Optimal Bus Dispatching Policy Under Variable Demand Over Time And Route Length

Abstract

The problems of scheduling and schedule co-ordination in bus operations have conflicting objectives related to user’s cost and operator’s cost. Passengers would like to have public bus services where there is less waiting time. Operators on the other hand would like to earn profit with lesser vehicle operating cost and a minimum number of buses. In developing countries where overloading of buses has long been considered necessary to ensure bus travel remains affordable to most socioeconomic groups, bus operators would in addition to larger headways, like to have higher load factors to increase revenue even though passengers would prefer less load factors as it provides a more comfortable journey. All these factors are further constrained by the fare levels, which may not make the revenue adequate to operate at the most economically optimal frequency and load factor. This paper considers a method that is an extension to Newell’s Optimal Dispatching Policy, to determine a fleet size and dispatching rate based on both operator’s cost and user’s cost including the disutility of standing, in order to arrive at a global cost optimum. It further investigates the financial viability of providing such a service and sets out a financial viability domain within which optimization can occur in practice. If the resulting dispatching rate is lower and does not fall within the domain of financial viability, then operating subsidies are considered necessary to maintain the economically optimum dispatching rate. This method to compute optimized dispatching rates is based on screen-line counts across given locations along a bus routes used in conjunction with a limited sample of on-board boarding and alighting surveys. Passenger revenues have been computed by a process of multiplication of the rationalized origin-destination matrix by the fare for distance travelled between the respective origins and destinations. Indicators have also been developed to determine average trip lengths for each route and average revenue per passenger together with the points of maximum capacity along the route. These indicators describe the nature of the demand that the bus route serves. The screen line counts provide the hourly variation in demand over a bus route throughout the day, which has been expressed in terms of a polynomial equation to determine the variation of demand over different time periods. By combining both functions, a composite function has been developed to determine; the daily passenger demand on a given route; the total revenue for operators, the average load factor and locations on the route where maximum loading occurs.