Segmented Multi-Tiered Capacitated Median-Covering Problem

Abstract The German banking landscape has undergone profound structural changes over the past two decades. Driven by digitalization, shifting customer behavior, and cost pressures, the number of physical bank branches has declined substantially. Despite this contraction, physical presence remains strategically important for regional institutions such as the Savings Banks (Sparkassen), which operate under a public mandate to ensure inclusive access to financial services, particularly in structurally weak regions. Against this background, this paper introduces the Segmented Multi-Tiered Capacitated Median-Covering Problem, or SMTC-MCP for short, a discrete, nested, and hierarchical location allocation model for the optimization of existing bank branch networks. Building on the classical $p$-median framework, the model integrates heterogeneous customer segments, differentiated facility types with service-specific accessibility radii, and a flexible multi-tiered capacity structure. The proposed capacity formulation allows for controlled overload, segment-to-segment reallocation, and penalized capacity extensions, enabling a realistic representation of advisory workloads and staffing constraints. The hybrid median-covering structure jointly balances distance minimization and service accessibility requirements. The applicability of the proposed framework is demonstrated through an empirical case study using real-world data from a German Savings Bank. The results provide actionable insights for operational and strategic branch network optimization under contemporary regulatory, demographic, and capacity constraints. JEL Classification: C61 , D24 , L20 , R30