Mobility service providers’ interacting strategies under multi-modal equilibrium

Equilibrium Problem with Equilibrium Constraints; Mobility service providers interacting strategies; Multi-modal user equilibrium; Variational Inequality Problem; Equilibrium constraint; Equilibrium problem; Equilibrium problem with equilibrium constraint; Mobility service; Mobility service provider interacting strategy; Multi-modal; Service provider; User equilibrium; Variational inequality problems; Civil and Structural Engineering; Automotive Engineering; Transportation; Management Science and Operations Research; Equilibrium Problem with Equilibrium; Constraints

Abstract :

[en] In this paper, we analyse the interactions between Mobility Service Providers (MSP) in a multi-modal system. We formulate the problem using a bi-level structure extending Multi-modal Network Design (MND) principles. The upper level models the profit maximization objectives of multiple MSPs operating and offering different services to the users. At the lower level, users are divided into heterogeneous classes based on their travel characteristics, and assigned to a multi-modal super-network characterized by non-separable cost functions to account for interactions between modes. The problem is formulated as an Equilibrium Problem with Equilibrium Constraints (EPEC), which is characterized by a Variational Inequality (VI) Problem at the lower level, and a Nash equilibrium condition at the upper level. We apply an iterative solution algorithm that combines the classical Diagonalization method with an adaptive Extragradient Method to solve this complex problem and test it on several examples, demonstrating the validity and interpretability of the model and its results. These computations illustrate the competitive landscape faced by MSPs and the ranges of solutions where MSPs can be profitable, for small and medium sized examples.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

BANDIERA, Claudia ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > FSTM Faculty administration > Research Facilitators

CONNORS, Richard ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Engineering > Team Francesco VITI

VITI, Francesco ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)

External co-authors :

Language :

English

Title :

Mobility service providers’ interacting strategies under multi-modal equilibrium

Publication date :

November 2024

Journal title :

Transportation Research. Part C, Emerging Technologies

ISSN :

0968-090X

eISSN :

1879-2359

Publisher :

Elsevier Ltd

Volume :

168

Pages :

104766

Peer reviewed :

Peer Reviewed verified by ORBi

Focus Area :

Sustainable Development

Development Goals :

11. Sustainable cities and communities

Additional URL :

https://api.elsevier.com/content/article/PII:S0968090X24002870?httpAccept=text/xml

FnR Project :

FNR13769009 - Maas4all, 2019 (15/10/2019-14/10/2022) - Francesco Viti

Name of the research project :

R-AGR-3625 - BRIDGES/19/13769009 MaaS4All - ACL - VITI Francesco

Funders :

Fonds National de la Recherche

Funding number :

13769009

Funding text :

This research is funded by Fonds National de la Recherche Luxembourg (GRANT NUMBER: 13769009).

Available on ORBilu :

since 29 December 2024

Statistics

Number of views

83 (0 by Unilu)

Number of downloads

0 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

WoS citations^™

Bibliography

Arentze, T.T., Molin, E.J.E., Travelers’ preferences in multimodal networks: Design and results of a comprehensive series of choice experiments. 2013.
Axhausen, K.W., Zimmermann, A., Schönfelder, S., Rindsfüser, G., Haupt, T., Observing the rhythms of daily life: A six-week travel diary. Transportation 29 (2002), 95–124.
Butler, L., Yigitcanlar, T., Paz, A., Barriers and risks of Mobility-as-a-Service (MaaS) adoption in cities: A systematic review of the literature. Cities, 109, 2021, 103036.
Chiu, Y.C., Bottom, J., Mahut, M., Paz, A., Balakrishna, R., Waller, T., Hicks, J., Dynamic traffic assignment: A primer. Transp. Res. Circ., 2011.
Christodoulou, G., Price of anarchy. Kao, M.Y., (eds.) Encyclopedia of Algorithms, 2008, Springer US, Boston, MA, 665–667.
Cohen, A., Shaheen, S., Planning for shared mobility. 2018.
Connors, R., Watling, D., Assessing the demand vulnerability of equilibrium traffic networks via network aggregation. Netw. Spat. Econ. 15 (2014), 365–395.
Cottle, R.W., Su, C.L., Equilibrium problems with equilibrium constraints: stationarities, algorithms, and applications. 2005.
Dafermos, S., Traffic equilibrium and variational inequalities. Transp. Sci. 14 (1980), 42–54.
Djavadian, S., Chow, J.Y.J., An agent-based day-to-day adjustment process for modeling ‘Mobility as a Service’ with a two-sided flexible transport market. Transp. Res. B 104 (2017), 36–57.
Djavadian, S., Chow, J.Y.J., Agent-based day-to-day adjustment process to evaluate dynamic flexible transport service policies. Transp. B Transp. Dyn. 5 (2017), 281–306.
Fan, W., Khan, M.B., Ma, J., Jiang, X., Bilevel programming model for locating park-and-ride facilities. J. Urban Plann. Dev., 140, 2014, 04014007.
Farahani, R.Z., Miandoabchi, E., Szeto, W.Y., Rashidi-Bajgan, H., A review of urban transportation network design problems. European J. Oper. Res. 229 (2013), 281–302.
Fotouhi, H., Miller-Hooks, E., Optimal time-differentiated pricing for a competitive mixed traditional and crowdsourced event parking market. Transp. Res. C, 132, 2021, 103409.
Fu, X., Wu, Y., Huang, D., Wu, J., An activity-based model for transit network design and activity location planning in a three-party game framework. Transp. Res. E, 168, 2022.
García, R., Marin, A., Parking capacity and pricing in park'n ride trips: A continuous equilibrium network design problem. Ann. OR 116 (2002), 153–178.
Garus, A., Alonso, B., Aloso Raposo, M., Ciuffo, B., et al. Impact of new mobility solutions on travel behaviour and its incorporation into travel demand models. J. Adv. Transp., 2022, 2022.
Gu, Y., Cai, X., Han, D., Wang, D.Z., A tri-level optimization model for a private road competition problem with traffic equilibrium constraints. European J. Oper. Res. 273:1 (2019), 190–197.
Guo, Z., Deride, J., Fan, Y., Infrastructure planning for fast charging stations in a competitive market. Transp. Res. C 68 (2016), 215–227.
Heikkilä, S., Mobility as a Service - A proposal for action for the public administration, case helsinki. 2014.
Ho, C.Q., Hensher, D.A., Mulley, C., Wong, Y.Z., Potential uptake and willingness-to-pay for Mobility as a Service (MaaS): A stated choice study. Transp. Res. A 117 (2018), 302–318.
Hoerler, R., Stünzi, A., Patt, A., Del Duce, A., What are the factors and needs promoting mobility-as-a-service? Findings from the Swiss Household Energy Demand Survey (SHEDS). Eur. Transp. Res. Rev. 12 (2020), 1–16.
Jiang, Z., Lei, C., Ouyang, Y., Optimal investment and management of shared bikes in a competitive market. Transp. Res. B 135 (2020), 143–155.
Kamargianni, M., Matyas, M., The business ecosystem of Mobility-as-a-Service. 2017.
Karlsson, I., Mukhtar-Landgren, D., Smith, G., Koglin, T., Kronsell, A., Lund, E., Sarasini, S., Sochor, J., Development and implementation of Mobility-as-a-Service – A qualitative study of barriers and enabling factors. Transp. Res. A 131 (2020), 283–295 Developments in Mobility as a Service (MaaS) and Intelligent Mobility.
Khobotov, E., Modification of the extra-gradient method for solving variational inequalities and certain optimization problems. USSR Comput. Math. Math. Phys. 27:5 (1987), 120–127.
Koh, A., Shepherd, S., Tolling, collusion and equilibrium problems with equilibrium constraints. Eur. Transp. Trasporti Eur., 2010, 3–22.
Koh, A., Shepherd, S., Watling, D., Competition between two cities using cordon tolls: an exploration of response surfaces and possibilities for collusion. Transp. A Transp. Sci. 9:10 (2013), 896–924.
Korpelevich, G.M., The extragradient method for finding saddle points and other problems. 1976.
Koutsoupias, E., Papadimitriou, C., Worst-case equilibria. Stacs, vol. 99, 1999, Springer, 404–413.
Leyffer, S., Munson, T., Solving multi-leader–common-follower games. Optimisation Methods Softw. 25:4 (2010), 601–623.
Liao, F., Arentze, T., Timmermans, H., Constructing personalized transportation networks in multi-state supernetworks: a heuristic approach. Int. J. Geogr. Inf. Sci. 25:11 (2011), 1885–1903.
Lo, H.K., Yip, C., Wan, K., Modeling transfer and non-linear fare structure in multi-modal network. Transp. Res. B 37:2 (2003), 149–170.
Luo, Z.Q.T., Pang, J.S., Ralph, D., Mathematical programs with equilibrium constraints. 1996.
Maerivoet, S., De Moor, B., Transportation planning and traffic flow models”. Appl. Math. 60:3 (2000), 916–938.
Meurs, H., Sharmeen, F., Marchau, V., van der Heijden, R., Organizing integrated services in mobility-as-a-service systems: Principles of alliance formation applied to a MaaS-pilot in the Netherlands. Transp. Res. A 131 (2020), 178–195 Developments in Mobility as a Service (MaaS) and Intelligent Mobility.
Meurs, H., Timmermans, H.J.P., Mobility as a service as a multi-sided market: Challenges for modeling. 2017.
Michelot, C., A finite algorithm for finding the projection of a point onto the canonical simplex of R n. J. Optim. Theory Appl. 50 (1986), 195–200.
Nagurney, A., A multiclass, multicriteria traffic network equilibrium model. Math. Comput. Modelling 32 (2000), 393–411.
Nair, R., Miller-Hooks, E., Equilibrium network design of shared-vehicle systems. European J. Oper. Res. 235:1 (2014), 47–61.
Najmi, A., Rashidi, T.H., Waller, T., A multimodal multi-provider market equilibrium model: A game-theoretic approach. Transp. Res. C, 146, 2023, 103959.
Panicucci, B., Pappalardo, M., Passacantando, M., A path-based double projection method for solving the asymmetric traffic network equilibrium problem. Optim. Lett. 1 (2007), 171–185.
Pantelidis, T.P., Chow, J.Y., Rasulkhani, S., A many-to-many assignment game and stable outcome algorithm to evaluate collaborative mobility-as-a-service platforms. Transp. Res. B 140 (2020), 79–100.
Papadimitriou, C., 2001. Algorithms, games, and the internet. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing. pp. 749–753.
Pinto, H.K., Hyland, M.F., Mahmassani, H.S., Ömer Verbas, I., Joint design of multimodal transit networks and shared autonomous mobility fleets. Transp. Res. C 113 (2020), 2–20.
Polydoropoulou, A., Pagoni, I., Tsirimpa, A., Roumboutsos, A., Kamargianni, M., Tsouros, I., Prototype business models for Mobility-as-a-Service. Transp. Res. A 131 (2020), 149–162 Developments in Mobility as a Service (MaaS) and Intelligent Mobility.
Rashidi, E., Parsafard, M., Medal, H., Li, X., Optimal traffic calming: A mixed-integer bi-level programming model for locating sidewalks and crosswalks in a multimodal transportation network to maximize pedestrians’ safety and network usability. Transp. Res. E 91 (2016), 33–50.
Shaheen, S.A., Chan, N.D., Mobility and the sharing economy: Potential to overcome first- and last-mile public transit connections. 2016.
Sprumont, F., Scheffer, A.H.M., Caruso, G., Cornélis, E., Viti, F., Quantifying the relation between activity pattern complexity and car use using a partial least square structural equation model. Sustainability, 2022.
Steffensen, S., Bittner, M., Relaxation approach for equilibrium problems with equilibrium constraints. Comput. Oper. Res. 41 (2014), 333–345.
Susilo, Y.O., Axhausen, K.W., Repetitions in individual daily activity–travel–location patterns: a study using the Herfindahl–Hirschman index. Transportation 41 (2014), 995–1011.
van den Berg, V.A., Meurs, H., Verhoef, E.T., Business models for Mobility as an Service (MaaS). Transp. Res. B 157 (2022), 203–229.
Vo, K.D., Lam, W.H., Chen, A., Shao, H., A household optimum utility approach for modeling joint activity-travel choices in congested road networks. Transp. Res. B 134 (2020), 93–125.
Wang, G., Li, Y., Xu, M., Gao, Z., Operating a public–private mixed road network via determining tradable credits and road tolls: An equilibrium problem with equilibrium constraints approach. Int. J. Sustain. Transp. 15:2 (2021), 87–96.
Wardrop, J.G., Road paper. some theoretical aspects of road traffic research. Proc. Inst. Civ. Eng. 1:3 (1952), 325–362.
Watling, D., User equilibrium traffic network assignment with stochastic travel times and late arrival penalty. European J. Oper. Res. 175:3 (2006), 1539–1556.
Watling, D.P., Shepherd, S.P., Koh, A., Cordon toll competition in a network of two cities: formulation and sensitivity to traveller route and demand responses. Transp. Res. B 76 (2015), 93–116.
Wright, S., Nocedal, J., et al. Numerical optimization. Springer Sci., 35(67–68), 1999, 7.
Wu, Z.X., Lam, W.H.K., Chan, K.S., Multi-modal network design: Selection of pedestrianisation location. J. East. Asia Soc. Transp. Stud. 6 (2005), 2275–2290.
Xi, H., Aussel, D., Liu, W., Waller, S., Rey, D., Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets. European J. Oper. Res., 2022.
Yang, S., Wu, J., Sun, H., Qu, Y., Wang, D.Z.W., Integrated optimization of pricing and relocation in the competitive carsharing market: A multi-leader-follower game model. Transp. Res. C, 2022.
Yang, H., Xiao, F., Huang, H.J., Private road competition and equilibrium with traffic equilibrium constraints. J. Adv. Transp. 43 (2009), 21–45.
Ye, J., Jiang, Y., Chen, J., Liu, Z., Guo, R., Joint optimisation of transfer location and capacity for a capacitated multimodal transport network with elastic demand: a bi-level programming model and paradoxes. Transp. Res., 156, 2021, 102540.
Zhou, J., Lam, W.H., Heydecker, B.G., The generalized Nash equilibrium model for oligopolistic transit market with elastic demand. Transp. Res. B 39:6 (2005), 519–544.