Duration
30h Th
Number of credits
| Doctoral training in economics and business management (Management) | 5 crédits |
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
The main focus of the seminar is on optimization methods, at an advanced level. The main topics addressed are:
- complexity theory: easy and hard optimization problems, complexity classes, polynomial transformations
- linear programming theory: (revised) simplex algorithm, duality theory, column generation algorithms
- combinatorial algorithms: network flows, shortest paths, spanning trees, etc.
- integer programming: branch-and-bound, tight formulations, introduction to cutting planes and to polyhedral theory
- approximation algorithms with guaranteed performance.
Learning outcomes of the learning unit
The course is mostly intended for doctoral students pursuing methodological advances in operations research and in optimization, or applying OR approaches to the solution of problems arising in disciplines such as supply chain management, transportation, marketing, finance, industrial economics, and so on.
Intended learning outcomes
- Knowledge: acquisition and in-depth understanding of linear and discrete optimization (theory and algorithms)
- Specific skills: ability to formulate and to solve optimization problems arising in management
- Specific skills: ability to use methodological knowledge in order to develop new algorithms and solution approaches
- Specific/transversal skills: ability to read and to understand the scientific literature in these fields
- Transversal skills: improvement of presentation skills
Prerequisite knowledge and skills
Prerequisites:
- A first course in operations research, including linear programming models and the simplex method.
- Proficiency in mathematics, especially linear algebra and analysis.
- Introduction to algorithms.
Planned learning activities and teaching methods
The students must prepare each meting by reading preassigned material (either chapters from advanced textbooks or research articles) and by solving homework problems. The homework problems are intended to clarify difficult concepts, as well as to deepen and to test the understanding of the material.
Classroom meetings are devoted to group discussions of the material and of the homework assignments.
A few meetings may be devoted to individual presentations by the students, based on their general scientific interests or on their own research projects.
Mode of delivery (face to face, distance learning, hybrid learning)
Face to face meetings.
Course materials and recommended or required readings
Required readings: chapters from several books, mostly
Bertsimas and Tsitsiklis, Introduction to Linear Optimization, Dynamic Ideas and Athena Scientific, Belmont, Massachusetts, 2008.
Chvátal, Linear Programming, WH Freeman & Co, San Francisco, 1983.
Cook, Cunningham, Pulleyblank and Schrijver, Combinatorial Optimization, John Wiley and Sons, New York, 1998.
Wolsey, Integer Programming, Wiley & Sons, New York, 1998.
The final grade is based on:
- homework assignments 60%;
- student's involvement (presence, density and quality of participation and presentations) 40%.
Work placement(s)
Organisational remarks and main changes to the course
Contacts
Bernard Fortz
bernard.fortz@uliege.be