Modeling Decision Problems under Uncertainty

BEA512 Modeling Decision Problems under Uncertainty

Autumn 2021

  • Topics

    The course will give the students in-depth knowledge of how to include uncertainty into mathematical planning models, with a focus on mathematical programming. There will be an emphasis on how to model uncertainty to obtain meaningful models for planning purposes within logistics / supply chains as well as resource planning. Basic algorithmic structures will also be presented, but the course is primarily modeling oriented, not algorithmically oriented.

    The course will cover:

    • The role of what-if analysis and parametric optimization in decision-making under uncertainty
    • How to handle feasibility in optimization under uncertainty
    • Basic algorithmic structures for stochastic programming
    • Scenario generation, that is, how to represent uncertainty in mathematical programming models
    • Alternative modeling concepts for handling uncertainty
    • Stochastic network design
    • Stochastic facility layout
    • Examples from energy systems modeling and logistics

  • Learning outcome

    Knowledge: Upon completion the student 

    • understands how uncertainty can be included in optimization models
    • knows about the main algorithmic approaches to stochastic programming
    • knows how uncertain phenomena can be modeled to fit into stochastic programs

    Skills: Upon completion the student is

    • able to argue coherently about uncertainty in mathematical programming models
    • able to see whether or not appropriate tools have been used by others when setting up models

    Competence: Upon completion the student will

    • Be able to formulate, understand and solve stochastic programming problems and make sure correct tools are used.

  • Teaching

    Lectures and student presentations. If feasible, it will take place physically, with three sessions in Bergen, each about 2 full days. If necessary, the course will run digitally, and concentrated over shorter periods of time. 

  • Restricted access

    The course is open to external PhD-students. But notice the background requirements. Internal Master students can check with the instructor if they have enough background. 

  • Recommended prerequisites

    It is necessary with solid knowledge of standard optimization theory, especially linear programming. Experience with stochastic programming is not expected. 

  • Required prerequisites

    Basic knowledge of mathematical programming modeling

  • Requirements for course approval

    Physical or electronic presence is required.

  • Assessment

    Each student must hand in a term paper after the course is finished, where the theories of the course are used on a mathematical programming model, preferably one the student is already working with in his / her thesis. Deadline will be end of January.

  • Grading Scale


  • Computer tools

    It is an advantage to know advanced modeling languages, such as AMPL, MPL or GAMS, but not required. But this will not be taught. A good basis would be ENE420 or something equivalent.

  • Literature

    Alan King and Stein W. Wallace, Modeling with stochastic programming, Springer, 2012.

    Peter Kall and Stein W. Wallace, Stochastic Programming, Wiley, Chichester, 1994. Available for free.

    Articles published in scientific journals.


ECTS Credits
Teaching language

Autumn. Offered Autumn 2021.

If necessary, depending on the Corona situation the course will be digital. 

Course responsible

Stein W. Wallace, Department of Business and Management Science