Optimization by simulation in manufacturing flow control models

Manufacturing flow control models (MFCM) for production planning of flexible manufacturing systems (FMS) with failure-prone machines are considered. To solve the control problem associated with an MCFM, most authors have used, at least formally, a continuous-time dynamic programming characterization of optimal policies. These optimality conditions take the form of a set of coupled Hamilton-Jacobi-Bellman (HJB) equations which are intractable for large-scale real-life systems. In this paper, the authors discuss an alternative approach, based on simulation and stochastic approximation for the computation of an approximation of the optimal policy in a class of policies indexed over a parameter set. This approach exploits the qualitative structure of the optimal feedback policy obtained from the solution of the HJB equations. By replacing the true Bellman value function with a quadratic approximation the policy depends in a known way on a finite number of parameters. The approach consists in optimizing the policy in the class thus defined