Mesquita, MartaMoz, MargaridaPaias, AnaPaixão, JoséPato, Margarida VazRespício, Ana2009-11-052009-11-052008Mesquita, Marta ... [et al.]. 2008. "Solving Public Transit Scheduling Problems". Universidade de Lisboa - Centro de Investigação Operacional – CIO - Working paper nº 1/2008http://hdl.handle.net/10400.5/1425Operational planning within public transit companies has been extensively tackled but still remains a challenging area for operations research models and techniques. This phase of the planning process comprises vehicle scheduling, crew scheduling and rostering problems. In this paper, a new integer mathematical formulation to describe the integrated vehicle-crew-rostering problem is presented. The method proposed to solve this multi-objective problem is a sequential algorithm considered within a preemptive goal programming framework that starts from the solution of an integrated vehicle and crew scheduling problem and ends with the solution of a driver rostering problem. Feasible solutions for the vehicle and crew scheduling problem are obtained by combining a column generation scheme with a branch-and-bound method. These solutions are the input of the rostering problem, which is tackled through a mixed binary linear programming approach. An application to real data of a Portuguese bus company is reported and shows the importance of integrating the three scheduling problems.engbinary linear programmingvehicle schedulingcrew schedulingdriver rosteringmulti-objective problemsworking paper