From algebra to industry: enhancing supply chain resilience with zero divisor graph

In the field of algebra, specifically in graph theory and ring theory, the zero divisor graph is defined as a graph where its vertices are the zero divisors of a ring and two vertices are adjacent if and only if the product of the vertices is zero. This project paper explores the innovative application of the zero divisor graphs, a concept rooted in abstract algebra, to business mathematics, with a particular focus on enhancing supply chain resilience. In this paper, the fundamental principles of the zero divisor graphs and their construction are introduced, followed by showcasing the practical applications in supply chain management. The zero divisor graphs can be used to represent suppliers, manufacturers, and distributors as their vertices, with edges indicating dependencies between them. By analyzing this graph, a business can identify which supplier failures (zero divisors) could cause significant disruptions (zero product) in the supply chain. This insight allows the company to develop contingency plans, diversify suppliers, and improve overall supply chain resilience.