Enhanced stochastic fluid approximation approaches for accurate performance measurement and efficient I.P.A. estimation

We consider stochastic fluid model (SFM) approximations of discrete stochastic models representing production systems with inventory control policies ranging from simple Kanban policies to multiple echelon policies. We propose several approximation strategies of the discrete model and synthesize them to construct enhanced SFMs that achieve significant reductions on the approximation error associated with simple fluid approximations used in the literature which ignore the impact of part integrality on performance statistics. Because of the computational efficiency that it introduces, fluid model approximation has been used widely to estimate system performance and to design system parameters. However, the associated estimation error of the fluid approximation is of ten excessive. By comparing system dynamics and event propagation rules in discrete models and simple SFMs, we conclude that the overwhelming portion of the observed estimation error is caused by the impact of integral relaxation on propagation delays. Several strategies are incorporated in enhanced SFMs to minimize the approximation error. We develop Monte Carlo simulation algorithms for discrete models and the associated enhanced SFMs for systems containing finite intermediate inventory storage/buffer capacities and failure-prone machines. Performance estimation error and computational complexity measured in simulation experiments demonstrate the benefits of our enhanced fluid approximation strategies. To take advantage of sensitivity information in the optimal design of system and inventory control parameters, we also implement Infinitesimal Perturbation Analysis (IPA) estimators in the context of the proposed SFMs. The analysis on the biased/unbiased properties of the IPA estimators supports the effectiveness of our enhanced SFMs. Computation experience supports the elegance of IPA estimators relative to finite difference estimators, the only option available in the context of discrete models, and the usefulness of IPA in the context of the enhanced SFMs that we propose.