Optimizing fare and operational strategies for an urban bus corridor using elastic demand

In order to better match supply and demand in public transit (PT) systems, this paper proposes operational strategies and fare models for a single bus line, subject to bus capacity constraints and budget restrictions. The objective of this model is to maximize the total social profit with a weighted combination of the operator's profit and consumer surplus. For the purposes of this study, operator profit results from PT services that generate welfare for the service provider, and consumer surplus is a result of the welfare of the users generated by PT services. To improve the efficiency of a PT system and the application of optimal models, we consider passenger demand as elasticity and formulate the function of demand with respect to generalized costs including travel fare, waiting time costs, in-vehicle time costs, as well as transfer costs. A case is given, and numerical results are presented. It is found that by maximizing total social profit, the optimal combination of bus fare and operational strategies can be efficiently reached. The results show that applying operational strategies could achieve greater social welfare, attract more passengers, and reduce the fleet size. With the optimal value of the objective function, operator profit accounts for a small proportion. When budget restrictions are considered in the model, operator profit only breaks even. Through analyzing components of passenger travel costs, we find that waiting times and transfer costs have a significant impact on passengers' travel behaviors. Furthermore, in comparison with bus fares determined by objective functions such as social welfare, social profit, etc., the optimal bus fare generated by maximization of operator profit is higher.