An Optimal Transit Fare and Frequency Design Model with Equity Impact Constraints
Publication: Journal of Transportation Engineering, Part A: Systems
Volume 147, Issue 12
Abstract
Distance-based fares have been applied widely in practice using automatic fare collection technology. This paper proposes an optimization model for the distance-based transit fare structure. A bilevel model was formulated to obtain the optimal fare functions with the aim of minimizing the Gini coefficient of the entire transit system. Passengers’ travel behavior is modeled by a stochastic transit assignment problem in the lower level. Considering the inherent complexity of the bilevel model, a heuristic algorithm, namely the artificial bee colony algorithm, is applied, which is incorporated with a method of successive averages to solve the transit assignment subproblem. The results show that the Euclidean distance–based fare has better performance in terms of social equity, but it is less equitable for passengers with middistance trips.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This study is supported by the Ministry of Education (China) Project of Humanities and Social Sciences (No. 20YJAZH083).
References
Bandegani, M., and M. Akbarzadeh. 2016. “Evaluation of horizontal equity under a distance-based transit fare structure.” J. Public Transp. 19 (3): 161–172. https://doi.org/10.5038/2375-0901.19.3.10.
Ben-Akiva, M., and S. Lerman. 1985. Discrete choice models: Theory and application to travel demand. Cambridge, MA: MIT Press.
Ben-Ayed, O., D. Boyce, and C. Blair III. 1988. “A general bilevel linear programming formulation of the network design problem.” Transp. Res. Part B Methodol. 22 (4): 311–318. https://doi.org/10.1016/0191-2615(88)90006-9.
Borndörfer, R., M. Karbstein, and M. Pfetsch. 2012. “Models for fare planning in public transport.” Discrete Appl. Math. 160 (18): 2591–2605. https://doi.org/10.1016/j.dam.2012.02.027.
Brown, A. E. 2018. “Fair fares? How flat and variable fares affect transit equity in Los Angeles.” Case Stud. Transp. Policy 6 (4): 765–773. https://doi.org/10.1016/j.cstp.2018.09.011.
Bureau, B., and M. Glachant. 2011. “Distributional effects of public transport policies in the Paris Region.” Transp. Policy 18 (5): 745–754. https://doi.org/10.1016/j.tranpol.2011.01.010.
Cervero, R. 1982. “The transit pricing evaluation model: A tool for exploring fare policy options.” Transp. Res. Part A 16 (4): 313–323. https://doi.org/10.1016/0191-2607(82)90058-9.
Cervero, R. 1990. “Transit pricing research.” Transportation 17 (2): 117–139. https://doi.org/10.1007/BF02125332.
Chin, A., A. Lai, and J. Y. J. Chow. 2016. “Nonadditive public transit fare pricing under congestion with policy lessons from a case study in Toronto, Ontario, Canada.” Transp. Res. Rec. 2544 (1): 28–37. https://doi.org/10.3141/2544-04.
Clark, D. J., F. Jørgensen, and T. A. Mathisen. 2011. “Relationships between fares, trip length and market competition.” Transp. Res. Part A Policy Pract. 45 (7): 611–624. https://doi.org/10.1016/j.tra.2011.03.012.
Daskin, M. S., J. L. Schofer, and A. E. Haghani. 1988. “A quadratic programming model for designing and evaluating distance-based and zone fares for urban transit.” Transp. Res. Part B Methodol. 22 (1): 25–44. https://doi.org/10.1016/0191-2615(88)90032-X.
Delbosc, A., and G. Currie. 2011. “Using Lorenz curves to assess public transport equity.” J. Transp. Geogr. 19 (6): 1252–1259. https://doi.org/10.1016/j.jtrangeo.2011.02.008.
Farber, S., K. Bartholomew, X. Li, A. Páez, and K. M. Nurul Habib. 2014. “Assessing social equity in distance based transit fares using a model of travel behavior.” Transp. Res. Part A Policy Pract. 67 (Sep): 291–303. https://doi.org/10.1016/j.tra.2014.07.013.
Fisk, C. 1980. “Some developments in equilibrium traffic assignment.” Transp. Res. Part B Methodol. 14 (3): 243–255. https://doi.org/10.1016/0191-2615(80)90004-1.
Hickey, R. L., A. Lu, and A. Reddy. 2010. “Using quantitative methods in equity and demographic analysis to inform transit fare restructuring decisions.” Transp. Res. Rec. 2144 (1): 80–92. https://doi.org/10.3141/2144-10.
Huang, D., Z. Liu, P. Liu, and J. Chen. 2016. “Optimal transit fare and service frequency of a nonlinear origin-destination based fare structure.” Transp. Res. Part E Logist. Transp. Rev. 96 (Dec): 1–19. https://doi.org/10.1016/j.tre.2016.10.004.
Huang, D., S. Wang, and Z. Liu. 2021a. “A systematic review of prediction methods for emergency management.” Int. J. Disaster Risk Reduct. 62 (Aug): 102412. https://doi.org/10.1016/j.ijdrr.2021.102412.
Huang, D., J. Xing, Z. Liu, and Q. An. 2021b. “A multi-stage stochastic optimization approach to the stop-skipping and bus lane reservation schemes.” Transportmetrica A 17 (4): 1272–1304. https://doi.org/10.1080/23249935.2020.1858206.
Jørgensen, F., and J. Preston. 2007. “The relationship between fare and travel distance.” J. Transp. Econ. Policy 41 (3): 451–468.
Lam, W. H. K., and J. Zhou. 2000. “Optimal fare structure for transit networks with elastic demand.” Transp. Res. Rec. 1733 (1): 8–14. https://doi.org/10.3141/1733-02.
Li, Y., and W. Fan. 2020. “Modeling and evaluating public transit equity and accessibility by integrating general transit feed specification data: Case study of the city of Charlotte.” J. Transp. Eng. Part A. Syst. 146 (10): 04020112. https://doi.org/10.1061/JTEPBS.0000426.
Li, Z.-C., W. H. M. Lam, and S. C. Wong. 2009. “The optimal transit fare structure under different market regimes with uncertainty in the network.” Networks Spatial Econ. 9 (2): 191–216. https://doi.org/10.1007/s11067-007-9058-z.
Liu, Z., S. Wang, and Q. Meng. 2014. “Optimal joint distance and time toll for cordon-based congestion pricing.” Transp. Res. Part B Methodol. 69 (Nov): 81–97. https://doi.org/10.1016/j.trb.2014.08.005.
Lo, H. H. K., C. W. Yip, and K. Wan. 2003. “Modeling transfer and non-linear fare structure in multi-modal network.” Transp. Res. Part B Methodol. 37 (2): 149–170. https://doi.org/10.1016/S0191-2615(02)00005-X.
Lorenz, M. O. 1905. “Methods of measuring the concentration of wealth.” Publ. Am. Stat. Assoc. 9 (70): 209–219. https://doi.org/10.2307/2276207.
Meng, Q., Z. Liu, and S. Wang. 2012. “Optimal distance tolls under congestion pricing and continuously distributed value of time.” Transp. Res. Part E Logist. Transp. Rev. 48 (5): 937–957. https://doi.org/10.1016/j.tre.2012.04.004.
Nahmias-Biran, B.-H., N. Sharaby, and Y. Shiftan. 2014. “Equity aspects in transportation projects: Case study of transit fare change in Haifa.” Int. J. Sustainable Transp. 8 (1): 69–83. https://doi.org/10.1080/15568318.2012.758525.
Nuworsoo, C., A. Golub, and E. Deakin. 2009. “Analyzing equity impacts of transit fare changes: Case study of Alameda–Contra Costa Transit, California.” Eval. Program Plann. 32 (4): 360–368. https://doi.org/10.1016/j.evalprogplan.2009.06.009.
Ranjbari, A., M. Hickman, and Y.-C. Chiu. 2020. “Network design with elastic demand and dynamic passenger assignment to assess the performance of transit services.” J. Transp. Eng. Part A. Syst. 146 (5): 04020030. https://doi.org/10.1061/JTEPBS.0000326.
Sun, S., and W. Y. Szeto. 2019. “Optimal sectional fare and frequency settings for transit networks with elastic demand.” Transp. Res. Part B Methodol. 127 (Sep): 147–177. https://doi.org/10.1016/j.trb.2019.06.011.
Szeto, W. Y., M. Solayappan, and Y. Jiang. 2011. “Reliability-based transit assignment for congested stochastic transit networks.” Comput.-Aided Civ. Infrastruct. Eng. 26 (4): 311–326. https://doi.org/10.1111/j.1467-8667.2010.00680.x.
Tsai, F.-M., S. Chien, and C.-H. Wei. 2013. “Joint optimization of temporal headway and differential fare for transit systems considering heterogeneous demand elasticity.” J. Transp. Eng. 139 (1): 30–39. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000468.
Tsai, F.-M., S. I.-J. Chien, and L. N. Spasovic. 2008. “Optimizing distance-based fares and headway of an intercity transportation system with elastic demand and trip length differentiation.” Transp. Res. Rec. 2089 (1): 101–109. https://doi.org/10.3141/2089-13.
Wang, J. Y. T., R. Lindsey, and H. Yang. 2011. “Nonlinear pricing on private roads with congestion and toll collection costs.” Transp. Res. Part B Methodol. 45 (1): 9–40. https://doi.org/10.1016/j.trb.2010.05.004.
Wang, S., Y. Liu, and J. Corcoran. 2021. “Equity of public transport costs before and after a fare policy reform: An empirical evaluation using smartcard data.” Transp. Res. Part A Policy Pract. 144 (Feb): 104–118. https://doi.org/10.1016/j.tra.2020.12.010.
Yang, H., and X. Zhang. 2002. “Multiclass network toll design problem with social and spatial equity constraints.” J. Transp. Eng. 128 (5): 420–428. https://doi.org/10.1061/(ASCE)0733-947X(2002)128:5(420).
Zhao, P., and Y. Zhang. 2019. “The effects of metro fare increase on transport equity: New evidence from Beijing.” Transp. Policy 74 (Feb): 73–83. https://doi.org/10.1016/j.tranpol.2018.11.009.
Zhou, J., M. Zhang, and P. Zhu. 2019. “The equity and spatial implications of transit fare.” Transp. Res. Part A Policy Pract. 121 (Mar): 309–324. https://doi.org/10.1016/j.tra.2019.01.015.
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© 2021 American Society of Civil Engineers.
History
Received: Apr 20, 2021
Accepted: Aug 31, 2021
Published online: Oct 8, 2021
Published in print: Dec 1, 2021
Discussion open until: Mar 8, 2022
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