Simultaneous Vehicle and Crew Scheduling for Extra Urban Transports Benoˆ ıt Laurent 1,2 and Jin-Kao Hao 2 1 Perinfo SA, 41 avenue Jean Jaur` es, 67000 Strasbourg, France blaurent@perinfo.com 2 LERIA, Universit´ e d’Angers, 2 boulevard Lavoisier, 49045 Angers Cedex 01, France jin-kao.hao@univ-angers.fr Abstract. We present a simultaneous approach to solve the integrated vehicle and crew scheduling problem in an extra urban context. We con- sider the single depot case with a heterogeneous fleet of vehicles. We pro- pose a constraint based model which is subsequently solved by a Greedy Randomized Adaptive Search Procedure. The construction phase of each initial solution relies on constraint programming techniques, while the local search phase exploits a powerful neighborhood exploration mecha- nism. The computational experiments conducted on real-world instances show the effectiveness and the flexibility of the approach compared with the classical sequential vehicle and crew scheduling. 1 Introduction Crews and vehicles are the main resources to provide services in transport sys- tems. The way these resources are employed directly impacts the quality of ser- vice and the cost of the whole transport system. It is thus primordial to optimize the utilization of these resources in any transportation scheduling systems. The conventional crew and vehicle scheduling process is the sequential ap- proach which determines first the vehicles schedule and then the crews schedule. This separation is mainly due to the complexity of each sub-problem. Indeed, the Multi-Depot Vehicle Scheduling Problem (MDVSP) is known to be NP- hard. The Bus Driver Scheduling Problem (BDSP) is usually modeled as a Set Covering or Set Partitioning Problem, both being NP-hard. In the early 1980s, Ball et al. criticized this sequential approach [1], but the first real integrated solutions, in which vehicles and crews are simultaneously scheduled, were only developed in 1995 [5]. This integrated management of both resources demonstrated its efficiency in [6] where relief locations, i.e. places where a driver can be relieved by a colleague, are spatially distant. Integration is also profitable when a driver is not allowed to change from one vehicle to another. The most popular approach to tackle the integrated scheduling problem is un- doubtedly integer linear programming (ILP). In [5], Freling et al. suggest, for the single depot case, an ILP formulation comprising a quasi-assignment structure for the vehicle scheduling, a set partitioning model for the crew scheduling, and a set of binding constraints. The solution approach is an approximated method N.T. Nguyen et al. (Eds.): IEA/AIE 2008, LNAI 5027, pp. 466–475, 2008. c  Springer-Verlag Berlin Heidelberg 2008