A Planning Model for Flexible-Route Bus Operations with Financial Constraints

Abstract

In suburban areas where the demand is not high enough, the fixed-route buses usually operate with infrequent services, which increase the cost of waiting transit services for fixedroute service users. For those low demand regions, flexible-route bus operations with doorstep services, which operate with flexible routes, flexible schedules, and smaller vehicles, can be a feasible alternative. This study formulates the social welfare for flexible-route bus operations under various financial constraints, seeking to jointly optimize the headway, fare, and zone size. Elastic demand functions are constructed as a part of problem formulations. Unlike many previous studies, this study does not presume the shape of the zone, so that the flexible-route bus services can be designed according to the geographical conditions in the regions. Moreover, the amount of subsidy for financially constrained policy is calculated based on the actual demand although many previous studies used the potential demand to calculate the subsidy amount. Numerical analyses are explored to evaluate and compare system-wide welfares for different financial perspectives, i.e., no financial constraint, break-even policy, and subsidized policy. The solution optimality for constrained nonlinear optimization problems is verified using analytical optimization or the Karush-Kuhn-Tucker (KKT) conditions. It is found that the welfare of subsidized transit operations is located between the welfare amounts of unconstrained and break-even cases; this finding of welfare variations over subsidy amounts can be a helpful resource for transportation mobility analysts in determining the appropriate service quality and the corresponding amount of subsidy. Sensitivity analyses are presented to explore the system-wide welfare with respect to critical input parameters, including a comprehensive analysis of the unit cost of bus operations, which offers implications toward Mobility-as-a-Service (MaaS) planning.

Joint Optimization of Distance-Based Fares and Headway for Fixed-Route Bus Operations

“…Employing an analytic approach, they optimized headway intervals, route configurations, and fare decisions. More recently, Han et al [25] formulated a maximum welfare problem for flexible-route bus systems while considering various financial constraints. A notable contribution of their paper lies in the calculation of subsidies, which is based on actual demand rather than potential demand.…”

“…As demonstrated in prior studies [24,27], it is advantageous to evaluate the profitability of bus transit operations while considering demand elasticities. Furthermore, when gauging profit or welfare, previous research efforts [4,25] typically assume a uniform average fare for all trips. This study presents contributions to the literature to advance this understanding by jointly optimizing the distance-based fare and service headways for the profit of fixed-route bus operations.…”