Techniques for Formulating ILP Problems
6. Formulation of Typical ILP Problems
Facility Location
Investment Selection
Activity Sequencing
Resource Allocation
Network Optimization
Transportation
Set Covering
Set Partitioning
Set Packing
Staff Shifts
7. Solution to Integer Linear Programming Problems
Branch and Bound
Dynamic Programming (DP) Techniques
Programme
1. Introduction to Mathematical ProgrammingConvex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
5. Introduction to Integer Optimization Problems
Integer Linear Programming (ILP)
Relationship between ILP and ILP
Equivalent Formulations
Relaxations
Standard Techniques for Formulating ILP Problems
6. Formulation of Typical ILP Problems
Facility Location
Investment Selection
Activity Sequencing
Resource Allocation
Network Optimization
Transportation
Set Covering
Set Partitioning
Set Packing
Staff Shifts
7. Solution to Integer Linear Programming Problems
Branch and Bound
Dynamic Programming (DP) Techniques
Core Documentation
Lecture notes available on the Moodle web page of the courseReference Bibliography
Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014.Attendance
Not mandatory but suggested.Type of evaluation
Verification of learning takes place through a selective written test, lasting 90-120 minutes, aimed at verifying the level of actual understanding of the concepts learned in the course and the students' ability to apply them in real contexts, and a possible oral exam. The course also includes an optional written test, which is held after the first part of the course, consisting of two exercises and a theory question, aimed at verifying the level of learning after the first part of the course. The expected time is 90-120 minutes. The exam consists of a written test, consisting of several exercises and theory questions. The expected time is 90-120 minutes. The exam texts of the last years are available on the course website (see the Moodle web page of the course ). teacher profile teaching materials
1. Introduction to Mathematical Programming
Convex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
*Second Part*
5. Introduction to Integer Linear Programming (ILP): relationship between ILP and LP, equivalent formulations, relaxations, standard techniques for ILP modelling.
6. ILP formulations: plant location, investment problem, sequencing problems, network optimization, transportation problems, set covering, set partitioning, set packing, crew scheduling
7. Exact algorithms: Branch and Bound, dynamic programming. Exact algorithms for binary and integer knapsack problems.
[2] Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa: programmazione lineare, intera e non lineare", Isedi, Italia, 2018.
[3] Lecture notes
Programme
*First Part*1. Introduction to Mathematical Programming
Convex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
*Second Part*
5. Introduction to Integer Linear Programming (ILP): relationship between ILP and LP, equivalent formulations, relaxations, standard techniques for ILP modelling.
6. ILP formulations: plant location, investment problem, sequencing problems, network optimization, transportation problems, set covering, set partitioning, set packing, crew scheduling
7. Exact algorithms: Branch and Bound, dynamic programming. Exact algorithms for binary and integer knapsack problems.
Core Documentation
[1] M. FISCHETTI, "LEZIONI DI RICERCA OPERATIVA", EDIZIONI LIBRERIA PROGETTO PADOVA, ITALIA, 1995. (CAP. 2, 5, PARTE DEL 6 E DEL 7).[2] Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa: programmazione lineare, intera e non lineare", Isedi, Italia, 2018.
[3] Lecture notes
Type of delivery of the course
Mostly lectures on blackboard plus some classes in the labAttendance
Not mandatory but suggested.Type of evaluation
Learning is assessed through a selective written exam lasting 90–120 minutes, aimed at verifying the level of actual understanding of the concepts learned during the course, followed by a possible oral exam. The course also includes optional written mid-term tests. The written exam consists of a number of exercises designed to assess both the level of understanding of the concepts and the students’ ability to apply the techniques explained during lectures. teacher profile teaching materials
Convex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
5. Introduction to Integer Optimization Problems
Integer Linear Programming (ILP)
Relationship between ILP and ILP
Equivalent Formulations
Relaxations
Standard Techniques for Formulating ILP Problems
6. Formulation of Typical ILP Problems
Facility Location
Investment Selection
Activity Sequencing
Resource Allocation
Network Optimization
Transportation
Set Covering
Set Partitioning
Set Packing
Staff Shifts
7. Solution to Integer Linear Programming Problems
Branch and Bound
Dynamic Programming (DP) Techniques
Programme
1. Introduction to Mathematical ProgrammingConvex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
5. Introduction to Integer Optimization Problems
Integer Linear Programming (ILP)
Relationship between ILP and ILP
Equivalent Formulations
Relaxations
Standard Techniques for Formulating ILP Problems
6. Formulation of Typical ILP Problems
Facility Location
Investment Selection
Activity Sequencing
Resource Allocation
Network Optimization
Transportation
Set Covering
Set Partitioning
Set Packing
Staff Shifts
7. Solution to Integer Linear Programming Problems
Branch and Bound
Dynamic Programming (DP) Techniques
Core Documentation
Lecture notes available on the Moodle web page of the courseReference Bibliography
Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa", Isedi, Italia, 2014.Attendance
Not mandatory but suggested.Type of evaluation
Verification of learning takes place through a selective written test, lasting 90-120 minutes, aimed at verifying the level of actual understanding of the concepts learned in the course and the students' ability to apply them in real contexts, and a possible oral exam. The course also includes an optional written test, which is held after the first part of the course, consisting of two exercises and a theory question, aimed at verifying the level of learning after the first part of the course. The expected time is 90-120 minutes. The exam consists of a written test, consisting of several exercises and theory questions. The expected time is 90-120 minutes. The exam texts of the last years are available on the course website (see the Moodle web page of the course ). teacher profile teaching materials
1. Introduction to Mathematical Programming
Convex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
*Second Part*
5. Introduction to Integer Linear Programming (ILP): relationship between ILP and LP, equivalent formulations, relaxations, standard techniques for ILP modelling.
6. ILP formulations: plant location, investment problem, sequencing problems, network optimization, transportation problems, set covering, set partitioning, set packing, crew scheduling
7. Exact algorithms: Branch and Bound, dynamic programming. Exact algorithms for binary and integer knapsack problems.
[2] Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa: programmazione lineare, intera e non lineare", Isedi, Italia, 2018.
[3] Lecture notes
Programme
*First Part*1. Introduction to Mathematical Programming
Convex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
*Second Part*
5. Introduction to Integer Linear Programming (ILP): relationship between ILP and LP, equivalent formulations, relaxations, standard techniques for ILP modelling.
6. ILP formulations: plant location, investment problem, sequencing problems, network optimization, transportation problems, set covering, set partitioning, set packing, crew scheduling
7. Exact algorithms: Branch and Bound, dynamic programming. Exact algorithms for binary and integer knapsack problems.
Core Documentation
[1] M. FISCHETTI, "LEZIONI DI RICERCA OPERATIVA", EDIZIONI LIBRERIA PROGETTO PADOVA, ITALIA, 1995. (CAP. 2, 5, PARTE DEL 6 E DEL 7).[2] Caramia, Giordani, Guerriero, Musmanno, Pacciarelli, "Ricerca Operativa: programmazione lineare, intera e non lineare", Isedi, Italia, 2018.
[3] Lecture notes
Type of delivery of the course
Mostly lectures on blackboard plus some classes in the labAttendance
Not mandatory but suggested.Type of evaluation
Learning is assessed through a selective written exam lasting 90–120 minutes, aimed at verifying the level of actual understanding of the concepts learned during the course, followed by a possible oral exam. The course also includes optional written mid-term tests. The written exam consists of a number of exercises designed to assess both the level of understanding of the concepts and the students’ ability to apply the techniques explained during lectures.