Mathematics of Transportation and Logistics
The mathematics of transport and logisitics aims at optimizing the design and the operation of networks for the movement of persons and goods. Such networks can be modeled as graphs, in which commodities flow from their sources to their destinations. The mathematical treatment of such models leads to large-scale integer programming problems, whose solution requires the development of novel efficient algorithms.
Transportation and logistics problems often have a special flavor that depends on the application. Train composition in railway planning leads to algorithmic hypergraph theory, user behavior in public and road traffic requires algorithmic game theory, aircraft performance is treated best by discrete-continuos models, sustainable manufacturing network gives rise to multicriteria optimization, operation theatre scheduling leads to robust optimization, and so on. To solve such problems, we combine problem specific research that aims at understanding this special structure with general approaches to deal with very large networks. Foci of our work are on the development of adaptive coarse-to-fine graph generation approaches in discrete analogy to finite element methods, and on decomposition methods for the integrated treatment of multiple model layers.
Applications range from vehicle rotation plannning for high speed trains, fuel efficient aircraft routing, toll enforcement on the German highway system, transfer friendly timetabling in public transit, sustainable bicyle manufacturing, and operation theatre scheduling.
Our projects are linked into collaborative research programs including Matheon, ECMath, MODAL, the BMBF Mathematics program, and the DFG CRC 1026. We cooperate with partners from industry and society including Deutsche Bahn, Lufthansa Systems, the Bundesamt für Güterverkehr, and the Charité.
We develop efficient optimization methods for challenging problems in transportation and logistics. Our aim is to advance the theory of large scale integrated network planning, to use this theory in order to implement compuationally efficient algorithms, to put these algorithms into every day practice by integrating them into the process environments of our industrial partners, and, in this way, to make a noticeable contribution to improve the efficiency of transportation and logistic.