Optimization Methods with Applications

The course covers developments of advanced optimization models and solution methods for technical and economic planning problems. The basis in the course is the optimization process, from a real planning problem to interpretation of the solutions of the underlying optimization problem. In the modeling part we focus on problems with discrete elements, but also knowledge about important classes of optimization problems and their properties are highlighted. Both linear and non-linear optimization are covered. Models with both known and uncertain parameters, i.e. both deterministic and stochastic modeling are discussed. Within solution methods, exact methods for problems with discrete decision variables are covered. Further, advanced linear programming theory including dual theory is taught. The analysis part includes interpretation of the solution also with regard to the underlying real problem. Finally, the course covers advanced use of commercial software for modeling and solving optimization problems.

Position and function within the study program: The course is compulsory in the 7. semester of the MTIØT program for the students specializing in applied economics and optimization. The course shall contribute to fulfill learning objective 4.2 in the detailed list of learning objectives for MTIØT, where an in-depth understanding of scientific principles underlying the chosen specialty is demanded. It provides deepened knowledge about mathematical modeling and the formulation of optimization problems. It also provides knowledge about algorithms and solution methods. A special focus is integer and mixed/integer programming. The course will provide knowledge to understand basic and advanced theory, models, methods, and concepts within optimization like: - strengths and weaknesses with different ways of formulating technical and economic planning problems - how different formulations and algorithms can be combined to efficient solution methods - theory about linear programming, integer programming, non-linear programming and stochastic programming - how to use commercial software to solve technical and economic planning problems - knowledge about many different models and when they can be good starting points for modeling richer problems. By the end of the course, the students should be able to: - structure technical and economic planning problems so that they can be formulated as mathematical programs - understand the pros and cons of different formulations and solution methods and the interaction between model and method - implement and solve real technical and economic planning problems in commercial software and interpret the results. Besides this the course should give: General knowledge about how quantitative methods and models can provide decision support in technical and economic planning situations.

Lectures and exercises with and without computers.