New edge-based Shapley value optimizes supply chain allocation in 7 network types

A new research paper from Taiki Yamada, Taisuke Matsubae, and Tomoya Akamatsu introduces the edge-based Shapley value (ESV), a novel allocation rule in cooperative game theory designed specifically for supply chain networks. Unlike traditional rules such as the Shapley value or Myerson value, which evaluate contributions based on node-level characteristics or connected subgraphs, ESV shifts the characteristic function from node sets to edge sets. This allows it to capture the functional role of edges that represent supply routes with associated costs and flow volumes. The authors establish theoretical foundations, showing ESV retains key properties like fairness and symmetry, and demonstrate its relationship to classical rules.

ESV is validated through empirical benchmarks on seven distinct supply network topologies: serial, parallel-redundant, asymmetric tier, scale-free, clustered, layered DAG, and single-point-of-failure structures. A key finding is that ESV rankings are more robust to prior network disruption than the standard single-node removal measure. When portions of the network have already failed, the ESV computed on the original intact network more accurately predicts the remaining nodes' importance because it inherently averages over all possible degradation states. This makes ESV a powerful tool for supply chain risk management and resource allocation.