Optimal threshold control for failure-prone tandem production systems

We consider the flow dynamics of a tandem production system formed by two failure-prone machines separated by a buffer stock. The production rates of the machines are regulated by a feedback mechanism which solves an associated optimal control problem with an average cost criterion. The cost structure penalizes both the entrance into and the sojourn on the buffer boundaries. The generic structure of the optimal control involves four buffer content thresholds. When the buffer content crosses these thresholds, the production rates are tuned to reduce the tendency to enter into the buffer boundaries. Using the fluid modelling framework, we obtain analytical results for the stationary buffer level distribution in the case where an operating machine can produce with, either a “nominal” or a “reduced” rate. In the stationary regime, the optimal positions of the buffer thresholds, the throughput and the average buffer content are presented.