Asymptotic Optimal Feedback Controls in Stochastic Dynamic Two-Machine Flowshops

In this paper, we treat an optimal control problem of a stochastic two-machine flowshop with machines subject to random breakdown and repair. While the problem is difficult to solve, it can be approximated by a deterministic problem when the rates of machine failure and repair become large. Furthermore, beginning with the solution of the deterministic problem, we can construct a feedback control for the stochastic flowshop that is asymptotically optimal with respect to the rates of changes in machine states. We also show that a threshold type control known also as Kanban control is asymptotically optimal in some cases and not in others