Production controls in stochastic tandem two-machine systems with state constraints

This paper concerns production controls in manufacturing systems with two tandem unreliable machines. Since the inventory level in the internal buffer can not be negative, and the sizes of both internal and external buffers are practically finite, the problem is one with state constraints. As optimal solutions to this problem are extremely difficult to obtain due to the uncertainty in machines´ capacities as well as the presence of the state constraints, a deterministic limiting problem in which the stochastic machines capacities are replaced by their mean capacities is considered instead. “Weak-Lipschitz” property of the value functions for both original and limiting problems is introduced and proved, and a “constraint domain approximation” approach is developed to show that the value function of the original problem converges to that of the limiting problem as the rate of change in machines´ states approaches infinity. Production controls for the original problem are explicitly constructed from near-optimal controls of the limiting problem in a way which guarantees their asymptotic optimality, and the error estimate for the constructed controls is obtained