An Exact Branch and Cut Algorithm for the Vehicle and Crew Scheduling Problem

We present a new model for the vehicle and crew scheduling problem in urban public transport systems by combining models for vehicle and crew scheduling that cover a great variety of real world aspects, including constraints for crews resulting from wage agreements and company regulations. The main part of the model consists of a set partitioning formulation to cover each trip. A column generation algorithm is implemented to calculate the continuous relaxation which is embedded in a branch and bound approach to generate an exact solution for the problem. To improve the lower bounds, polyhedral cuts basing on clique detection and a variant of the column generation algorithm that suits the cuts were tested.