Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


After successfully completing this course, the students will:

  1. Understand the basic concepts of optimization, implementation, and solution approaches.
  2. Formulate their ideas and decide which model is the most computationally efficient way.
  3. Recast their original model into LP, MILP, or convex models, if required.
  4. How to struggle with the operating and planning problems and make their model as solver-friendly as possible.
  5. Understand the basic concept of convex optimization, check the convexity of a model, and how to convexify a non-convex model.
  6. Consider the existing uncertainties in the model via stochastic or robust programming approaches.
  7. How to interpret the outcomes of the models. 

Credits: 5

Schedule: 01.03.2021 - 24.05.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Matti Lehtonen, Mahdi Pourakbari Kasmaei

Teacher in charge (applies in this implementation): Matti Lehtonen, Mahdi Pourakbari Kasmaei

Contact information for the course (valid 10.02.2021-21.12.2112):

The students may contact the teacher via email at any time. Also, a Zoom/Teams meeting can be arranged upon request.  

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    The course will introduce Linear Programming (LP) problems and methodology, bilevel optimization, mixed-integer linear programming, the formulation and solving of non-linear programming and mixed integer nonlinear programming problems. Convex programming is covered, as are the non-deterministic techniques, stochastic and robust programming.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    The course evaluation will be based on midterm exam, graded homework exercises and assignments.

  • Valid 01.08.2020-31.07.2022:

    Contact teaching 24 h, Assignments 45 h, independent studies and work-based learning 45 h, revision 20 h, exam 3 h.


Study Material
  • Valid 01.08.2020-31.07.2022:

    Presentation slides, recommended text books.

  • Valid 01.08.2020-31.07.2022:

    Some basic mathematical knowledge;

    A master’s degree. 

SDG: Sustainable Development Goals

    4 Quality Education

    7 Affordable and Clean Energy

    11 Sustainable Cities and Communities

    12 Responsible Production and Consumption

    13 Climate Action