Abstract
In this paper, we consider a production planning problem in an N-machine flowshop subject to breakdown and repair of machines and subject to non-negativity constraints on work-inprocess. The machine capacities and demand processes are assumed to be finite state Markov chains. The problem is to choose the rate of production over time so as to minimize the expected discounted cost of production and inventory/backlog over an infinite horizon. The problem is formulated as a stochastic dynamic prograrmming problem. It is shown that the value function of the problem is locally Lipschitz and is a solution to the dynamic prograrmming equation together with certain boundary conditions. Optimal feedback control policies are obtained
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