Control of a reentrant manufacturing system with setup times : the Kumar-Seidman case

In this paper we consider the control of a reentrant manufacturing system with setup times, as introduced by Kumar and Seidman. In most literature on control of a network of servers with setup times, first a policy is introduced and then the resulting network behavior is analyzed. In manufacturing systems the network typically is fixed and given a priori. Furthermore, optimal steady state behavior is desired. Therefore, this paper follows a different approach. First optimal steady state network behavior is determined, then a feedback controller is presented which makes the network converge towards this desired steady state behavior. The resulting controller is a non-distributed controller: each server needs global state information. For a manufacturing system this is not a problem, since global information typically is available. Finally it is shown that also a distributed controller (each server needs only local state information) can be used to achieve the same result.