The phantom SPA method: an inventory problem revisited

It is widely accepted today that the Infinitesimal Perturbation Analysis (IPA) method for estimating sensitivities is the preferred method, when it is applicable. The major problem with IPA is handling certain kinds of discontinuities, such as thresholds. The Smoothed Perturbation Analysis (SPA) method was conceived applying a conditional expectation to a dynamic system, similar to the Filtered Monte Carlo Simulation. Conditioning smoothes out the discontinuities and then IPA can be applied to the conditional estimator. Since this alternative estimator has been partly integrated through the conditioning, some knowledge about the underlying distribution is required. When this is not available, SPA estimators require additional estimation. Traditionally, this has been implemented via off-line simulations that produce independent replications of a difference process. We propose here to bypass this operation by using parallel phantom systems: replicas of the original system that are conditional to the critical events of interest yet use common random numbers instead of independent replications. We show how the efficiency can dramatically improve from the gain in correlation (variance reduction) as well as the gain in computational effort (random variables are generated once and used for all parallel phantoms).