Dynamics of flexible manufacturing systems

In this paper we consider the problem of the dynamical control of a system composed of two working stations; each station is modeled by a queue which feeds one or more machine tools. This system can be considered as a first simple Flexible Manufacturing System (FMS) which allows to be dynamically controlled and, if necessary, in real time too. Each queue has a limited capacity and is characterized by a set of differential equations, in which the variables are the queue state probabilities (Equations of Chapman-Kolmogorov). The queues are related each other by the condition that the throughput of the first queue is equal to the input rate of the second one. Control inputs are the service rates of the working stations and are obtained by minimizing a suitable functional. The minimization problem, formulated in terms of Pontryagin´s minimum principle, is solved numerically by using the method of steepest descent. Optimal control was evaluated by simulation; the mean cost is substantially equal to the one obtained by computation.