Optimization Models for Public Transit Operations Under Subsidization and Regulation

Document Type

Journal Article

Publication Date


Subject Area

policy - fares, economics - subsidy, organisation - governance, organisation - regulation


optimization model, public transit, subsidization schemes, regulation policies


This paper presents a bilevel optimization framework for analyzing the effects of external subsidies and service policy constraints (i.e., fare and service frequency limits) on the operation of public transportation systems. After reviews of existing optimization models for public transit operations, a major deficiency within the centralized optimization framework is identified, namely, its inability to model decision interactions between multiple decision-making agents. A benchmark model that maximizes social welfare is formulated and then extended into a series of bilevel models with combinations of regulation policies and subsidization schemes to explore the relations between operators and government (both subsidizer and regulator). Single-level problems, including both the benchmark and those bilevel programs that can be reduced to one level, are solved analytically. Bilevel programs are solved with a hybrid method combining analytical and numerical techniques. Numerical evaluations that consider the cost of public funds show that (a) the combination of regulation and subsidization scheme yields the highest social welfare, (b) any subsidization scheme without regulation produces socially worse results than the benchmark, and (c) two thresholds can be identified to distinguish the three proposed subsidization methods.


Permission to publish the abstract has been given by Transportation Research Board, Washington, copyright remains with them.