Flow balance equations for the steady-state distribution of a flexible manufacturing system

Flow balance equations are formulated for the steady-state distribution of machine state and production surplus when a flexible manufacturing system is operated under a feedback control law. The long-run average cost is equal to the expectation in steady state of the instantaneous expenditure rate if the system is ergodic, and the optimum in a given family of control laws can be obtained by minimizing this cost criterion. Although the equations have a very intuitive interpretation, analytic solutions are known only in the one-dimensional case when a single commodity is produced according to a hedging point strategy