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| GDOC0005-1 | Seminar of Operations Research
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| Duration : | 30h Th |
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| Number of credits : |
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| Lecturer : | Yves Crama |
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Language(s) of instruction :
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| English language |
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Organisation and examination :
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| All year long |
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Course contents :
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| 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 progamming: branch-and-bound, tight formulations, introduction to cutting planes and to polyhedral theory
- approximation algorithms with guaranteed performance.
The selection of topics can be adapted to a certain extent, depending on the level and on the research interests of the participants. |
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Learning outcomes of the course :
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| 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 disiciplines 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 oral presentation skills
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Prerequisites and co-requisites/ Recommended optional programme components :
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| 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.
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Planned learning activities and teaching methods :
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| 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 parts, 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 are devoted to individual presentations by the students. These can be based on their general scientific interests or on their own research projects. |
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Mode of delivery (face-to-face ; distance-learning) :
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| Group discussions and presentations by the students |
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Recommended or required readings :
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| 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. |
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Assessment methods and criteria :
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| The final grade is based on:
- homework assignments 50%;
- oral presentations (contents and form) 20%;
- student's involvement (presence, density and quality of participation) 30%.
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| Prof. Yves Crama
Y.Crama@ulg.ac.be |
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