Modelling for flexible manufacturing systems and structural properties of optimal work routing policy

We consider flexible manufacturing systems (FMSs) which are composed of a set of workstations linked together with a material handling system (MHS). Each workstation consists of an input buffer, a single machine and an output buffer. The MHS consisting of a single cart routes work among the workstations according to the process paths required by the work. We deal with an optimal control problem in this FMS. We model the FMS as a closed queueing network. In the model, the cart routes the work to the workstations in accordance with a Markov routing with exponentially distributed routing time, and the machines process work with exponentially distributed processing time. An objective is to find a work routing policy that maximizes the total expected reward earned by operating machines. This optimal control problem is formulated as an undiscounted semi-Markov decision process. Structural properties of an optimal policy are analysed. Moreover, a sufficient condition is derived for the optimal policy to be of control limit type. An example is given to illustrate the result.