Uncovering illicit supply networks and their interfaces to licit counterparts through graph-theoretic algorithms

Abstract

The rapid market growth of different illicit trades in recent years can be attributed to their discreet, yet effective, supply chains. This article presents a graph-theoretic approach for investigating the composition of illicit supply networks using limited information. Two key steps constitute our strategy. The first is the construction of a broad network that comprises entities suspected of participating in the illicit supply chain. Two intriguing concepts are involved here: unification of alternate Bills-of-materials and identification of entities positioned at the interface of licit and illicit supply chain; logical graph representation and graph matching techniques are applied to achieve those objectives. In the second step, we search for a set of dissimilar supply chain structures that criminals might likely adopt. We provide an integer linear programming formulation as well as a graph-theoretic representation for this problem, the latter of which leads us to a new variant of Steiner Tree problem: Generalized Group Steiner Tree Problem. Additionally, a three-step algorithmic approach of extracting single (cheapest), multiple and dissimilar trees is proposed to solve the problem. We conclude this work with a semi-real case study on counterfeit footwear to illustrate the utility of our approach in uncovering illicit trades. We also present extensive numerical studies to demonstrate scalability of our algorithms.

Keywords:

• Illicit trade
• bill-of-materials
• Steiner tree problem
• dissimilar trees
• illicit supply chains
• generalized group Steiner tree

Data availability statement

The (anonymized) case study data (see Section 6) is available to download from the code repository at https://github.com/moonzadihsar/Dissimilar_Supply-Networks (Anzoom et al., 2022b).

Additional information

Notes on contributors

Rashid Anzoom

Rashid Anzoom is a PhD student in the Department of Industrial and Enterprise Systems Engineering at University of Illinois, Urbana-Champaign. He received his MSc (2019) and BSc (2017) degrees in Industrial and Production Engineering (IPE) from Bangladesh University of Engineering and Technology. Rashid’s research interest includes operations research, data analytics, and supply chain.

Rakesh Nagi

Rakesh Nagi is Donald Biggar Willett Professor of Engineering at the University of Illinois, Urbana-Champaign. He served as the Department Head of Industrial and Enterprise Systems Engineering (2013-2019). He is an affiliate faculty in CS, ECE, CSL, and CSE. Previously he served as the Chair (2006-2012) and Professor of Industrial and Systems Engineering at the University at Buffalo (SUNY) (1993-2013). He has more than 200 journal and conference publications. Dr. Nagi’s academic interests are in big graphs/data, social networks, GPU-accelerated computing, graph algorithms, production systems, applied/military operations research and data fusion using graph-theoretic models.

Chrysafis Vogiatzis

Chrysafis Vogiatzis is a Teaching Assistant Professor in the Department of Industrial and Enterprise Systems Engineering at the University of Illinois, Urbana-Champaign. Previously he was an Assistant Professor of Industrial and Systems Engineering at North Carolina A&T State University. He received his PhD (2014) and MS (2012) degrees in Industrial and Systems Engineering at the University of Florida, and his Dipl. Eng. (2009) degree in Electrical and Computer Engineering at the Aristotle University of Thessaloniki in Greece. His academic interests include network optimization and analysis, decomposition techniques for combinatorial optimization, and applied operations research.