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 bu er control. Our goal is to obtain an optimal bu er-control policy to minimize a long run average cost function. Concentrating on threshold type of control policies, our e ort 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 su cient 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 su cient 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.