Flow Control of Stochastic Manufacturing Systems: A Simulation-based Design Approach using Perturbation Analysis for Second Derivative Estimation

The optimal production control of a flexible manufacturing system subject to random Markov disturbances is considered. The resulting optimality conditions, which are expressed as a system of stochastic partial differential equations, are analytically unsolvable for non-trivial systems. An alternative, simulation-based, numerical technique has been proposed in [2]. It uses infinitesimal perturbation analysis to estimate first-order sensitivities ties of the parameters of a quadratic approximation to the value function that characterises the optimal policy. Using this gradient estimate, a stochastic optimization alorithm is applied to optimize the parameters. This technique is extended here to generate second-order information of the design parameters to speed up convergence.