A multi-objective train scheduling model and solution Keivan Ghoseiri a,b , Ferenc Szidarovszky a, * , Mohammad Jawad Asgharpour b a Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721-0020, USA b Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran Received 24 January 2003; received in revised form 13 June 2003; accepted 6 February 2004 Abstract Thispaperdevelopsamulti-objectiveoptimizationmodelforthepassengertrain-schedulingproblemon a railroad network which includes single and multiple tracks, as well as multiple platforms with different train capacities. In this study, lowering the fuel consumption cost is the measure of satisfaction of the railway company and shortening the total passenger-time is being regarded as the passenger satisfaction criterion.Thesolutionoftheproblemconsistsoftwosteps.FirsttheParetofrontierisdeterminedusingthe e-constraint method, and second, based on the obtained Pareto frontier detailed multi-objective optimi- zation is performed using the distance-based method with three types of distances. Numerical examples are given to illustrate the model and solution methodology. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Multi-objective programming; Train scheduling; Pareto frontier; e-Constraint method; Distance-based methods 1. Introduction Public rail transport planning is a highly complex task. It is based on the interaction of many elements which must be managed simultaneously. Due to the tremendous size of the public rail traffic system, the planning process is usually divided into several steps (see also Assad, 1980; Lindner, 2000; Bussieck et al., 1997). A diagram of this hierarchical decomposition is given in Fig. 1. Inthefirststep,the passenger demand hastobeassessedandanalyzed.Asaresult,theamount of travelers wishing to go from certain origins to certain destinations is determined. As a * Corresponding author. Tel.: +1-520-621-6557; fax: +1-520-621-6555. E-mail address: szidar@sie.arizona.edu (F. Szidarovszky). 0191-2615/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2004.02.004 Transportation Research Part B 38 (2004) 927–952 www.elsevier.com/locate/trb