Average cost optimal policy for a stochastic two-machine flowshop with limited work-in-process

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a Stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.