Optimal dynamic load distribution in a class of flow-type flexible manufacturing systems

This paper studies optimal dynamic load-distribution among parallel single-stage stations in flexible manufacturing systems and characterizes the form of the optimal policies as a function of the system state. Each work station maintains its own buffer and has independent input and output processes. At each decision epoch, a central Work-In-Process controller redistributes and routes jobs among all stations to minimize the total expected operating cost of the network system. The optimal policy for the system prescribes how many jobs will be sent to (taken from) each station so that optimal load balancing among all stations is implemented. The model takes into account holding and shortage costs for all the stations, which are assumed to be convex increasing functions, and routing costs as well. It is proved that the optimal action (number of jobs to be received) for a station is monotonically decreasing, as the number of jobs at the station grows, and is monotonically increasing, as the number of jobs at any other station grows. The resultant properties of the optimal policies for the model give fundamental guidelines on how optimal routing can be done among parallel stations by generalizing from a single-stage situation. Finally, a numerical example is presented to display the analytically proven properties of the optimal policies.