Hierarchical decomposition of production and capacity investment decisions in stochastic manufacturing systems

This paper is concerned with hierarchical decisions regarding production and investment in capacity in manufacturing systems with production subject to breakdown and repair. The production capacity can be increased by investing continuously in new capacity which is available upon completion. The decision variables are the rates of production and investment in capacity. The investment rate is assumed to have an upper bound. If, as assumed, the rates of breakdown and repair of production equipment are much larger than the rate of discounting of costs, the given problem can be approximated by a simpler problem in which the stochastic production capacity is replaced by the average capacity. Asymptotically optimal controls for the given problem are constructed from nearly optimal controls of the limiting problem. In addition, the behavior of the solution as the investment rate is allowed to become arbitrarily large is analysed.