Average cost optimality for an unreliable two-machine flowshop with limited internal buffer

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 p roduction rates over time to minimize the long-run average inventory/backlo g and production costs. For sufficiently large upper bound on the work-in-p rocess, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the opti mal control policy if it exists.