On Optimality of 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 break-down and repair. The machine capacities are modeled by a Markov chain. The objective is to choose the input rates at the various machines over time in order to meet the demand for the system’s production at the minimum long-run average cost of production and surplus, while ensuring that the inventories in internal buffers between adjacent machines remain nonnegative. The problem is formulated as a stochastic dynamic program. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the potential function.