Operational Research

Teacher(s)

Aghezzaf El-Houssaine (compensates Papavasiliou Anthony); Papavasiliou Anthony;

Language

English

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, ...

Aims

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

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.

Content

• Modelling in stochastic programming
• Value of information and value of the stochastic solution
• Two-Stage Recourse Problems
• Multistage Stochastic Programs
• Stochastic Integer Programs
• Decomposition techniques:
  • Benders decomposition
  • Nested Benders decomposition
  • Lagrangian relaxation
• Stochastic dual dynamic programming algorithm
• Approximation and sampling methods

Teaching methods

2 hours of magistral courses per week, and 2 hours of training sessions per week. Homeworks will be evaluated by the instructor and/or the teaching assistant.

Evaluation methods

• Written exam
• Regular homework assignments

Online resources

Moodle link

Bibliography

• Reference Book (Course Textbook): "Introduction to Stochastic Programming", John Birge and Francois Louveaux, (2011), Springer Series in Operations Research and Financial Engineering.
• Other references:
  • “Modeling with Stochastic Programming”, King, A.J. and Wallace, S.W., (2012), Springer Series in Operations Research and Financial Engineering.
  • “Stochastic Programming “, Kall, P. and Wallace, S.W., (1995), John Wiley and Sons.
  • “Lectures on Stochastic Programming: Modeling and Theory”, Alexander Shapiro, Darinka Dentcheva, Andrzej Ruszczynski, (2009), MPS-SIAM Series on Optimization.

Faculty or entity

MAP