Models and algorithms for integration of vehicle and crew scheduling

This paper deals with models, relaxations, and algorithms for an integrated approach to vehicle and crew scheduling for an urban mass transit system with a single depot. We discuss potential benefits of integration and provide an overview of the literature which considers mainly partial integration. Our approach is new in the sense that we can tackle integrated vehicle and crew scheduling problems of practical size. We propose new mathematical formulations for integrated vehicle and crew scheduling problems and we discuss corresponding Lagrangian relaxations and Lagrangian heuristics. To solve the Lagrangian relaxations, we use column generation applied to set partitioning type of models. The paper is concluded with a computational study using real life data, which shows the applicability of the proposed techniques to practical problems. Furthermore, we also address the effectiveness of integration in different situations.