Joint production, inventory rationing, and order admission control of a stochastic manufacturing system with setups

In this paper, we examine a single-stage, manufacturing system with setups, which produces a single part type to satisfy demand from two customer classes. We address the problem of coordinating production control, stock rationing, and order admission decisions. The optimal policy, in respect to minimizing holding, backorder, lost sales, and setup costs, is derived by formulating the underlying problem as a Markov Decision Process and solving it by means of Dynamic Programming. The structure of the optimal policy is investigated numerically and, on that basis, a parametric control policy is proposed. The Markov chain model of the single-machine manufacturing system, operating under the proposed policy, is developed. Furthermore, analytical expressions of the steady-state probabilities and of the expected total cost are obtained. The proposed policy is compared to the optimal, as well as to three heuristics, in an extended series of experiments. The numerical results indicate that the proposed policy is a very good approximation of the optimal one, and that it largely outperforms the alternative control policies.