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Invariant Set of the Lorenz System Show image information
Attractor of the Mackey-Glass Equation Show image information
Unstable manifold of the Kuramoto-Sivashinsky equation Show image information
Petersen Graph Show image information

Invariant Set of the Lorenz System

Attractor of the Mackey-Glass Equation

Unstable manifold of the Kuramoto-Sivashinsky equation

Petersen Graph

Chair of Applied Mathematics

Professor Dr. Michael Dellnitz

The primary strength of this chair is the development of efficient algorithms for the numerical treatment of Dynamical Systems and Optimization Problems. Research activities concentrate on both theoretical aspects of these algorithms and their numerical realization.

Research activities:

Current research projects:

IBOSS

Information-Based Optimization of Surgery Schedules

The health care sector is one of the most important economy branches in Germany which is subject to steadily increasing expenses over the last years. One of the main cost components are hospitals. In particular, operating rooms generate a huge portion of the hospitals expenses. In the future, a more efficient operation room management is needed to reduce operating cost and staff overtime to allow patient therapies of higher quality.

Project Description

The project Information-Based Optimization of Surgery Schedules (IBOSS) focuses on the development of new and efficient methods to improve the individual work- and patient flow in hospitals.  We work closely with our project partner Charité Berlin in order to bring new algorithmic concepts for difficult problems into practice. One part of the project includes the predictive analysis of activity durations to accurately model the involved sub-processes in a hospital. On that basis, we develop algorithms to compute optimized micro- and macro-level surgery schedules. The particular focus lies on the algorithmic treatment of stochastic influences on the planned schedule, such as operational delays and sudden emergencies. Our solution methodologies are based on the following techniques 

  • Optimal learning of classificators in data analysis;
  • Stochastic/robust resource-constrained project scheduling;
  • Multiobjective Optimization and Stochastic Control of Markov Chains;
  • Dynamic interplay between micro- and macro models.

The future goal is to integrate an adaptive self-learning optimization system that automatically recognizes variations and trends in a changing therapy evironment.  A further objective is the implementation of a first computational test and evaluation system for practical usage.

Multiobjective Optimization of Dynamic Operation Room Models

Besides determining an optimal schedule for operations, there are numerous additional factors that can influence the quality of operation planning. These are, for example, allocation of personnel and medication as well as starting times for the individual subtasks. The corresponding decisions can be made with respect to multiple, in general conflicting criteria, amongst which are the quality of the medical treatment, the ability to react to unforeseen events, the satisfaction of personnel as well as patients and economic factors. This requires the computation of the set of optimal compromises between these objectives, the so-called Pareto set.

The goal of the part of the project carried out in Paderborn is therefore to develop a dynamic model of the operating process which is then used in an optimization algorithm running in parallel to the real process. Hence, concurrent objectives which are subject to uncertainties as well as  real-time applicability have to be taken into account. Based on the current priorities, an operation planner can select an optimal compromise from the Pareto set. Furthermore, the results can be utilized to assist and enhance the task of operation scheduling.

This is a joint project with the following institutions: Zuse Institute Berlin (ZIB), FU Berlin, Charité

Project Homepage: Information-Based Optimization of Surgery Schedules

Further information:
Head

Prof. Dr. Michael Dellnitz

Chair of Applied Mathematics

Michael Dellnitz
Phone:
+49 5251 60-2649
Fax:
+49 5251 60-4216
Office:
TP21.1.27

Secretary

Marianne Kalle

Chair of Applied Mathematics

Marianne Kalle
Phone:
+49 5251 60-2658
Fax:
+49 5251 60-4216
Office:
TP21.1.27

Office hours:

Mo.-Fr. 08:00-12:00 Uhr

The University for the Information Society