Traffic and Logistics
In public transport as well as in production process numerous logistic problems have to be solved. This invloves for example the allocation of vehicles and crews in a public transport company or the organization of manufacturing processes that are distributed over different places. Especially, in service design of public transport mathematical optimization methods are not applied. Our goal is to further establish the use of discrete mathematics in problems of logistics and service design in public transport.
In order to organize the complex production processes of modern goods in an efficient way numerous logistic problems have to be solved. This pertains both to the operation of the production process in a single factory as well as to the organization of manufacturing processes that are distributed over different places and to the distribution of the products.
Service design produces challenging new mathematical problems beyond classical discrete optimization. Considering the interplay between supply and demand, e.g., leads to game theoretic or auctioneering formulations, forecasting demand leads to stochastic models, maximizing quantities such as the revenue creates non-linearities etc. We investigate these problems on the basis of several different, concrete applications.
Often, logistic decisions must be taken online, i.e., one can use only the information that is available at the time of the decision. The quality of the decision, however, will be affected by future events, which are largely unknown.
Even more difficult are situations in which decision have to be taken in real time, e.g., in elevator control. In such an environment, algorithms do not only have to find good solutions, they must also provide them within a guaranteed timeframe.