A Lagrangian heuristic for the real-time vehicle rescheduling problem

When a public transit vehicle breaks down on a scheduled trip, one or more vehicles need to be rescheduled to serve that trip and other service trips originally scheduled for the disabled vehicle. In this paper, the vehicle rescheduling problem (VRSP) is investiaged to consider operating costs, schedule disruption costs, and trip cancellation costs. The VRSP is proven to be NP-hard, and a Lagrangian relaxation based insertion heuristic is developed. Extensive computational experiments on randomly generated problems are reported. The results show that the Lagrangian heuristic performs very well for solving the VRSP.