BEA512 Modeling Decision Problems under Uncertainty

• 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 

  • has advanced knowledge about how uncertainty can be included in optimization models
  • can identify the main algorithmic approaches to stochastic programming
  • can model uncertain phenomena so that they fit into stochastic programs

  Skills

  Upon completion the student 

  • can argue coherently about uncertainty in mathematical programming models
  • can evaluate the appropriateness of tools when setting up models

  General competence

  Upon completion the student

  • can apply his/her knowledge and skills to formulate, understand and solve stochastic programming problems

• Teaching

  Lectures and student presentations. All teaching takes place during one week, be that in Bergen, Trondheim or Copenhagen. For 2025 it will be at NHH, Bergen.

• Restricted access

  • PhD candidates at NHH
  • PhD candidates at Norwegian institutions
  • PhD candidates at other institutions
  • PhD candidates from the ENGAGE.EU alliance
  • Master's students at NHH may be admitted after application, but are subject to the approval from the course responsible on a case by case basis. Notice the background requirements. The only limitation is the room capacity.
  • Academics with a PhD may be admitted after application, but are subject to the approval from the course responsible and the Vice Rector for Research on a case by case basis.

• Recommended prerequisites

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

  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 BAN402 or something equivalent.

• Required prerequisites

  Basic knowledge of mathematical programming modeling

• Compulsory Activity

  Attendance is required.

  Compulsory activities (work requirements) is valid for one semester after the semester it was obtained.

• Assessment

  Each student must hand in an essay 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. Submission deadline is 7 weeks after the last lecture.

  Compulsory activities (work requirements) is valid for one semester after the semester it was obtained. 

• Grading Scale

  Pass/Fail

• 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 BAN402 or something equivalent.

• Literature

  Alan King and Stein W. Wallace, Modeling with stochastic programming,  Second edition, Springer, 2024.

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

  Articles published in scientific journals.

• Retake

  Re-take is offered the semester after the course was offered for students with valid compulsory activities (work requirements). Additionally, the students must fulfill one of the two requirements listed below in order to be eligible for re-take:

  • Students who, at the original exam failed or got a grade below C
  • Students who were sick on the day of the exam and has provided a valid sick note ("sykemelding")

  Students will have the opportunity to submit a revised version of their work for the re-take assessment. If a revised version of the work is submitted, this must be clearly indicated on the front page.