Stability of Flexible Manufacturing Systems

We consider a flexible manufacturing facility that can be operated in any of m different modes. While running in mode k certain intermediate products are consumed and other intermediate or finished products are created. There may be variability in the manufacturing process, as well as random arrivals of raw materials and orders for finished products. We establish conditions that ensure demands can be satisfied while maintaining bounded levels of inventories. These results that may be viewed as generalizing to the flexible manufacturing context the notion of stability for a queueing system. The aim of a manufacturing system is to transform raw materials, parts, and subassemblies into other parts, subassemblies, and finished products. In this paper, we consider a model of a flexible manu-facturing facility (FMS) in which production can take place in any of m different modes or configurations. There is no cost or delay in changing modes. When production takes place in mode k certain intermediate products are consumed and other intermediate or fin-ished products are created. We suppose that in total the system is concerned with n different products. Here we use the word product to refer to any unit of order, raw material, component, subassembly, work in progress, or finished product. Suppose that running production for one period in mode k changes the inventory level of product i by Sk,i units. It is a key idea in this paper that Sk,i may be a random variable. This reflects the fact that unpredictable variations in both the demand and production processes are usu-ally major sources of difficulty in managing a manu-facturing facility. It is often the case that inventories of intermediate products or raw materials are required to cope with these variations. However, there is usu-ally a cost to carrying inventories and it is desirable that inventories remain small, even zero. Other re-searchers have considered such questions. For exam