A Multi-class Approximation Technique for the Analysis of Kanban-Like Control Systems

Analytical methods have been proposed in the literature for performance evaluation of kanban control systems. Among them, the method presented in [Di Mascolo et al. 96] appears to be of special interest since it can handle manufacturing stages consisting of any number of machines and it is fairly accurate. In this paper, we present a new way of deriving the analytical method presented in [Di Mascolo et al. 96]. The approach is to see the queueing network of the kanban control system as a multiclass queueing network in which each kanban loop is represented by a class of customers. This allows us to use the general technique proposed in [Baynat and Dallery 96] for analyzing multiclass queueing network using product-form approximation methods. In terms of equations, the new method is equivalent to that presented in [Di Mascolo et al. 96]. However, the computational algorithm is much more efficient since it avoids the two levels of iterations involved in the original algorithm. Another major advantage of the new method over that originally proposed in [Di Mascolo et al. 96] is that it provides a general framework for the analysis of more general kanban systems. Indeed, we show in this paper how this approach can easily be extended in order to handle kanban systems with multiple consumers and multiple suppliers, kanban controlled assembly systems and generalized kanban systems [Buzacott 89].