### Industrial Cooperation

Questions arising in industry can provide a host of interesting problems that are not only relevant for practice but also mathematically challenging. This holds particularly for someone like me doing research in Optimization, Discrete Mathematics, and Operations Research. OR can be seen in this context as the *art of mathematical modelling of real-world applications*. Optimization comes in because there are always issues of efficiency and goals such as making best use of scarce resources. Discreteness arises, for instance, because yes or no decisions have to be made, and there is nothing in-between.

I have enjoyed cooperations with industrial partners for more than 20 years. Demands from practice have, in particular, driven my contributions to the design, analysis, and implementation of algorithms. Many combinatorial optimization problems coming from practice tend to be of very large scale and are often not solvable with commercial standard software. This makes special purpose developments necessary - if the expected savings are of significant size - and this requires the mathematical analysis of large scale combinatorial structures.

- In many cases, applications have driven me to investigate
**new problem types**. Here is one example:

The *via minimization problem* of printed circuit boards (roughly: finding the fewest number of holes to be drilled into a board so that all electrical wires can be routed without crossing) that came up in a cooperation with Siemens and the computation of *ground states for spin glases* that colleagues in statistical mechanics investigate have started my interests in the **Max-Cut-Problem** and in the **problem of finding a maximum weight cycle in a binary matroid.**

- In some cases, questions from industrial partners have even lead me to work in
**new research areas**, here is an example:

The scheduling of stacker cranes at a PC production site of Siemens has started my interest in **Online Optimization**. I realized that this type of problems is much more frequent in practice than theoreticians think and now have a research group at ZIB that addresses this particular type of optimization problems.

Online problems came up later, for instance, at two projects with Herlitz: the *scheduling of commissioning vehicles* and the *optimization of heterogeneous transport systems* in a large storage facility. They also showed up at *the dispatching of service vehicles* ("Gelbe Engel") of ADAC (German Automobile Association) and at the *routing of requests in optical telecommunication networks*, a project carried out with T-Systems Nova. Practical applications of this type have resulted in a DFG-Forschungsschwerpunkt: "Online Optimization of Large Scale Systems".
And when you are asked to optimize the pumping of gas through the pipelines of Ruhrgas you will immediately learn that without integrating stochastic, nonlinear and combinatorial aspects you will not arrive at an adequate mathematical model.

For someone not in the field, topics such as Computational Logic may sound quite esoteric. I encountered the practical importance of this area for the first time when Klaus Truemper and I tried to help the Grob-Werke in Mindelheim to make the *transfer lines *(assembly lines consisting of twenty or more robots connected by transportation systems) that Grob produces for the automobile industry "safer". The problem here is to generate safe robot actions (in particular in failure situations) by analyzing sensor data and the various logical and geometrical dependencies of all parts of the whole system. Encouraged by this and other applications (e.g., in language analysis) Klaus Truemper wrote a book about this topic: Effective Logic Computation.
My research group at ZIB returned to Computational Logic due to a project with Infineon aiming at the *verification of systems-on-chips*.

Two application areas had a particular impact on my work since the late eighties: telecommunication and public transport. My interest in combinatorial aspects of telecommunication was started by Clyde Monma in the late eighties when Clyde was working for Bell Communications Research, and I will write more on this as soon as I have time.