Quantitative Methods of Decision Making

Course Leader: Dr Marketá Matulová

Home Institution: Masaryk University, Brno, Czech Republic

Course pre-requisites: basics of linear algebra, MS Excel.

Course Overview
The course is designed for students who want to get acquainted with quantitative tools suitable for supporting decision-making occurring in business, economics, and finance. The main goal of the course is to show how to model real decision-making problems and to present methods of their solving. The secondary goal is to familiarize students with the use of MS Excel and its add-in Solver for computation of solutions to optimization problems. Participants will be introduced to common application areas of Operations Research/ Management Science (ORMS) and necessary solution procedures (simplex method, MODI, Hungarian method, CPM, and others). At the end of the course, they will apply gained skills in a team project in which they formulate mathematical models for given case studies and employ the procedures mentioned above to solve arising decision problems.

Learning Outcomes
After completing the course, students will be able to:

  • formulate mathematical models for decision problems that occur in management, economics, and finance.
  • apply suitable methods to solve optimization problems representing decision-making situations
  • implement optimization algorithms using software (MS Excel)
  • interpret and validate the results

Course Content

  • Linear programming (formulation, graphical solution, simplex algorithm)
  • Duality and sensitivity analysis in LP
  • Production Management problems
  • Distribution problems (formulation, heuristic algorithms and MODI method)
  • Assignment problems (formulation, Hungarian method)
  • Integer programming (Branch and Bound algorithm)
  • Network optimization (methods CPM and PERT for project management)
  • Multi-criteria decision analysis, Portfolio optimization
  • Multi-criteria and goal programming
  • Data envelopment analysis for performance evaluation

Instructional Method
The time will be divided between theoretical training (lectures) and seminars (problem-solving using computers). More complex problems and case studies will be solved as team projects, and the results will be presented and discussed on the last day of the course.

Required Course Materials
Students will be provided with all course materials including training problems for the seminars (assignments, data, spreadsheets), lecture slides, and other documents with a theoretical background.

The course is ended with a written test. Students are allowed to perform some computations on computers. It is necessary to get at least 50% of the maximum points. The prerequisite of successful completion of the course is participation in a team project.