WELFARE MAXIMIZATION WITH FINANCIAL CONSTRAINTS FOR BUS TRANSIT SYSTEMS

Abstract

A bus system with time-dependent demand and supply characteristics is analytically optimized to maximize a welfare objective, subject to financial constraints. With some approximations, equations for optimal route spacing, headways in various periods, and fares are obtained for unconstrained, break-even, and subsidy cases. The relationships between the optimized decision variables and system parameters are thus identified analytically. A numerical example is given for a bus transit system with three service periods. In the vicinity of the maximum welfare solution, the welfare is found to be relatively flat with respect to subsidies. Since subsidy increments yield disproportionately smaller welfare increments, break-even or constrained subsidy solutions may be preferable to pure welfare maximization. A minimum allowable ratio of welfare change to subsidy change is suggested as a criterion for optimizing individual bus systems and efficiently allocating resources among alternatives.