Information on individual educational components (ECTS-Course descriptions) per semester

Introduction to Programming (Python)

Business mathematics (especially linear systems of equations)

• Vectors and matrices
• Linear algebra applications
• Classification of optimisation problems
• Modelling and formulation of linear and mixed-integer linear programmes
• Solving optimisation problems with the help of the solver GLPK
• Interpretation of the solution (sensitivity analysis)
• Integrating the GLPK solver into Python applications
• Standard business applications e.g.: Production programme planning, transport and allocation problems, location planning, network analyses (maximum flows, shortest paths),...
• Modelling patterns/tricks: Binary variables for linearisation of e.g.: logical expressions, piecewise linear functions, distance functions (Manhattan distance, maximum metric)

Operations Research, especially mathematical optimisation (modelling, solving and interpreting optimisation problems), can be used to find more efficient solutions for business problems. The aim of this course is to give students an insight into the procedures and algorithms of operations research.

The students can apply algorithms and methods of vector and matrix calculus and are able to solve linear systems of equations with the computer, can summarise the possibilities and limitations of linear (LP) and mixed-integer linear (MILP) programming. They can select and evaluate suitable methods on the basis of a taxonomy and the properties of the solution methods. Students are in the position to model (implement) an optimisation problem in Python from an informal description and use a suitable solver (GLPK) to solve the problem and are able to interpret the solution of LPs and MILPs and compare different solutions.

Interactive course with lecture, case studies, exercises in individual and group work, presentations and homework.

Exercises and case study (50 %)
Final exam (50 %)

None

Boyd, Stephen; Vandenberghe, Lieven (2018): Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares. Cambridge, UK; New York, NY: Cambridge University Press.

GLPK - GNU Project - Free Software Foundation (FSF) (o. J.): GLPK. Online im Internet: URL: https://www.gnu.org/software/glpk/ (Zugriff am: 21.05.2018).

Hillier, Frederick S.; Lieberman, Gerald J. (2014): Introduction to Operations Research. 10th edition edition. New York, NY: Mcgraw-Hill Education.

Nahmias, Steven; Olsen, Tava Lennon (2015): Production and Operations Analysis: Strategy - Quality - Analytics - Application. 7 edition. Long Grove, Ill: Waveland Pr Inc.

Python Software Foundation (o. J.): python. Online im Internet: URL: https://www.python.org/ (Zugriff am: 21.05.2018).

Sierksma, Gerard; Zwols, Yori (2015): Linear and Integer Optimization: Theory and Practice, Third Edition.Boca Raton: CRC Press (= Advances in Applied Mathematics).

Classroom-based course with distance learning components and compulsory attendance in individual teaching units (exercise discussions). In addition to the content discussed in the lecture, students receive supplementary materials and exercises. The exercises serve to deepen the material covered in the lecture and are intended to give students the opportunity to check whether the knowledge acquired can actually be implemented. Individual sample solutions are discussed during the attendance hours.