Timed matrix-based model of flexible manufacturing systems

Flexible manufacturing systems, sometimes involving hundreds of operations and tens of machines, are very complex in the sense of design, modelling, simulation and control. Their complexity has been a challenge for scientists and engineers through the years. The aim of this paper is to introduce timed matrix-based model of flexible manufacturing systems (FMS). Standard tools, such as timed Petri nets (PN) and max/plus algebra, become inconvenient when one tries to solve difficulties that arise in large FMS which contain shared resources. In order to make a matrix-based model capable of dealing with the problems of modelling and analysis of FMS dynamic behaviour, new matrices that contain operational times are included in the matrix model. That leads to simple procedures for determination of a resource cycle vector and timed wait relation matrix as well as mechanism for writing a marking transition equation as a nonlinear difference equation.