There is an increasing interest in using computers for scheduling both fleet and crews of transportation systems. Programs that accomplish this have to be for a large part heuristic, however for some aspects an optimization approach is feasible and may improve the results. Moreover, the heuristic programs may benefit from theoretical studies that increase our knowledge of the processes involved. The purpose of this paper is to present a general fleet scheduling model together with a survey of applications to various modes of transportation. It will be shown that a general fleetsize formula for transportation systems, that expresses the transportation capacity needed in terms of vehicle departure and arrival patterns, can be applied to various situations: suburban railways, buses and airlines. In each of these models the passenger origin-destination statistics are assumed to be given, the vehicle arrivals and departures during the scheduling period (normally a day) constitute the variables. Basically these are dispatching models. Generally, there is room for another objective, apart from the fleetsize, as the number of schedules with minimum fleetsize is normally large. This approach leads to mathematical programming models for suburban railway and airline systems, which are applicable to practical situations, as is illustrated by computational results. The bus dispatching model leads to a theoretical model for optimal bus departure rates, as a function of the time of day; the model provides some clues concerning the construction of bus timetables. (a). For the covering abstract of the symposium, please see irrd abstract no. 224453.
Abstract