Operational Research

Teacher(s)

Lété Quentin;

Language

English
> French-friendly

Prerequisites

·         A course in linear, non-linear, and integer programming.
·         An introductory course to probability theory: probability space, probability, random variable, mathematical expectation, independence, law of large numbers, '.
·         Knowledge of a mathematical programming language (AMPL, Matlab, OPL-Studio, ...)

Main themes

How to formulate an optimization problem in which data are prone to uncertainty? How to take into account disclosed information and revealed values of the parameters during the stages of the optimization process? How to solve the optimization models thus obtained? Stochastic optimization is the ideal framework for dealing with such issues. Various solution techniques for large-scale problems will also be discussed: Benders decomposition, Nested Bendersdecomposition, Lagrangian methods, ... Applications: Production, logistics, finance, ...

Learning outcomes

At the end of this learning unit, the student is able to :
1	·         Formulate problems of decision-making under uncertainty as mathematical programs, Identify mathematical structures in large-scale mathematical programs that enable their decomposition, Design algorithms for solving large-scale optimization problems under uncertainty, Implement algorithms for solving large-scale stochastic optimization problems, Evaluate the quality of alternative policies for problems of decision-making under uncertainty

Content

The course will cover some or all of the following topics:

• Mathematical background (LP/QP duality, probability theory)
• Lagrange duality
• Stochastic programming models
• Value of Information and the Stochastic Solution
• Cutting plane algorithms (Benders decomposition, L-shaped method, nested L-shaped decomposition)
• Lagrangian-based methods
• Stochastic dual dynamic programming
• Approximation and Sampling methods
• Dynamic Programming
• Introduction to Robust Optimization
• Adaptive Robust Optimization

Teaching methods

2 hours of lecture per week, and 2 hours of training sessions per week. The course will also include a project and/or homeworks (to be clarified during the first lecture).

Evaluation methods

• Written and/or oral exam
• Homework and/or project

Online resources

https://moodle.uclouvain.be/

Bibliography

• Notes on Moodle
• Textbooks that can be used as a support (relevant sections will be mentioned on Moodle and during the lecture):
  • [Deterministic models] Conforti, M., Cornuéjols, G., Zambelli, G., Conforti, M., Cornuéjols, G. and Zambelli, G., 2014. Integer Programming. Springer International Publishing.
  • [Stochastic Programming] Birge, J.R. and Louveaux, F., 2011. Introduction to stochastic programming. Springer Science & Business Media.
  • [Robust Optimization] Sun, X.A. and Conejo, A.J., 2021. Robust optimization in electric energy systems. Springer International Publishing.

Faculty or entity

> MAP