3rd Copenhagen School of Stochastic Programming
PhD School at the Faculty of SCIENCE at University of Copenhagen
This is a specialised course where 50% of the seats are reserved to PhD students enrolled at the Faculty of SCIENCE at UCPH and 50% of the seats are reserved to other applicants. Seats will be allocated on a first-come, first-served basis and according to the applicable rules.
Anyone can apply for the course, but if you are not a PhD student at a Danish university (except CBS), you will be placed on the waiting list until enrollment deadline. After the enrollment deadline, available seats will be allocated to applicants on the waiting list.
Aim and Content
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 parameters are unknown to the decision-maker and only distributional information is available. Examples include the scheduling of power generation under uncertainty in renewable supply, investments in assets with uncertain future returns or production of goods for which demand is stochastic. The purpose of the course is to prepare the students for carrying out independent research, including developments and applications of the methodology.
The days of the course will be divided into a morning and an afternoon session. During the morning session, the course will host lectures by world-renowned scientists on the subject. During the afternoon sessions, the students will have a chance of presenting their own work and discuss their research challenges between themselves and with the experts.
A plan of the activities is as follows (the order may change):
• Day 1: - Morning: Formalization of decision problems under uncertainty as stochastic programs. Brief account of the main mathematical properties (speaker: Trine Boomsma, KU).
• Day 1 – Afternoon: First round of student presentations (in progress) on stochastic programming.
• Day 2 – Morning: Introduction scenario generation (speaker: Stein Wallace, Norwegian School of Economics)
• Day 2 – Afternoon: Second round of student presentation (in progress) on stochastic programming.
• Day 3 – Morning: Chance-constrained stochastic programming (speaker: Miguel Lejeune, George Washington University)
• Day 3 – Afternoon: Third round of student presentations (in progress) on stochastic programming.
• Day 4 – Morning: Introduction to multi-stage models (speaker: Steffen Rebennack, Karlsruhe Institute of Technology)
• Day 4 – Afternoon: Fourth round of student presentation (in progress) on stochastic programming.
• Day 5 – Morning: Stochastic programs with endogenous uncertainty (speaker: Giovanni Pantuso, KU)
• Day 5 – Afternoon: Fifth round of student presentations (in progress) on stochastic programming.
Learning outcomes
Intended learning outcome for the students who complete the course:
Knowledge:
• Formulations of two-stage, multi-stage and chance-constrained stochastic programming problems, possibly with endogenous uncertainty
• Properties of stochastic programming problems
• Solution and approximation methods
Skills:
• Formulate different types of stochastic programming problems, depending on the interplay between decision-making and information disclosure, on the required probability of feasibility, and on the relationship between uncertainty and decisions
• Approximate the uncertain data by means of scenarios
• Develop solution strategies for different types of stochastic programming problems
Competences:
• Recognize and structure a decision problem affected by uncertainty and propose a suitable mathematical formulation
• Identify a suitable way of representing or approximating the uncertain data of the problem and its effect on decisions
• Devise appropriate solution methods for the decision problem
• Quantify and analyze the impact of uncertainty on the decision problem and its solution
Target Group
PhD students from e.g., mathematics, engineering, economics, working with optimization under uncertainty.
Recommended Academic Qualifications
Linear programming and probability theory.
Research Area
Optimization and decision-making.
Teaching and Learning Methods
• Self-study before and during the course.
• 3 hours of lectures per day for 5 days.
• 4 hours of student presentations per day for 5 days.
• Final assignment.
Type of Assessment
The students will be assessed based on an assignment to be delivered after the end of the course.
Literature
J. R. Birge and F. Louveaux (2011) Introduction to Stochastic Programming.
Selected research papers.
Course coordinator
Trine Krogh Boomsma (Professor)
Guest Lecturers
Prof. 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, including 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.
Dr. Miguel Lejeune is a Professor of Decision Sciences at the George Washington University School of Business and a Professor of Electrical and Computer Engineering at the School of Engineering & Applied Science. His research expertise spans stochastic programming, distributionally robust optimization, mixed-integer nonlinear programming, with a notable reputation for his contributions to chance-constrained optimization. Dr. Lejeune’s work has been published in the most prestigious academic journals, and he has received numerous honors for his research and teaching, including the 2019 Koopman Award from the INFORMS Society and the 2024 Excellence in Research Award in Applied Mathematics from the Washington Academy of Sciences, where he is a fellow. In addition, Dr. Lejeune is an Associate Editor for several prominent journals such as INFORMS Journal on Computing and Mathematical Programming.
Prof. Dr. Steffen Rebennack is Chair of Stochastic Optimization at the Institute of Operations Research, Karlsruhe Institute of Technology (KIT). His research focuses on stochastic programming, large-scale and mixed-integer nonlinear optimization, decomposition algorithms, and applications in energy systems, as reflected by his more than 100 publications. He is particularly recognized for his work on multi-stage stochastic programming and stochastic dual dynamic programming. Dr. Rebennack is the recipient of several awards, including the INFORMS ENRE Best Publication Award in Energy, the ENRE Young Researcher Prize, in addition to teaching and dissertation honors. He serves as Co-Editor-in-Chief of the European Journal of Operational Research and as an editor for a number of other leading journals in operations research.
Dates
June 22-26, 2026.
Course location
HCØ, Nørre Campus
Course fee
• Participant fee: 800 DKK
• PhD student enrolled at SCIENCE: 0 DKK
• PhD student from Danish PhD school Open market: 0 DKK
• PhD student from Danish PhD school not Open market: 3000 DKK
• PhD student from foreign university: 3000 DKK
• Master's student from Danish university: 0 DKK
• Master's student from foreign university: 3000 DKK
• Non-PhD student employed at a university (e.g., postdocs): 3000 DKK
• Non-PhD student not employed at a university (e.g., from a private company): 8400 DKK
Cancellation policy
• Cancellations made up to two weeks before the course starts are free of charge.
• Cancellations made less than two weeks before the course starts will be charged a fee of DKK 3.000
• Participants with less than 80% attendance cannot pass the course and will be charged a fee of DKK 5.000
• No-show will result in a fee of DKK 5.000
• Participants who fail to hand in any mandatory exams or assignments cannot pass the course and will be charged a fee of DKK 5.000
Course fee and participant fee
PhD courses offered at the Faculty of SCIENCE have course fees corresponding to different participant types.
In addition to the course fee, there might also be a participant fee.
If the course has a participant fee, this will apply to all participants regardless of participant
type - and in addition to the course fee.