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Discrete Modelling

  • Number of credits 7.5 credits
  • Level Master’s level
  • Starting Autumn Term 2023

Admitted to the course

Here you will find everything you need to know before the course starts.

About the course

The course consists of two parts.

Part 1 (4,5 hp): Theory of discrete modelling.
This part of the course treats theory for discrete modelling, from problem formulation and choice of model, via specific model formulation and implementation, to evaluation of appropriateness and effectiveness of the model.

This part of the course starts with general theory for formulating an integer program from a given problem description, and general theory for SAT formulations of optimization and decision problems. In connection to this, complexity theory and the general theory of polynomial reduction from one problem to another. Integer formulations and SAT formulations are then connected to different classes of graph models, in particular network flow problems, matchings, shortest path, graph colouring and the travelling salesman problem. Both exact and heuristic models are studied with regard to effectiveness. Following this, concrete large scale examples of applied discrete modelling are studied, and an introduction to literature search in the area of discrete modelling is given. The theory is concluded with an introduction to simulation using randomized scenarios.

Part 2 (3 hp): Lab assignment.
This part of the course treats implementation of discrete models, and comparisons between different formulations as regards computational efficiency. Further, simulation methods for discrete models are implemented.


In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.

Application and eligibility

Discrete Modelling, 7.5 credits

Visa tillfällen för föregående termin Autumn Term 2023 Det finns inga senare terminer för kursen


31 October 2023


30 November 2023

Study location




Type of studies

Daytime, 100%

Required Knowledge

The course requires 90 ECTS including 15 ECTS in Computer Programming, a course in Linear Programming, a course in Integer Programming on advanced level and a basic course in Mathematical Statistics or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies

Entry requirements


Guaranteed place Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.

Application code



Application deadline was 17 April 2023. Please note: This second application round is intended only for EU/EEA/Swiss citizens. Submit a late application at Universityadmissions.se.

Application and tuition fees

As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.

Application fee

SEK 900

Tuition fee, first instalment

SEK 17,850

Total fee

SEK 17,850

Contact us

Please be aware that the University is a public authority and that what you write here can be included in an official document. Therefore, be careful if you are writing about sensitive or personal matters in this contact form. If you have such an enquiry, please call us instead. All data will be treated in accordance with the General Data Protection Regulation.

Contactperson for the course is:
Study counselor Lars-Daniel Öhman