Copenhagen School of Stochastic Programming

Copenhagen skyline

International PhD School, 
University of Copenhagen
4-8 April 2022

The Copenhagen School of Stochastic Programming is a PhD course that 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 uncertain future returns or production of goods for which demand is stochastic.

The course is taught by world-renowned experts on the subject (see below). It will start by formalizing decision problems under uncertainty as mathematical optimization problems and analyzing their fundamental mathematical properties. From a computational perspective, these problems may be extremely challenging. Thus, a major part of the course will discuss approximations, mainly of the underlying probability distributions (so-called scenario generation), and stability of the optimization problems. The course will then 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.

The course is primarily aimed at PhD students who require a solid introduction into decision making under uncertainty. Nevertheless, it is open to anyone who would like to approach the subject, ranging from master's students to more experienced researchers and professionals. A participant can earn a certificate of 3.5 ECTS upon successful completion the course. The course is open to students from all over the world and the registration is free.



The course will be taught by the following experts on stochastic programming. In order of appearence in the course:

  • Stein W. Wallace is a Professor of Operational Research and leader of the Centre for Shipping and Logistics at NHH. He is best known for his seminal work in stochastic programming -- in particular the two books Stochastic Programming (with Peter Kall from 1994) and Modeling with stochastic programming (with Alan King from 2012) -- but also for extensive work in logistics and energy systems. His work has received more than 10.000 citations. He is on numerous editorial boards, in particular INFORMS Journal on Computing (since 1990), and founded the Norwegian OR Society and has held elected positions in The British OR Society as well as The Society for Transportation and Logistics in INFORMS and The Mathematical Programming Society.
  • Mike Hewitt is a Professor in the Information Systems and Supply Chain Management Department in the Quinlan School of Business at Loyola University Chicago. His research includes developing quantitative models of decisions found in the transportation and supply chain management domains, particularly in freight transportation and home delivery. In this research he has developed cutting-edge techniques for solving complex stochastic programs. His work has assisted the decision-making of companies such as Exxon Mobil, Saia Motor Freight, and Yellow Roadway. His research has been funded by agencies such as the National Science Foundation, the Material Handling Institute, and the New York State Health Foundation.
  • Stein-Erik Fleten is a Professor of Operations Research at the Norwegian University of Science and Technology. His work is centered mainly around the development of models of energy markets, such as power scheduling and risk management. In addition his research produces reference applications of stochastic programming for investment under uncertainty. Fleten is currently Editor-in-chief of Computational Management science, one of the most prestigious journals focusing on stochastic optimization research. His work appears regularly in the leading operations research and energy scientific journals. He is a broadly recognized energy expert in the stochastic programming community.
  • David Wozabal is a Professor at the Technical University of Munich. His research deals with the development of algorithms for stochastic optimization problems, risk measurement and risk management. The impressive theoretical results of his research are successfully applied to crucial planning problems in energy management as well as classical problems in finance such as portfolio optimization. His research focuses on the structural problems of the European energy markets with particular regard to electricity markets. A major part of this work involves modeling price processes and examining the efficiency of electricity markets. The results of this research are of central importance for the entire European energy sector.



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.

Prerequisites for a successful participation in the course are 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). Knowledge of a linear/mixed-integer programming solver is also beneficial.








This is a preliminary schedule of the PhD School's activities. Each day is led by an international expert on Stochastic Programming and consists of three hours of lectures and two hours of exercises or project work on the same topic.

    Monday April 4th
    09:30-10:00 Introduction to the PhD course
    10:00-12:00 Stochastic Programming Models
    12:00-14:00 Lunch break
    14:00-17:00 Mathematical Properties of Stochastic Programs
    Tuesday April 5th
    09:30-12:00 Stein W. Wallace: Scenario Generation and Stability
    12:00-14:00 Lunch break
    14:00-17:00 Stein W. Wallace: Scenario Generation and Stability -- practical cases
    Wednesday April 6th
    09:30-12:00 Mike Hewitt: Benders decomposition strategies for two-stage stochastic programs
    12:00-14:00 Lunch break
    14:00-17:00 Mike Hewitt: Benders decomposition strategies for two-stage stochastic programs -- practical cases
    Thursday April 7th
    09:30-12:00 Stein-Erik Fleten: Stochastic Programming in the energy sector
    12:00-14:00 Lunch break
    14:00-17:00 Stein-Erik Fleten: Stochastic Programming in the energy sector -- practical cases
    Friday April 8th
    09:30-12:00 David Wozabal: Approximate Dynamic Programming and Stochastic Dual Dynamic Programming
    12:00-14:00 Lunch break
    14:00-17:00 David Wozabal: Approximate Dynamic Programming and Stochastic Dual Dynamic Programming -- practical cases










    The course/masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the course venue. More precise instructions on the exact teaching rooms will be provided shortly before the course.

    Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation.

    A journey planner in English is available.

    More information on the "find us" webpage.



















    Registration is free. You can register by filling this online form (deadline March 4th 2022).