Customized bus service design for uncertain commuting travel demand

This study proposes an interesting customized bus service design problem by considering travel demand uncertainty. Given a fleet of heterogeneous vehicles, a mixed integer linear programming (MILP) model is put forward for the complex decision making on bus routing, timetabling and bus deployment, with the objective of generating a set of profitable bus services to cater for diverse commuting-trip requests. To capture the risk-averse level of the bus operator in uncertain travel demand environment, a random variable describing the likelihood that the offered bus services are rejected by potential passengers and two associated control parameters are embedded in the MILP model, facilitating an adjustable robust optimization framework. A branch-and-price method is implemented to solve the model exactly. A column-generation-based heuristic method is proposed to solve large-scale problems. The effectiveness of both the exact and heuristic methods is assessed in numerical experiments.