Stochastic coloured Petri net (SCPN) models of traditional and flexible kanban systems

Modelling and analysis of kanban-controlled (just-in-time) production syste ms under realistic assumptions presents a number of challenges, including t he ability to conduct both qualitative and quantitative analysis, and the a bility to model control policies. These challenges are due, in part, to sta tion interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modelling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modelling manufactu ring systems. PNs are a graphical and mathematical technique useful for mod elling concurrent, asynchronous, distributed, parallel, non-deterministic a nd stochastic systems. PN models can be analysed to determine both their qu alitative and quantitative properties. In this paper, we develop stochastic , coloured PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible k anban system (FKS) policy. The resulting models can be used to represent JI T systems of arbitrary size, producing single or multiple types of products , with fixed order points greater than or equal to 1. The models are shown to be live and bounded, and can be simulated to produce quantitative result s. Sample simulation results are presented to illustrate the models' capabi lities.