oAssessment of Different Proximity Metrics in Clustering of Geometric Features: An Optimal Stock Design for Hybrid Manufacturing CAPP

Abstract

Stock design is a critical yet underexplored factor in Hybrid Manufacturing (HM) process planning, directly influencing material efficiency and production cycle time. This study extends a constrained clustering framework for HM stock design by systematically evaluating how the choice of proximity metric influences cluster formation and downstream manufacturing performance. Four distance measures, Hausdorff, Modified Hausdorff, Chamfer, and Sum of Minimum Distances, were incorporated into a clustering optimization model and evaluated across multiple cluster counts on two industrially representative prismatic components: a 22-feature part (15 additive, 7 subtractive) and a 15-feature clip-holder (7 additive, 8 subtractive). Cluster similarity, quantified via the Adjusted Rand Index and validated through a blocked two-way ANOVA with replication across three aspect-ratio variants, revealed strong consensus at low cluster counts but increasing divergence as partitioning granularity grew, indicating that metric selection becomes critical at higher partitioning levels. The resulting configurations were integrated into an extended HM Computer-Aided Process Planning model to assess manufacturing cycle time. For the 22-feature part, the Sum of Minimum Distances achieved a 9.1% cycle time reduction relative to the Hausdorff baseline. For the clip-holder, multiple metrics converged to the same minimum cycle time, indicating that metric sensitivity is part-dependent. These findings provide a structured methodology for proximity metric selection in HM stock design and demonstrate its tangible impact on manufacturing efficiency.