Course content

The course aims to give the student an understanding of how to use advanced optimization methodologies to formulate, solve and analyze decision problems in industry and public services. The main focus of the course is on how large mixed integer linear optimization problems can be modeled and structured and how to solve the models. The course exposes the students to several applications from different branches of industry and public services. Through these, the students are given an understanding about differences and similarities between models from different industries. This understanding together with the theoretical knowledge is then used to evaluate appropriate formulations and solution methods when designing decision support system.

Learning outcome

The course is an elective course for MTIØT students in th 8th semester, and obligatory for students following the main profile AØO. At the end of this course, the students should be able to: - Explain advanced theory, models, methods and concepts within mathematical programming, with a special focus on solving technical and economical planning problems. - Master decomposition techniques dealing with common resources. This involves defining and formulating the Lagrangean dual problem and the Lagrangean subproblem as well as designing algorithms to solve the Lagrangean dual problem. It also involves stating the Dantzig-Wolfe reformulation of a problem and the corresponding master and subproblem. - Demonstrate how different formulations and algorithms can be combined to efficient solution methods. This involves valuing different approaches and arguing for the appropriate choices of models and methods. - Describe when a planning problem can be solved exactly and when a heuristic is preferable. This involves analyzing an application and based on sound arguments assess the appropriate choice. - Explain how commercial software can be used to solve technical and economical planning problems. - Recognize and name common models in different branches of industry and public services and when they can be good starting points for modeling richer problems. - Structure technical and economical planning problems so that they can be formulated as mathematical programs. - Describe the pros and cons of different formulations and solution methods and the interaction between model and method. - Implement real technical and economical planning problems in commercial software, solve the problems and interpret the results. - Use commercial software as a part of a larger framework to create decision support systems that can be used in different branches of industry and public services.

Learning methods and activities

Lectures, exercises, cases and small computer projects. Computer projects are performed in groups.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course requires knowledge from basic courses in mathematics, statistics, computer science and is built upon TIØ4130 Optimization Methods, or similar knowledge.

Course materials

Is given at the start of the semester.

Credit reductions