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A highly informative graphical technique for the problem of finding the least number of buses required to service a given schedule of trips is described. The purpose is to develop the methodology for variable bus scheduling in which trip departure times can vary within acceptable tolerances. This is a continuation of a research project concerned with the problem of fixed scheduling where the timetable of trips and length of trip times are fixed. The motivation for this study comes from the Israel National Bus Carrier, Egged, which is responsible for scheduling an average of 54,400 daily trips by about 5200 buses. Consequently, the research takes on a practical nature. The approach used is based on the deficit-function theory where the deficit function at time t defines the total number of trips that have departed from a given terminal k less the number of trips that have arrived at k up to an including time t. The method developed is capable of aiding the scheduler to perform his or her tasks through a person-machine conversational mode. It allows the scheduler to interject his or her own practical suggestions and to see immediately their effects on the final schedule. The method is based on the deficit-function graphical multiterminal display, which guides and advises the schedulers of possible directions in reducing fleet size. In addition, this methodology aids schedulers in evaluating the results of their own suggestions. The potential of this person-machine interactive bus-scheduling procedure is presented by using several practical examples.
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