Optimal Production Planning in a Stochastic N-machine Flowshop with Long-Run Average Cost

This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines that are subject to breakdown and repair. The machine capacities are modeled as Markov chains. Since the number of parts in the internal buffers between any two the problem is inherently a state constrained problem. The objective is choose the input rates at the various machines over time in order to meet formulated as a stochastic dynamic programming problem. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the potential function