Action-based modeling asks: What’s behind what’s happening?

Complex systems are ubiquitous in today’s technological world — whether they be supply chain networks, protein interactions, climate change, or a whole host of other examples — and a better understanding of them can lead to deeper scientific insights and more effective engineered systems. Supply chains are a good example, and have become part of the everyday lexicon, what with all the disruptions that have emerged during the COVID-19 pandemic, including unavailability of goods, long shipping delays, overbooked contractors, and high car prices.

Supply chain networks are complicated, deeply interconnected systems of producers, suppliers, distributors, retail and e-commerce sellers, and others who fashion — and frequently reconfigure — connections and information flows in building and selling their products. The goal is efficiency, continuity, and elasticity in the face of unexpected constraints and events.

A model is a computational representation of something in the real world, used to gain insight into the real system. In particular, complex network models, such as action-based approaches, are being used increasingly to model supply chain interactions and performance, with the aim of synthesizing supply chain networks for more resilience and improved operation.

Action-based modeling is a general framework to model complex systems like supply chains from the perspective that we aren’t trying to recreate an observed network, but rather, the system that generated it. Our approach assumes a system is composed of a set of nodes — in supply chain, each with a specialized task — that are able to interact with one another according to one or more rules and actions.

A procedure for determining action matrix M: Algorithm S1 probabilistically adds the required number of edges using ABNG-PA(1). Algorithm S2 compares a set of synthesized networks to the target using the user-defined structural characteristics in order to determine the representativeness of action matrix M. Algorithm S3 perturbs M and retains a set of best-fit solutions. The process repeats until a termination criteria (e.g., number of iterations) is satisfied. (Arora, V., Ventresca, M. Action-based Modeling of Complex Networks. Sci Rep 7, 6673 (2017). https://doi.org/10.1038/s41598-017-05444-4)

Modelers represent this as a vector (a quantity with both magnitude and direction) of probabilities for the node, whose “dimension” is then equal to the number of possible actions that can be taken. Each node has a vector of such probabilities; we can classify nodes based on how similar their vectors are. This results in a matrix of dimension, which is equal to the number of node classes by the number of actions. A stochastic algorithm — one that estimates the probability of various outcomes, factoring in randomness — then takes this matrix as input, and can synthesize networks by iterating over the matrix.

We believe that action-based modeling has the potential to help us understand and sustain the operations of supply chains in the face of disruption. This ability is vital, as supply chain disturbances — whether from the pandemic, cyberattacks, natural disasters, or other causes — can jeopardize economic recovery and weaken national security. The White House takes this so seriously that it created a Supply Chain Disruptions Task Force, signaling a “whole-of-government approach to assessing vulnerabilities in, and strengthening the resilience of, critical supply chains,” according to a June 8, 2021 briefing.

In sum, modeling has the potential to play an essential role in enhancing supply chains and other complex systems. It’s still an evolving discipline — there are always more questions to answer in the world of modeling! We are continually trying to improve existing methods, for example, by extending the action-based model through increased data integration, and using machine learning in concert with optimization methodology to make both more robust.

If the research community can gain deeper insight into complex systems through modeling, the impact will be significant, given how pervasive these systems are in modern society. Discoveries could aid in a multitude of innovations — such as devising cancer cures, designing social robot swarms, creating adaptive monitoring systems to detect and mitigate new diseases, and alerting policymakers to illicit behavior in supply networks like human trafficking.

It is possible that we can develop high-quality solutions to these problems without major advances in complex systems modeling. But I believe we can progress further, and faster, if tools like action-based modeling are further refined, and then deployed widely.

Mario Ventresca, PhD

Associate Professor, School of Industrial Engineering

Co-Director, Network Morphospace Lab

College of Engineering

Member, Purdue Institute for Inflammation, Immunology, and Infectious Disease

Purdue University

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