NMAK26004U Optimization under Uncertainty

Volume 2026/2027
Education

MSc Programme in Mathematics-Economics
MSc Programme in Actuarial Mathematics

Content

In countless real-life situations, decision makers are required to make decisions under uncertainty, that is while relevant information is uncertain, noisy, imprecise. Examples are investments in assets or projects with uncertain returns, scheduling of taks with uncertain duration, or production of goods with uncertain demand. Decision problems with these features are central in the modern finance, energy, and logistics sector, to name a few.

 

This course introduces the students to optimization in conditions of uncertainty. The course presents different mathematical formulations, illustrates the corresponding mathematical properties, shows how to exploit these properties in various solution methods, and discusses how uncertain parameters can meaningfully be transfortmed into sound input data (scenarios). The students of this course will independently handle practical problems in project work and exercises, hereby gaining the practical experience necessary to work on complex decision problems under uncertainty. 

Learning Outcome

Knowledge:

  • Formulations of stochastic optimization problems
  • Approximation techniques and scenario generation
  • Mathematical properties of stochastic optimization problems
  • Solution methods

 

Skills:

  • Formulate different types of stochastic optimization problems
  • Recognize and prove mathematical properties
  • Represent/approximate the uncertain data by means of scenarios, when necessary
  • Apply the solution methods presented in the course
  • Implement a (simplified version of a) solution method using optimization software

 

Compentences:

  • Recognize and structure a decision problem under uncertainty and propose a suitable mathematical formulation
  • Recognize mathematical properties and design a suitable solution method for a given stochastic optimization problem
  • Identify a suitable way of representing the random data of the problem
  • Quantify the benefit of using stochastic optimization in a particular decision making problem

Lecture notes provided by the teacher (see Absalon).

Required competencies: Linear Programming (Operations Research 1 or similar) in addition to basic Probability Theory.

Recommended but not required: Applied Operations Research.

Academic qualifications equivalent to a BSc degree is recommended.
2x2 hours of lectures per week, 2 hours of classroom exercises or project work supervision. Individual or group-based project work throughout the course.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 28
  • Theory exercises
  • 14
  • Project work
  • 55
  • Exam Preparation
  • 80
  • Exam
  • 1
  • Total
  • 206
Oral
Feedback by final exam (In addition to the grade)

Lecturer's oral or written feedback (collective and/or individual) on the project work.

Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (30-minute preparation time)
Examination prerequisites

Approval of one project report is a prerequisite for enrolling for examination.

Aid
Only certain aids allowed (see description below)
  • All aid can be used during the preparation time.
  • No aid can be used during the oral examination.
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Re-exam

Same as the ordinary exam, conditional on the approval of the project work.

If the required project report was not approved before the ordinary exam it must be (re)submitted no later than three weeks before the beginning of the re-exam week (contact the teacher for further details).

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.