Operational Research [ LINMA2491 ]

> https://icampus.uclouvain.be/claroline/course/index.php?cid=LINMA2491

• Fluency in English at the level of course LANGL1330
• Linear programming , integer programming
• Familiarity with probability theory
• Familiarity with math programming languages (AMPL, Mosel)

• Mathematical background (duality, KKT optimality conditions, monotone operators)
• Mathematical programming models and languages
• Applications: finance, logistics, risk management, energy

In reference to the AA standard, this course contributes to the development, acquisition and evaluation of the following learning outcomes:

• AA1.1, AA1.2, AA1.3
• AA2.2, AA2.5

At the end of the course, students will be able to:

• Formulate problems of decision-making under uncertainty as mathematical programs
• Identify structure in large-scale mathematical programs that enables their decomposition
• Design algorithms for solving large-scale optimization problems under uncertainty
• Implement algorithms for solving large-scale optmization problems in AMPL
• Evaluate the quality of policies for making decisions under uncertainty

• Written exam
• Course project and regular homework assignments

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

• Stochastic programming models
• Value of perfect information and the value of the stochastic solution
• The L-shaped method in two and multiple stages
• Multi-cut L-shaped algorithm
• Stochastic dual dynamic programming
• Scenario selection and importance sampling
• Lagrangian relaxation
• Stochastic integer programming
• Monotone operators, proximal point algorithms and progressive hedging

• Course notes
• Printouts from textbooks or archived journals will be provided during lectures. The following textbook will be followed closely for most of the course: John Birge, Francois Louveaux, "Introduction to Stochastic Programming"