In: International Journal of Production Research, Vol. 77, No. 9, pages 2135-2158. 1999.
Abstract: Modelling and analysis of kanban-controlled (just-in-time) production systems under realistic assumptions presents a number of challenges, including the ability to conduct both qualitative and quantitative analysis, and the ability to model control policies. These challenges are due, in part, to station interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modeling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modeling manufacturing systems. PNs are a graphical and mathematical technique useful for modeling concurrent, asynchronous, distributed, parallel, non-deterministic and stochastic systems. PN models can be analyzed to determine both their qualitative and quantitative properties. In this paper, we develop stochastic, colored PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible kanban system (FKS) policy. The resulting models can be used to represent JIT 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 results. Sample simulation results are presented to illustrate the models' capabilities.
Keywords: Petri nets, automated manufacturing systems, cell coordination, colored, just-in-time manufacturing, kanban systems, stochastic Petri nets.