Capacitated Network Design: Multi-Commodity Flow Formulations, Cutting Planes, and Demand Uncertainty

Christian Raack received his diploma (master's) degree in mathematics from the Technical University Berlin in 2006 and later his Ph.D. in 2012. As a full-time researcher at the Zuse Institute Berlin he has been involved in a large variety of projects mainly stemming from optimization problems in the telecommunications sector. In this thesis, the author develops methods in mathematical optimization to dimension networks at minimal cost. The considered planning problems typically arise in the strategic design of telecommunication or public transport networks and also in logistics. Given hardware and cost models, the challenge is to provide network topologies and efficient capacity plans that meet the demand for network traffic (data, passengers, freight). The author tries to incorporate crucial aspects of practical interest, such as the discrete structure of available capacities as well as the uncertainty of demand forecasts. One of the essential aspects studied in this work is the use of cutting planes to enhance solution approaches based on multi-commodity flow formulations. Providing theoretical and computational evidence for the efficacy of inequalities based on network cuts , existing theory and algorithmic work is extended in different directions.