Interlinked combinatorial and geometrical optimization problems in an autonomous automotive manufacturing industry

Research Project, 2017 – 2022

This PhD project aims to face some industrial challenging problems revealed in "Smart Assembly 4.0" and to develop suitable tools to solve them, where the goal is to connect mathematical modelling and analysis, algorithm development, and software implementation.

A first case to study in the project is to investigate the possible gains - in terms of robustness and throughput - of employing intersection-free robot programs, in which each robot is assigned to a private workspace. This construction simplifies the required mathematical models by removing the synchronization signals that prevent robot-robot collisions but also introduce time delays and other hardware costs, and reduce the robustness of the assembly cell. Hence, by developing mathematical models and algorithms to solve the intersection-free load balancing problem the suitability of this simplification for different types of assembly cells can be investigated.

Some relevant problem classes for study and modelling within the project are generalizations of vehicle routing problems and generalized Voronoi diagrams. The modelled problems will be analysed with respect to properties such as (computational) complexity and polyhedral and integrality properties. Solution approaches to be developed are, e.g., mathematical decomposition methods (such as column generation or cutting plane algorithms) and branch-and-price methods.