A topological analytics framework for preserving decision structure in supply chain inventory classification

Abstract

Ineffective inventory classification compromises supply chain resilience when criteria selection methods conflate statistical prominence with decision utility. Standard techniques, specifically Principal Component Analysis (PCA), Recursive Feature Elimination (RFE), and Mutual Information (MI), risk inducing projection loss by excising structurally critical variables. We apply the Topological-Structural Axiomatic Validation (T-SAV) framework, which models criteria sets as simplicial complexes (structures built from points and their higher-order connections) and maps the decision axioms of completeness and non-redundancy to computable topological invariants. Using empirical data from a telecommunications infrastructure provider, we benchmark T-SAV against PCA, RFE, and MI. Results indicate distinct failure modes: PCA fragments the decision manifold into 14 disconnected components (consensus bias), while RFE discards control variables lacking predictive correlation (target dependency). T-SAV instead retains orthogonal keystone criteria that bridge financial and physical operational dimensions. T-SAV achieves a 99.63% variation capture ratio, against PCA (99.24%), MI (99.28%), and RFE (97.39%). Bootstrap resampling (B = 10,000) indicates these differences are statistically significant (p < 0.001), though the margin over PCA and MI is modest and the principal distinction is structural, since T-SAV alone satisfies both topological axioms. T-SAV also shows the lowest resampling variance (SD = 0.26), against markedly greater instability in RFE (SD = 1.84). In this empirical setting, topological validation can reveal structural weaknesses that statistical covariance and predictive error minimisation may miss. Practically, the framework lets managers check, before deployment, whether a criteria set holds together, lowering the risk of discarding criteria that are statistically quiet but operationally critical.