Optimal timetables for public transportation

This paper analyzes the optimal timetable for a given number of public tran sport vehicles on a single transit line when riders differ with respect to the times at which they prefer to travel and the schedule delay costs they incur from traveling earlier or later than desired. The problem of minimizi ng riders' total schedule delay costs is formulated in continuous time and first-order optimality conditions are identified. An explicit solution is d erived for the "line" model in which preferred travel times are uniformly d istributed in the population over part of the day and trips cannot be resch eduled between days. This solution is compared with the optimal schedule fo r the "circle" model in which preferred travel times are uniformly distribu ted over the full 24 h day and trips can be rescheduled between days. (C) 2 001 Elsevier Science Ltd. All rights reserved.