Hierarchical production controls in a stochastic two-machine flowshop with a finite internal buffer

The authors present an asymptotic analysis of hierarchical production planning in a manufacturing system with two tandem machines that are subject to breakdown and repair. The buffer between the two machines is assumed finite. Therefore, the number of parts in that buffer needs to be nonnegative and bounded above by the buffer size. As the rate of change in machine state approaches infinity, the analysis results in a limiting problem in which the stochastic machine capacity is replaced by the equilibrium mean capacity. The value function for the original problem is proved to converge to the value function of the limiting problem. Controls for the original problem are constructed from near optimal controls of the limiting problem in a way which guarantees their asymptotic optimality. The convergence rate of the value function of the original problem to that of the limiting problem together with the error estimate for the constructed asymptotically optimal controls are obtained