Using algorithms to find the best possible decision

There are many routes from Berlin to Passau. Route planners calculate in real time which route is the best, taking into account the current conditions. According to Professor Marc Goerigk, this specific problem can be solved quickly. But what if there are several possible scenarios? In other words, different weather conditions or traffic volumes? And what if it is not yet clear which of these will occur and with what probability?

Professor Goerigk's research is a bit like looking into a crystal ball: "I'm looking at how to make decisions - namely the best decision out of many possible alternatives when there are still uncertainties," explains the scientist, who has held the Chair of Business Decisions and Data Science at the University of Passau since spring 2023. "In other words, I don't yet know exactly what I want to find, but I still want to find the best possible solution."

Conventional calculation methods quickly reach their limits with such questions. Professor Goerigk relies on a combination of algorithms and mathematical models to search for solutions that are stable in the face of uncertainties in the underlying data.

Marc Goerigk is 39 years old and has long been established in his field. The latest ranking by the German business magazine "WirtschaftsWoche", which honours the most prolific business administration professors under the age of 40 every two years, shows just how much. The Passau academic came first in the current ranking - out of more than 3,000 authors from German-speaking countries. The number and quality of the publications he has written to date have been rated. Professor Goerigk's publication list includes 166 entries since 2010, including a book that is particularly close to his heart: it is an introduction to his field of research, the methods of robust combinatorial optimisation.

It deals with the solution of abstract and complex mathematical problems. The methodology can be applied to a wide range of use cases, such as traffic optimisation, but also to questions of planning or warehousing in companies. His research is now moving away from specific applications and towards the structures behind the problems to be solved.

Beauty in the abstract

"I find the abstract much more beautiful than the concrete," says Goerigk. Because the concrete limits him too much: "If you get stuck on the specific, then the details take centre stage." These can vary greatly from problem to problem. "I find it much more elegant to find the structures that are present in every problem of a certain type."

His favourite problem starts with the suitcase game. "I pack my suitcase and take with me ..." - for example, a selection of five out of ten things. Each thing has its own value. "If I know the value, the game is trivial. It becomes more difficult when the values are unknown." This is a combinatorial problem in which - depending on the size of the selection - there are exponential possibilities. "Above a certain size, it is so abstract that it is no longer concrete." The difficulty does not lie in the underlying optimisation problem, but results from the uncertainty. "This is uncertainty as it can be studied in its purest form." In mathematics, the problem is known as a selection problem. He refers to this in many of his publications.

Sharpening his understanding of the problems of robust combinatorial optimisation in turn helps him to link these methods with the right data-driven algorithmic approaches. And this is where the second part of his chair's name comes into play, which was created by the Free State of Bavaria as part of the Hightech Agenda: data science.

Back to the road example mentioned at the beginning. If you have historical traffic measurements available, i.e. you know what the traffic was like on each day, at each hour, then these measurements can be taken into account for possible scenarios. However, not all data may be suitable, as there may have been extreme scenarios in which all traffic on the route collapsed, but these should not be included in the data basis. Professor Goerigk then uses the available data to model a suitable core set of uncertainties against which the route planning process should be safeguarded. This in turn also influences which algorithm is suitable for calculating the best possible route.

From mathematics to business administration

The Berlin-born Goerigk came to Passau in a roundabout way, just as he did to the subject of business administration: he initially studied mathematics at the University of Göttingen and gained his doctorate in applied mathematics. At the TU Kaiserslautern, he developed optimisations for evacuation plans. He switched to economics when he went to the University of Lancaster in the UK. His department was based at the Management School. Since then, he has remained loyal to business studies, even when the University of Siegen brought him back to Germany as a professor.  The transition between business administration and mathematics is fluid in his field, he says. After all, his search for the best possible decisions is also central to many processes in companies.

At the University of Passau, Professor Goerigk is at home in a research-intensive environment. The Faculty of Business and Economics at the University of Passau is also one of the top 25 universities in Germany, Austria and Switzerland for business studies in the current WirtschaftsWoche ranking. "I am very happy to have found a new home here in Passau," says Professor Goerigk. "Passau is a wonderful place to research and study." And he hopes that the success in the ranking will put Passau even more on the map for others.

This text was machine-translated from German.