Bi-level optimisation for minimising externalities in DRT station placement

Demand-responsive transport (DRT) can expand urban accessibility. However, pickup-point design is often guided by user convenience while neglecting system costs, including detour delays for onboard passengers and additional road congestion. This paper develops a decision-support framework for DRT pickup-point siting that explicitly internalises these externalities. The problem is formulated as a Stackelberg bi-level optimisation model. At the upper level, a planner selects feasible pickup-point locations within a predefined search area to minimise total social cost, defined as the sum of network travel time and detour-related passenger delay. At the lower level, travellers’ demand response is represented by a utility-based logit model that updates mode shares. The proposed framework translates welfare objectives into implementable siting rules and supports the specification of service standards, such as bounds on detours for existing riders and thresholds for acceptable congestion impacts. It further enables systematic evaluation of trade-offs among ridership, equity, and network performance under budget and operating constraints. A case study using real-world network and demand data indicates that the approach provides evidence-based guidance on pickup-point spacing and placement while maintaining DRT competitiveness.