Many optimization problem exhibit a modular structure and decompose into smaller units. Algorithms and analytic tools for the evaluation of individual models have been succesfully investigated. However, little is known about the interplay of heterogenous modules in complex systems.

The goal of the project is to exploit the structure of modular real-time(online) systems in order to develop concepts for the mathematical evaluation of composed algorithms. A key question in this context is, whether and when a performance guarantee for all the (comparatively simple) modules does ensure a good behavior of the whole (complex) system. We focus on combinatorial optimization problems arising in transportation and logistics. To substantiate our theoretical findings, we perform simulation experiments with special purpose tools developed at ZIB.

• DFG Research Center Matheon "Mathematics for key technologies" , Project B8 "Time-dependent Multicommodity Flows: Theory and Applications"
• DFG Research Center Matheon "Mathematics for key technologies" , Project C5 "Stochastic and nonlinear methods for solving resource constrained scheduling problems"
• DFG Research Center Matheon "Mathematics for key technologies" , Project C6 "Stability, Sensitivity, and Robustness in Combinatorial Online Optimization"
• DFG Research Center Matheon "Mathematics for key technologies" , Project C7 "Mean-risk models for electricity portfolio management and stochastic programming"
• eCom-Logistik, Falkensee (Mr. Eckle)
• Hermes Technischer Kundendienst GmbH & Co. KG (Frank Hinsch)
• Allgemeiner Deutscher Automobilclub (Renate Ahlers)
• Intergraph Public Safety (Sebastian Stepfer)