Zonal-based flexible bus service under elastic stochastic demand

This study investigates flexible bus that provides door-to-door service with multiple passengers sharing the vehicle, which reduces congestion on the urban network. The service area is divided into zones, and flexible buses are assigned to zonal routes based on the historical demand characteristics before demand realization. Passengers are served by either regular service or ad hoc service after the demand realization to minimize the sum of ad hoc service cost and detour time cost. The elastic and stochastic natures of demand are captured in the formulation by the volume stochasticity of demand, detour time stochasticity, and elasticity of demand with respect to the flexible bus service price and quality. The profit of the flexible bus service is maximized while accounting for the detour time cost. To effectively solve the problem, volume and detour time reliability measures are introduced to separate the problem into a vehicle-to-route assignment problem and a passenger-to-vehicle assignment problem. A gradient-based solution approach is devised to determine the flexible bus routing plans by optimizing the associated reliability measures. The solution approach is further improved by combining the gradient-based approach with a greedy search solution approach and relaxing the formulations. The formulation and solution approaches are implemented using real data in Chengdu, China, with promising results.