is one of the prime tasks in the telecommunication industry. In this talk I survey the development of mathematical models that formally describe this problem and that have been used in practice in the last ten years. These models range from simple topology design problems to models that take care of many details such as special types of available capacities, routing protocols, or path length restrictions.
I will show how algorithms integrating polyhedral combinatorics, linear programming, and various heuristic ideas can help solve real-world network dimensioning instances to optimality or within reasonable quality guarantees in acceptable running times. I will also report on experiences with this approach in practice and indicate the improvements that can be achieved compared to the standard "engineering approach".