A hybrid metaheuristic algorithm for the Integrated Vehicle and Crew Scheduling Problem

This work deals with the Integrated Vehicle and Crew Scheduling Problem (VCSP) in urban mass transit. The Vehicle Scheduling Problem (VSP) consists in creating a daily routine of operation for a fleet of vehicles of a company so that all timetabled trips are covered and the operational costs of such activity reduced, making the best use of the fleet. In the Crew Scheduling Problem (CSP) each crew corresponds to a duty, and the goal is the generation of its schedule, satisfying a set of labor agreement and operational rules of the company, as well as the workforce optimization. Traditionally, the VSP and the CSP are solved sequentially by the vehicles-first duties-second approach, but these methodologies do not explore the link between both problems. The difficulty of solving VCSP is greater than the individual problems since it contains all the degrees of freedom of vehicle scheduling and all the degrees of freedom of crew scheduling. Since VCSP is NP-hard, an algorithm based on metaheuristics approaches is proposed here. This algorithm combines Iterated Local Search (ILS), Variable Neighborhood Descent (VND) and Tabu Search with Adaptive Relaxation (TSAR). In order to explore the solution space, we defined six movements based on relocation and swap of both, trips of the vehicles schedule and tasks of the duties schedule. The algorithm was tested with real data of a Brazilian city. The results show the effectiveness of the proposed approach.