Vehicle and Crew Scheduling for Flexible Bus Transportation Systems

•Drivers duty and Vehicles usage directly affects the operation costs of bus transportation agencies.•We introduce a new integration of the Vehicle Scheduling Problem (VSP) and the Crew Scheduling Problem (CSP).•The integration of the VSP and the CSP provides a more flexible transportation system and aims to reduce the overall operation cost.•We do not consider a fixed duty structure, and we include labor regulation constraints for the daily duty of the drivers.•The proposed Variable Neighborhood Search Algorithm can provide high quality solution in a short processing time for the real size instances. This article deals with the Flexible Vehicle and Crew Scheduling Problem faced by urban bus transport agencies that have to assign their resources (vehicles and drivers) to cover timetables generated at the tactical level. We aim for high quality and fast to compute solutions for this problem, considering vehicle characteristics, driver qualifications requirements for each line, and labor regulations, that is, drivers have a limited duty length, mandatory rests, a restricted consecutive driving time, and a limited extra working hours. Moreover, the starting time of the drivers shift is not fixed a priori and the breaks can be allocated anywhere in the schedule as long as labor regulations are satisfied. Thus, flexibility is required to compute drivers duty but it is also needed in scenarios where the available number of drivers and vehicles changes almost everyday. We propose a mixed-integer linear programming model and a variable neighborhood search for this problem and show the efficiency of our approaches with a large set of instances.