Overview of our research activitiea
- At every point in time there has to be an optimal schedule for ADAC-vehicles which covers all jobs.
The research of the chair of business mathematics focuses on Discrete Optimization as well as the corresponding fundamental research in the fields of Analysis of Algorithms and Discrete Mathematics.
Major applications of these discrete optimization methods include telecommunications, logistics and transport.
Problems with dynamic character are of particular interest to us: As of today many problems cannot be solved by simply finding a schedule which is optimal at one point in time and using this continuously thereafter. Instead, the process has to be optimized in an event based manner. This is called Online-Optimization.
- Heuristic (S2), but especially mathematical optimizaition (S3) allows for a considerable reduce in average flow time during peak load in respect to conventional methods (S1).
Since an optimization of this kind typically has to be computed while the system is running the optimization method has to respond sufficiently quick in order to avoid dramatic delays. This is called real-time constraint.
Examples of this kind which we dealt with include the scheduling of support vehicles for the ADAC, the control of freight elevators or field work scheduling of service technicians. Hospital ressource planning is currently pending.
- Heuristic (S2), but especially mathematical optimization (S3) allows for the saving of 3 freight elevators in respect to conventional methods (S1). Note that additionally average flow time has been decreased.
Currently we are interested in scheduling problems that are complicated due to incomplete information of the future. On behalf of NKD – the large textile discounter – we analyzed how clothing sizes could be optimally distributed among over one thousand branches with respect to a demand that is hard to estimate and maximum estimated benefits (please see here for further information).
In the field of fundamental mathematical structures we are concerned with a method to enumerate geometrical objects. Especially the software package TOPCOM has to be noted here.
