A bundle method for integrated multi-depot vehicle and duty scheduling in public transit

Abstract

This article proposes a Lagrangean relaxation approach to solve integrated duty and vehicle scheduling problems arising in public transport. The approach is based on a version of the proximal bundle method for the solution of concave decomposable functions that is adapted for the approximate evaluation of the vehicle and duty scheduling components. The primal and dual information generated by this bundle method is used to guide a branch-and-bound type algorithm. Computational results for large-scale real-world integrated vehicle and duty scheduling problems with up to 1,500 timetabled trips are reported. Compared with the results of a classical sequential approach and with reference solutions, integrated scheduling offers remarkable potentials in savings and drivers' satisfaction. © 2008 Springer-Verlag Berlin Heidelberg.