A Step Function for Improving Transit Operations Planning Using Fixed and Variable Scheduling

Abstract

This work describes an informative graphical technique for the problem of finding the least number of vehicles required to service a given timetable of trips. The technique used is a step function, a deficit function that was introduced during the last 20 years as an optimization tool for minimizing the number of vehicles in a fixed trip schedule, within given tolerances, and to the deficit function use for additional elements in the transit operations planning process. The work has the following objectives: to develop improved lower bound to the fixed schedule fleet size problem; to use the deficit function for minimizing the fleet size with variable schedules (possible shifts in departure times); to allow for the combination of deadheading trip insertions and shifts in departure times in the fleet size minimization problem; and to outline example applications of the deficit functions use in designing better transit services.

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