Integration of Vehicle and Crew Scheduling with Application to Bus and Driver Scheduling in Rotterdam.

In this paper, the problem of integrating vehicle and crew scheduling is considered. Traditionally, vehicle and crew scheduling have been dealt with in a sequential manner, were vehicle schedules are determined before the crew schedules. The few papers that appeared in the literature have in common that no comparison is made between simultaneous and sequential schedules, so that there is no indication of the benefit of a simultaneous approach. In order to get such an indication before even solving the integrated problem, we propose a method to solve crew scheduling independently of vehicle scheduling. We introduce a mathematical formulation for the integrated problem, and briefly outline algorithms. The paper is concluded with computational results for an application to bus and driver scheduling at the public transport company RET in Rotterdam, The Netherlands. The results show that the proposed techniques are applicable in practice. Furthermore, we conclude that the effectiveness of integration as compared to a sequential approach is mainly dependent on the flexibility in changing of a bus during a duty.