Further results on approximation of the optimal threshold values for manufacturing systems

The main goal in this work is to develop numerical algorithms for approximating the optimal threshold values of manufacturing systems. The key idea is to construct gradient estimates of the objective function with respect to the threshold values, and to use stochastic recursive algorithms for locating the optimal value. Motivated by designing more feasible methods of solutions, for systems described by differential equations with long run average cost functions, the authors previously developed stochastic optimization algorithms. The main idea is that instead of finding the optimal control of the systems, the authors turn the problem into an optimization problem by focusing their attention to the threshold control type of policies. The underlying problem is then converted to an optimization problem, namely, finding the optimal threshold values. In this paper, after briefly discussing the convergence of the algorithm, the authors concentrate on the rate of convergence issues