Asymptotic Optimality in Hierarchical Control of Manufacturing Systems under Uncertainty : State of the Art

This paper presents a state-of-the-art review of asymptotic analyses of hierarchical manufacturing systems with stochastic demand and machines subject to breakdown and repair. The rate of change in machine states is much larger than the rate of fluctuation in demand and the rate of discounting of costs. The machine state process is modelled as a Markov process which may depend on the rate of production, a control variable in the system. Results for construction of feedback and open loop asymptotic optimal controls and associated error bounds are discussed