Modelling and Stochastic Simulation of Supply Chains

Summary

Supply chains are coordinated flows of materials from the suppliers to the locations where they are consumed [1]. Their dynamics can be very complex due for instance to the increasing complexity of today's industry. Severe disruptions of supply chains is another reason that makes the modelling and simulation of supply chains very challenging. For instance, during Covid-19 pandemic, supply chains were severely disrupted, and the production were negatively affected [2]. For these reasons, accurate modelling and simulation of complex supply chains are of paramount practical interest to avoid severe disruptions and to enhance supply chain's resilience.

The aim of the project is to use stochastic reactions networks (SRNs) to model supply chains dynamics [1]. SRNs are pure jump Markov processes that have been extensively used in the modelling of chemical reactions [3]. A preliminary plan of the project is
- Understand the notion of SRNs and how they are used to model chemical reactions. Moreover, get familiar with exact and approximate schemes used to simulate SRNs.
- Build the analogy between chemical reactions and supply chains modelling. Moreover, introduce the notion of delayed processes to count for delays in the supply chains processes (for instance, delays that are due to disruptions).
- Using the previous two steps, implement the algorithms to simulate the dynamics of supply chains.

The student may work on other research directions such as

- Use the concept of Monte Carlo methods to compute several statistical quantities (for instance, the expected number of a given part in the supply chain at a given future time).
- Another possible idea is to perform several simulations to motivate the importance of optimal inventory management. Moreover, suggest various strategies for optimal inventory management.
- Incorporate weather and climate information into the simulation process, to investigate how supply chains could be disrupted under future climate change.

References:

[1] Nai-Yuan Chiang, Yiqing Lin, and Quan Long. Efficient propagation of uncertainties in manufacturing supply chains: Time buckets, L-leap, and multilevel monte carlo methods. Operations Research Perspectives, 7:100144, 2020.

[2] Christopher W. Craighead, David J. Ketchen Jr., and Jessica L. Darby. Pandemics and supply chain management research: Toward a theoretical toolbox*. Decision Sciences, 51(4):838–866, 2020.

[3] David F Anderson. A modified next reaction method for simulating chemical systems with time dependent propensities and delays. The Journal of chemical physics, 127(21):214107, 2007

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