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

Uncertainty quantification 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 D-leap method [3] developed in the chemical engineering community for the acceleration of stochastic DES of chemical reactions. The L-leap method updates the system state vector at discrete time points and imposes constant production rates and Boolean values associated with the logic of a supply chain 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. The MLMC approach can be $10$ times faster than the standard Monte Carlo (MC) method which computes the samples exactly using DES. We demonstrate the efficiency and accuracy of our methods using five material flow examples. The first three examples demonstrate the performance of the time bucket method in both deterministic and stochastic settings for a simple push system, a simple pull system and a complex pull system with features like back-ordering, priority-production and transportation. The fourth example considers multilevel uncertainty propagation of the push system under parametric uncertainties. The fifth example considers multilevel uncertainty propagation of the complex pull system under both parametric and stochastic uncertainties.