Hypervolume-based scalar metrics for skill-driven flexibility assessment in manufacturing system (re)design

The transition towards sustainable and resilient production systems, central to Industry 5.0, requires manufacturing systems that can accommodate evolving product-process requirements across multiple product generations. Nevertheless, current system (re)design practices often remain rigid and project-oriented. Driven by short-term payback expectations that downplay the immediate impact of demand uncertainty, decision-makers frequently neglect the long-term value of flexibility, favouring equipment replacement over reconfiguration and reuse. This paper introduces a skill-driven assessment methodology that formally connects product-process requirements to the functional (re)use potential of production resources through a skill-driven assessment of resource-requirement alignment. The methodology evaluates the alignment of available resource skill sets with evolving requirements through three scalar metrics: compatibility, utilisation, and a geometric expansion effort ratio. In contrast to the binary feasibility checks prevalent in skill-based matching, these metrics quantify the degree and direction of geometric resource-requirement alignment within skill-specific property spaces. The resulting metrics rank resources by degree of alignment and trace the underlying gaps to their origin, supporting two critical manufacturing use cases: prioritising brownfield retention or retrofit candidates and comparing how well greenfield candidates cover future requirements. The mathematical fundamentals rely on skill-based hypervolume calculations, evaluated through a controlled illustrative example and case study using industrially representative data.