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. Its main focus 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.

The selection of topics can be adapted to a certain extent, depending for instance on the research interests or on the previous education of the participants.

Pedagogy:

All students must prepare each meeting by reading preassigned material (either chapters from advanced textbooks or research articles) and by answering a number of questions (either questions intended to clarify difficult parts of the material, or additional proofs, or numerical exercises). The classroom meetings are entirely devoted to a group discussion of the material and of the homework assignments. A few meetings may be devoted to (individual) oral presentations by the students, based either on their general scientific interests or on their own research projects

Evaluation:

There is no final exam for this course. The final grade is based on several elements:

• the evaluation of each student’s involvement (presence, density and quality of participation);
• grading of homework assignments and
• quality of oral presentations (both content and form).