PhD Courses in Denmark

2nd Copenhagen School of Stochastic Programming

PhD School at the Faculty of SCIENCE at University of Copenhagen


This course provides a rigorous and research-oriented introduction to stochastic programming, a mathematical framework for decision-making in the presence of uncertainty. In many real-life problems, important information is unknown to the decision-maker and only distributional information is available. Examples include the scheduling of power generation while demand and renewable production is uncertain, investments in assets with uncertainty in future returns or production of goods for which demand is stochastic.

The course will start by formalizing such decision problems as mathematical optimization problems and analyzing their fundamental properties. From a computational perspective, these problems may be extremely challenging. Thus, a major part of the course will discuss approximations, either of the underlying distributions or of the optimization problem itself. The former involves so-called scenario generation and stability of the optimization problems. The latter covers various approximation and bounding techniques. The course will proceed with a number of applications in the energy sector, an area for which stochastic programming has become increasingly important with the adoption of intermittent renewable energy sources. Finally, a selection of solution methods will be addressed, including exact decomposition procedures and approximate methods with strong connections to emerging approaches in machine learning.

Formel requirements

A solid understanding of linear programming theory and some knowledge of probability theory (e.g., understanding what probability distributions are for both continuous and discrete random variables).

Learning outcome

The students will become well acquainted with the theory of stochastic programming and the challenges involved when applying stochastic programming in practice. Particularly, upon completion of the course, the students will be able to formulate two-stage and multi-stage stochastic programs, analyze their properties and discuss their practical implications. They will also learn how to approximate these problems, generate scenarios and address stability with respect to these, bound and assess the value of stochastic optimization. Finally, they will be able to apply and adapt selected traditional and novel solution methods.


Lecture notes and hand-ins provided by the organizers of the course..

Teaching and learning methods

Every day consists of three hours of lectures and two hours of exercises or project work on the same topic.


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