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Discrete Modelling

  • Number of credits 7.5 Credits
  • Level Master’s level
  • Starting Autumn Term 2020

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 hp

Det finns inga tidigare terminer för kursen Autumn Term 2020 Det finns inga senare terminer för kursen


2 November 2020


2 December 2020

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 equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.


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 15 April 2020. Please note: This second application round is intended only for EU/EEA/Swiss citizens. Submit a late application at

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


Tuition fee, first instalment


Total fee


Contact us

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Contact person for the course is:
Study counselor Lars-Daniel Öhman