An integrated line planning and timetabling model is formulated with the objective of minimizing both user inconvenience and operational costs. User inconvenience is modeled as the total time passengers spend in a railway system, including waiting at origin and transfer stations. The model is solved using a cross-entropy metaheuristic. The line plan and timetable of Israel Railways is used as a benchmark. Using the same amount of resources, the average journey time of passengers is reduced by 20%.
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Kaspi et al. (2012) studied this question.