On Applications of Graph Theory in Inventory Management: A Comprehensive Review

Modern supply chains have inventory systems that are networked in nature with various echelons, facilities, and products interacting with uncertain demand and lead times. This network structure is often simplified or ignored by classical inventory models, which restricts their use in complex and globalised systems. Graph theory provides a natural language for modelling inventory systems in terms of a network of nodes and edges, and offers the means to integrate modelling of classification, control, routing, and risk. This essay is a detailed literature review of the use of graph theory in inventory management. The review is divided into four major themes: (i) graph- theoretic modeling of multi-echelon and time-space inventory networks, (ii) multi-criteria inventory classification through graph-based decision models, (iii) graph-based optimization of inventory and inventory-routing decisions, and (iv) vulnerability, risk, and data-driven methods with the use of graph neural networks (GNNs). Within these themes, the article combines over twenty-five major contributions, describes the patterns in modelling and techniques of solution, and notes how the factor of graph-theoretic thinking has transformed the analysis of inventory systems. It is shown that the research ends with an agenda of the research, which highlights dynamic graphs, combined classification-control frameworks, and hybrid OR-ML networks operating directly on network data.