4EK632 Optimization Modelling

Aims of the course:

The aim of the course is to acquaint students with optimization methods and models and other techniques for decision-making in the economic environment.

Learning outcomes:

Upon successful completion of this course, students will be able to apply standard optimization models for solving real-life decision-making problems. They will also be familiar with selected software packages for mathematical modeling and optimization.

Course contents:

  1. Traditional application areas of optimization models. Classification of optimization techniques.
  2. Introduction to linear programming (LP). Objectives, constraints, decision variables, and solutions.
  3. Formulation of typical LP problems. Manufacturing, transportation, and nutrition problems.
  4. Solving LP problems and interpreting the results. Graphical solution and general algorithms. Sensitivity analysis.
  5. Software support for LP problems.
  6. Mixed-integer linear programming problems (MILP). Assignment, traveling salesman, set-covering, and crew-scheduling problems.
  7. MILP and computational limits. Heuristics for selected problems, meta-heuristics.
  8. Optimization problems on graphs. Optimal paths and flows, LP formulation, and its comparison against custom-tailored algorithms.
  9. Project management and optimization, CPM, and PERT methods.
  10. Deterministic and stochastic inventory models. Optimizing order times and quantities.
  11. Queueing models. Applications of queuing models in computer science, manufacturing, and services. Analytic and simulation approach.
  12. Multiple criteria decision-making. Multiple-criteria evaluation and design problems, solution principles.