Optimal control of production systems with unreliable machines and finite buffers

We present a formulation for the optimal control of discrete event dynamic processes which represent production systems with unreliable machines and buffers of finite capacity. We derive an optimum control strategy that is critically based on the fact that the discrete event dynamic behavior of the system is approximately represented with a hybrid model. We introduce a deterministic fluid network model where the average flow rates through the machines are the control variables and with an original approach we show that the dynamics of the system easily translate into a discrete-time, time-varying state variable model, where the optimum machine production rates can be easily obtained by solving a sequence of linear programming problems.