Content (Syllabus outline)

  • Introduction to modelling: principles of modelling and decision making, types and scope of the models; formulation of the problems, generating the models, types of the methods (linear vs. nonlinear, deterministic vs. stochastic, static vs. dynamic, discrete vs. continuous, inductive, deductive,...), input data, feasible and optimal solutions, analysis of the results, sensitivity analysis.
  • Linear models: recapitulation of linear programming principles, linear programming extensions, primal and dual linear program, sensitivity analysis, introduction to parametric programming, examples of linear models in economic and environmental research.
  • Decision making and game theory: general decision principles in deterministic, stochastic and heuristic environment, introduction to game theory, zerosum games, saddle point games, games without saddle point, domination strategies, linear program and zero-sum games, perfect information and its value.
  • Multiphase modelling: basic definitions in networks and graphs, discrete deterministic dynamic programming, Bellman’s principle of optimality, graphical solution of discrete deterministic dynamic programming, examples of discrete dynamic programming in economic and environmental issues.
  • Multiple criteria decision making: principles of multicriteria modelling, goal programming, hierarchical models, analytic hierarchy process (AHP), DEXi method, deterministic data envelopment analysis (DEA).
  • Stochastic models: Markov chains, stochastic discrete dynamic programming.

Prerequisites

1) Prerequisites for inclusion in study process:

  • Enrolment in the corresponding (1st) year of the master study program.
  • Completed exam of at least one course with mathematical contents at BSc (1. Bologna level), like Mathematics, Practical Course in Mathematics, Mathematical Methods, Selected Chapters in Mathematics or similar.

2) Formative coursework and assessment:

  • Attendance at tutorials
  • Colloquium or written examination from tutorials
  • Seminar
  • Exam (colloquium or written examination)