Approximating an optimal production policy in a continuous flow line : Recurrence and asymptotic properties

This work is concerned with manufacturing systems with two failure-prone tandem machines. The production is regulated by a continuous version of buffer control. Our goal is to obtain an optimal buffer-control policy to minimize a long-run average cost function. Concentrating on threshold type of control policies, our effort is devoted to parameter optimization problems for the continuous material produce-to-stock models. We estimate the gradients of the cost function with respect to the parameter using perturbation analysis techniques, and approximate the optimal value of the parameter via a constant step-size stochastic approximation algorithm. An analysis for error accumulation in perturbation propagation is undertaken, and a sufficient condition for breaking the propagation chain is derived. In addition, we show that the event of breaking the perturbation propagation chain is recurrent if the system has sufficient capacity, derive the consistency of the gradient estimators, and establish the convergence of the iterative algorithm. We also treat non-Markovian models with the machine repair time following an Erlang distribution, and provide numerical examples to illustrate the proposed algorithm.