Modelling and optimisation of assembly processes

The following article is a case study for scheduling of assembly processes. Two optimisation methods, mixed integer programming solver and heuristic simulation-based optimisation are compared to each other. It can be shown, up to which model complexity the solver methods have the advantage over the simulation-based methods concerning a possible online application. Both the mathematical formulation as well as the discrete event simulation system, bases on a meta-model - a special Petri net. It is shown that bipartite graphs, i.e. Petri nets, avoid ambiguities in the case of alternative assembly sequences and have advantages in comparison to the usual simple precedence graphs. The results of optimisation experiments are described by the example of assembling a numeric controlled milling table. The model is capable of reflecting multiple parallel assembly processes, alternative assembly steps and can predict characteristics like utilisation, stock or adherence to schedules.