Rare-Event Simulation for Multistage Production-Inventory Systems

We consider the problem of precise estimation of service-level measures in multistage production-inventory systems when the system is managed for high levels of service. Precisely because the service level is high, stockouts, large backorders, and unfilled demands are rare and thus difficult to estimate by straightforward simulation. We propose and analyze alternative estimators, based on changing the demand distribution to make these rare events less rare. Whereas straightforward simulation for a fixed relative error results in computational requirements that grow exponentially in certain stock-level parameters, the requirements for our importance sampling estimators remain bounded for all parameter values. We provide bounds making it possible to determine the maximum number of replications required before any are generated. Numerical examples illustrate the effectiveness of our method.