Modeling and optimization of kanban controlled manufacturing systems with GSPN including QN

We investigate the kanban assignment problem for assembly kanban systems. We use REMO, a general purpose tool for optimization. REMO includes several algorithms like hill climbing and genetic algorithms and has an easily adaptable interface to performance analysis tools. As we try to find an optimal kanban assignment with respect to certain performance measures of the system, a fast performance analysis is a crucial factor for sensible and successful application of optimization algorithms. For this purpose we introduce Petri nets including queueing nets (PNiQ) as modeling formalism especially suited for optimization of arbitrary kanban systems. At modeling level, PNiQ allow the use of both the concise description of queueing nets where possible and the notation of stochastic Petri nets where needed, e.g. to model fork/join needed for the matching of kanbans and parts. Approximate performance analysis is carried out by decomposition and aggregation of the queueing net parts. This technique provides a fast numerical solution even for large systems as important requirement for the application of optimization algorithms. The optimization not only yields optimal kanban assignments for various kanban systems but also a common pattern in the set of solutions can be recognized.