Research Article Profit Maximization Model with Fare Structures and Subsidy Constraints for Urban Rail Transit Qing Wang , 1,2 Paul Schonfeld , 3 and Lianbo Deng 1 1 School of Traffic and Transportation Engineering, Rail Data Research and Application Key Laboratory of Hunan Province, Central South University, Changsha 410075, China 2 Department of Civil and Environmental Engineering, University of Washington, Seattle, WA 98105, USA 3 Department of Civil and Environmental Engineering, University of Maryland, College Park 1173 Glenn Martin Hall, College Park, MD 20742, USA Correspondence should be addressed to Lianbo Deng; lbdeng@csu.edu.cn Received 15 November 2020; Revised 29 December 2020; Accepted 13 January 2021; Published 25 January 2021 Academic Editor: Erfan Hassannayebi Copyright©2021QingWangetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is paper analyzes government subsidies based on the service design (i.e., headway) and fare structures of an urban rail transit system while considering necessary financial support from the government. To capture the interactions among the operator performance,governmentsubsidies,andpassengersinanurbanrailtransitsystem,aprofitmaximizationmodelwithnonnegative profitconstraintisformulatedtodeterminetheoptimalfareandheadwaysolutions.en,thesocialwelfarethatresultsfromthe operator profit maximization model is analyzed. Finally, a numerical example from Changsha, China, is employed to verify the feasibility of the proposed model. e major results consist of optimized solutions for decision variables, i.e., the fares and train headways, as well as subsidies to the operator. e fare elasticity factor under two fare structures significantly affects fares and demand.Asthefareelasticityfactorincreases,thesocialwelfaregraduallydecreasesandadeficitoccursatlowfaresanddemand, while subsidies rise from 0 to ¥24658.00 and ¥38089.16 under the flat fare and distance-based fare structures. 1. Introduction Inrecentdecades,large-scaleinvestmentbylocalauthorities inChinahasgreatlypromotedthepaceofurbanrailtransit (URT) construction and operation. According to the “An- nual Statistics and Analysis Report of URT 2019”, up to the endof2019,therewere208URTlinesin(mainland)China, distributed in 40 cities, including Shanghai, Beijing, Guangzhou,andNanjing,withatotallengthof5180.6kmin operation, and the ridership has exceeded 237.1 billion passengers per year. In general, operators in most cities are overdependent on the government’s subsidies (data source: China Association of Metros, 2019 [1]). Acomprehensivereviewofthetransportationissueswas conducted by Farahani et al. [2], which discussed and compared the models and solution methods of trans- portation network design problem. Although many studies have investigated the optimization of public transportation, the literature on methods for optimizing URT system op- eration with subsidy constraints while considering different fare structures is still relatively scarce. For instance, Li and Love[3]conductedaretrospectiveanalysisofaraillinethat was procured using a public-private partnership in con- junction with land value capture. ey showed that the economic viability of that URTsystem could be ensured by considering the land value capture. Canca et al. [4] devel- opedamathematicalprogramingmodelthatmaximizednet profit by simultaneously determining the infrastructure network and line planning problem. e effect of a sur- charge-reward scheme relieving crowding and queuing congestion in a URTsystem was investigated in Tang et al. [5], who formulated a bilevel model to design and optimize the surcharge-reward scheme. Since fares are closely related to operator profit and subsidies, the implementation of fare differentiation is one of the practical policies adopted in public transport management [6]. Further studies on the Hindawi Journal of Advanced Transportation Volume 2021, Article ID 6659384, 14 pages https://doi.org/10.1155/2021/6659384