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 ta ndem machines. The production is regulated by a continuous version of buffe r control. Our goal is to obtain an optimal buffer-control policy to minimi ze a long-run average cost function. Concentrating on threshold type of con trol 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 anal ysis techniques, and approximate the optimal value of the parameter via a c onstant step-size stochastic approximation algorithm. An analysis for error accumulation in perturbation propagation is undertaken, and a sufficient c ondition for breaking the propagation chain is derived. In addition, we sho w that the event of breaking the perturbation propagation chain is recurren t if the system has sufficient capacity, derive the consistency of the grad ient estimators, and establish the convergence of the iterative algorithm. We also treat non-Markovian models with the machine repair time following a n Erlang distribution, and provide numerical examples to illustrate the pro posed algorithm.