Lagrangean Relaxations and Subgradient Methods for Multiple-depot Vehicle Scheduling Problems Lagrangean Relaxations and Subgradient Methods for Multiple-depot Vehicle Scheduling Problems

This paper presents two Lagrangean relaxation approaches for the NP-hard multiple-depot vehicle scheduling problem in public mass transit and reports on computational investigations. Our Lagrangean relaxation approaches can be applied to generate very tight lower bounds and to compute feasible solutions eeciently. A further application is to use the Lagrangean relaxations as new pricing strategies for a delayed column generation of a branch-and-cut approach. The computational investigations are based on real-world test sets from the cities of Berlin and Hamburg having up to 25 thousand timetabled trips and 70 million dead-head trips.