A new generic timed Petri net model for design and performance analysis of a dual kanban flexible manufacturing system

A new generic black token timed Petri net (PN) model of FMS based on the process plan is presented. The model allows modelling the FMS configuration, determining the optimal work in process, the number of kanban cards and the required capacity for a given maximum production rate. The lead-time and utilization of each station can be determined. Each station can have multiple identical servers. The approach is based on modelling the FMS as an event graph with part circuits, kanban circuits and sequencing circuits. The part circuits contain tokens that represent parts with attached kanban cards. In the kanban circuits there will be places containing tokens that represent kanban Move Cards (MC) and Production Cards (PC). Circuits called sequencing circuits will model the sequencing of the parts on each station. The tokens in these sequencing circuits represent the number of identical servers. The optimal solution of the model is obtained in three steps. The first step is the initial marking of the PN. The second step involves determination of the invariants of the PN. The third is solving a linear programming model.