Customised bus route design with passenger-to-station assignment optimisation

As an emerging and innovative public transportation mode, the customised bus (CB) has drawn widespread attention. Existing studies of the CB mainly focus on issues regarding the bus station location, route design, timetabling, and fare setting, but rarely consider the passenger to bus station assignment problem which can significantly influence passengers' benefit and the buses' operating scheme. Thus, this study focuses on the customised bus routing problem with passenger-to-station assignment (CBRP-PSA) aiming to simultaneously minimise passengers' CB service access cost and the bus route cost. A time-discretized multi-commodity network flow model is developed to jointly determine the CB routes, timetables, and passenger-to-station assignment by allowing split loads and mixed loads. Through the dualization, the developed model is decomposed into two solvable sub-problems, and a Lagrangian-based heuristic solution algorithm is proposed. The model and algorithm are implemented in illustrative, medium-scale, and large-scale transportation networks to demonstrate their effectiveness under different scenarios.