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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