Defining and assessing the structural flexibility of transportation networks

• Transportation network flexibility is conceptualized as a structural, network-level capability. • A probabilistic, residual-network-based index is introduced to assess network flexibility under capacity constraints. • Network topology systematically enables or constrains flexibility, independent of operational decision-making. • Common network metrics (e.g., density, connectivity) are insufficient indicators of transportation network flexibility. • Transportation network structure is a key determinant of logistics service providers’ flexibility capabilities. International supply chains increasingly require flexibility in transportation services supplied by logistics service providers (LSPs) to deal with uncertainty and disruption. Despite the literature on transportation flexibility, current studies primarily emphasize operational service attributes or isolated node- and arc-level capacities, with limited attention to the role of the transportation network structure in enabling system-level flexibility. Consequently, the concept of transportation network flexibility and its relationship to network topology is poorly understood. This research fills these gaps by conceptualizing transportation network flexibility as an attribute of the network structure at the network level, defined as the existence of at least one feasible origin–destination itinerary under joint volume and time capacity constraints. Drawing on graph theory and complex adaptive systems theory, the study formally distinguishes between arc-, node-, mix-, and network-level flexibility and finds that only network-level flexibility can consistently handle shipper change requests. A simulation-based transportation network flexibility index, grounded in residual network theory, is developed to test seven canonical transportation network topologies under stochastic capacity degradation. The results show that network structure systematically influences flexibility outcomes: scale-free networks have much greater network-level flexibility than other network topologies, irrespective of common network metrics such as density, connectivity, or centralization. By decoupling structural flexibility from operational performance, the study establishes the unit of analysis for transportation flexibility. It provides LSPs with a principled foundation for designing, evaluating, and ranking flexible transportation services without resorting to expensive, fully flexible network designs.