Title: Efficient Propagation of Uncertainties in Manufacturing Supply Chains: Time Buckets, L-leap and Multilevel Monte Carlo,
Abstract: Uncertainty propagation of large scale discrete supply chains can be
prohibitive when a large number of events occur during the simulated period and
discrete event simulations (DES) are costly. We present a time bucket method to
approximate and accelerate the DES of supply chains. Its stochastic version,
which we call the L(logistic)-leap method, can be viewed as an extension of the
leap methods, e.g., tau-leap, D-leap, developed in the chemical engineering
community for the acceleration of stochastic DES of chemical reactions. The
L-leap method instantaneously updates the system state vector at discrete time
points and the production rates and policies of a supply chain are assumed to
be stationary during each time bucket. We propose to use Multilevel Monte Carlo
(MLMC) to efficiently propagate the uncertainties in a supply chain network,
where the levels are naturally defined by the sizes of the time buckets of the
simulations. We demonstrate the efficiency and accuracy of our methods using
four numerical examples derived from a real world manufacturing material flow.
In these examples, our multilevel L-leap approach can be faster than the
standard Monte Carlo (MC) method by one or two orders of magnitudes without
compromising the accuracy.