• July 22, 2019 - July 27, 2019
    9:00 am - 5:30 pm

This event is developed by the Project Training and Education in Digitalization and Transformation (WDT).


Participation fees:

3 days: 1.785 EUR incl. 19% VAT (excl. accommodation and travelling)

6 days: 2.856 EUR incl. 19% VAT (excl. accommodation and travelling)

Lunch: included at all days!



Friedrich-Alexander-Universität Erlangen-Nürnberg

Lehrstuhl für Wirtschaftsmathematik

Cauerstraße 11

91058 Erlangen


Target group:

Planning professionals at an operational or management level, data scientists and consultants working with quantitative methods, interested people with a background in mathematical, natural, technical or economic sciences.

Min. number of participants: 6

Max. number of participants: 20



Basic knowledge in linear algebra, especially the solution of systems of linear equations and elementary matrix computations. Elementary programming skills are helpful. If possible, participants should bring their own laptop with administrator rights to install the software used in this course. It is also possible to work with computers provided by FAU during this course.



The course teaches the foundations of mathematical optimization with a special focus on the solution of planning problems from an industrial environment. It gives planners all the necessary tools to formulate and solve optimization tasks as mathematical models, covering both linear and integer problems. At the hand of many practical and detailed examples, the participants learn to build optimization models for problems occurring in logistics and transport, production, energy systems, telecommunication and many further contexts. They obtain a basic understanding of the most important algorithms in linear and integer optimization: the simplex method and the branch-and-bound scheme. In extensive hands-on training sessions, they acquire the ability to use state-of-the-art optimization software to solve large-scale optimization tasks and to interpret the computed solutions in terms of the application context at hand. As an add-on, university experts give advice for the beneficial implementation of optimization approaches in small and major companies, drawing from vast their experience in industrial cooperations over the last 20 years.


Course material:

  • Course book and lecture slides
  • The course includes a free 30-day trial license for the optimization software Gurobi which is used in the practical exercises.


Programme outline (modules/days):

each day: 2-3 morning lectures, 60 min. each: 09:00 a.m. – 12:30 p.m., 1 afternoon practice session of 4 h: 01:30 p.m. – 05:30 p.m.

Day 1: Elementary models and applications in linear programming, the challenges of integer programming

Day 2: Properties of linear programs, the simplex algorithm

Day 3: Introduction to integer programming, characteristics of integer models

Day 4: Branch-and-bound, cutting planes, good and bad formulations for integer models

Day 5: The travelling salesman problem (applications in logistics and many further areas, model formulations, cutting planes)

Day 6: Fixed-charge and general network design problems



We are happy that we were able to win Professor Paul Williams as an external lecturer for our “Industrial Training Course on Mathematical Optimization”.

Professor Paul Williams, London School of Economics (http://personal.lse.ac.uk/WILLIAHP/publications.htm) is a Cambridge graduate in mathematics and obtained his PhD in mathematical logic at Leicester University. He has gained extensive experience in linear and integer optimization during his research and consulting work at IBM, where he established optimization modelling as a subject of study and made important contributions to the algorithmic and computational advancement of the field. He has held a number of academic positions, lecturing at Sussex University, Edinburgh University and Southampton University before joining the London School of Economics, where he has served as head of the Department of Operational Research, which is now the Management Science Group. Nowadays, he consults companies and organisations in formulating and solving their planning problems as mathematical models.