Efficient propagation of uncertainties in manufacturing supply chains: Time buckets, L-leap, and multilevel Monte Carlo methods

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., τ -leap [34], Dleap [6], 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.

Using stochastic simulation modelling to study occupancy levels of decentralised admission avoidance units in Norway

“…We are not aware of other studies that have modelled admissions and discharges to MAUs nor of other examples of studies that have assessed the operational impacts of MAU specific policies. Time bucket modelling and other stochastic approaches, however, have been used to answer similar questions in supply chain modelling e.g., in warehouse management, where discrete event simulation may be computationally too costly or where a simpler approach is preferable (Chiang et al, 2020 ; Gong & de Koster, 2011 ; Thierry et al, 2008 ).…”

“…Discrete simulations can be used to represent complex systems and behaviours occurring within and between individuals, populations, and their environments (Günal & Pidd, 2010 ; Karnon et al, 2012 ; Ramwadhdoebe et al, 2009 ; Robinson, 2014b ; Zhang, 2018 ). There are two main approaches to making time advance in discrete simulation – from one event to the next, also known as discrete event simulation or in fixed increments, known as discrete time simulation (Chiang et al, 2020 ; Phillips, 2007 ; Robinson, 2014a ; Thierry et al, 2008 ).…”

“…It thus made sense to represent the model time in steps of 24 h. This simplified the implementation, as all events were drawn at midnight each day and thus the usual discrete event mechanism of jumping to the next time point when an event occurs was not required. However, discrete time simulation requires aggregation of multiple events during a fixed time period, which results in the loss of some interactions between events thus making it less accurate than discrete event simulation (Chiang et al, 2020 ).…”

Agent-based models under uncertainty

“…in discrete event simulation, the introduction of “time buckets” which are intervals of time in which multiple events can occur. 15 The equivalent strategy for an ABM would be a coarsening strategy that increases the fixed time step. This might be considered as introducing temporal epistemic uncertainty into an ABM, but as it handles this uncertainty in a simplistic way (in other words, by ignoring it) and with the simulation losing some of its detail depending on the magnitude of the time-step increase, which may not be desirable.…”

High dimensional reliability analysis based on combinations of adaptive Kriging and dimension reduction technique

“…In engineering practice, the uncertainty from physical system and external environment has an important impact on system reliability and safety 1,2 . ] Uncertainty propagation 3,4 and uncertainty quantification 5,6 are two important aspects in reliability engineering. Reliability analysis aims to estimate probability of failure under various uncertainties.…”