Hierarchical feedback controls in two-machine flowshops under uncertainty

This paper deals with an optimal control problem of stochastic two-machine flowshops with machines subject to random breakdowns and repairs. Since the sizes of both internal and external buffers are practically finite, the problem is one with state constraints. As the problem is extremely difficult to solve, it can be approximated by a deterministic problem in which the stochastic machines´ capacities are replaced by their average capacities when the rates of machine failures and repairs become large. An explicit optimal feedback control for the deterministic problem is obtained based on a “constraint domain approximation” approach. Furthermore, beginning with the solution of the deterministic problem, a feedback control for the stochastic flowshops is constructed, which is proved to be asymptotically optimal with respect to the rate of change in machine states