Efficient Propagation of Uncertainties in Manufacturing Supply Chains: Time Buckets, L-leap and Multilevel Monte Carlo

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.