IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i19p3048-d1488336.html
   My bibliography  Save this article

Optimizing Fleet Size in Point-to-Point Shared Demand Responsive Transportation Service: A Network Decomposition Approach

Author

Listed:
  • Fudong Xie

    (Lingnan College, Sun Yat-sen University, Guangzhou 510275, China)

  • Ce Wang

    (Energy Development Research Institute, China Southern Gird, Guangzhou 510700, China)

  • Housheng Duan

    (School of Management, Guangzhou University, Guangzhou 510006, China)

Abstract

With increasing urbanization and the demand for efficient, flexible transportation solutions, demand-responsive transportation services (DTRS) has emerged as a viable alternative to traditional public transit. However, determining the optimal fleet size to balance the investment and operational revenue remains a significant challenge for service providers. In this article, we address the optimization of fleet size in point-to-point shared demand DRTS, which widely operates within many cities. To capture the uncertain passenger demands in the future when planning the fleet size currently, we model this problem with a framework of two-stage stochastic programming with recourse. Fleet sizing decisions are made in the first stage before the uncertain demands are revealed. After the uncertainty is revealed, the second stage involves making additional decisions to maximize operational revenue. The objective is to optimize the total revenue of the first-stage decisions and the expected revenue of the recourse actions. To solve this practical problem, we resort to the Model Predictive Control method (MPC) and propose a network decomposition approach that first converts the transportation network to a nodal tree structure and then develops a Nodal Tree Recourse with Dependent Arc Capacities (NTRDAC) algorithm to obtain the exact value of the expected recourse functions. In the experiments, NTRDAC is able to produce results within seconds for transportation networks with over 30 nodes. In contrast, a commercial solver is only capable of solving networks with up to five nodes. The stability tests show that NTRDAC remains robust as the problem size varies. Lastly, the value of the stochastic solution (VSS) was evaluated, and the results indicate that it consistently outperforms the expected value solutions. Numerical experiments show that the performance of the NTRDAC algorithm is quite encouraging and fit for large-scale practical problems.

Suggested Citation

  • Fudong Xie & Ce Wang & Housheng Duan, 2024. "Optimizing Fleet Size in Point-to-Point Shared Demand Responsive Transportation Service: A Network Decomposition Approach," Mathematics, MDPI, vol. 12(19), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3048-:d:1488336
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/19/3048/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/19/3048/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. George J. Beaujon & Mark A. Turnquist, 1991. "A Model for Fleet Sizing and Vehicle Allocation," Transportation Science, INFORMS, vol. 25(1), pages 19-45, February.
    2. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    3. Ho, Sin C. & Szeto, W.Y. & Kuo, Yong-Hong & Leung, Janny M.Y. & Petering, Matthew & Tou, Terence W.H., 2018. "A survey of dial-a-ride problems: Literature review and recent developments," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 395-421.
    4. Hui Wang & Jinyang Li & Pengling Wang & Jing Teng & Becky P. Y. Loo, 2023. "Adaptability analysis methods of demand responsive transit: a review and future directions," Transport Reviews, Taylor & Francis Journals, vol. 43(4), pages 676-697, July.
    5. Hongyun Si & Jiangang Shi & Wenwen Hua & Long Cheng & Jonas De Vos & Wenxiang Li, 2023. "What influences people to choose ridesharing? An overview of the literature," Transport Reviews, Taylor & Francis Journals, vol. 43(6), pages 1211-1236, November.
    6. Alejandro Tirachini, 2020. "Ride-hailing, travel behaviour and sustainable mobility: an international review," Transportation, Springer, vol. 47(4), pages 2011-2047, August.
    7. Paul Czioska & Ronny Kutadinata & Aleksandar Trifunović & Stephan Winter & Monika Sester & Bernhard Friedrich, 2019. "Real-world meeting points for shared demand-responsive transportation systems," Public Transport, Springer, vol. 11(2), pages 341-377, August.
    8. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    9. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
    10. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    11. Diana, Marco & Dessouky, Maged M. & Xia, Nan, 2006. "A model for the fleet sizing of demand responsive transportation services with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 651-666, September.
    12. Daganzo, Carlos F. & Ouyang, Yanfeng, 2019. "A general model of demand-responsive transportation services: From taxi to ridesharing to dial-a-ride," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 213-224.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. T. Glenn Bailey & Paul A. Jensen & David P. Morton, 1999. "Response surface analysis of two‐stage stochastic linear programming with recourse," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 753-776, October.
    2. Chia-Hung Chen & Shangyao Yan & Miawjane Chen, 2010. "Short-term manpower planning for MRT carriage maintenance under mixed deterministic and stochastic demands," Annals of Operations Research, Springer, vol. 181(1), pages 67-88, December.
    3. MELIS, Lissa & SÖRENSEN, Kenneth, 2021. "The real-time on-demand bus routing problem: What is the cost of dynamic requests?," Working Papers 2021003, University of Antwerp, Faculty of Business and Economics.
    4. V.I. Norkin & G.C. Pflug & A. Ruszczynski, 1996. "A Branch and Bound Method for Stochastic Global Optimization," Working Papers wp96065, International Institute for Applied Systems Analysis.
    5. Riis, Morten & Andersen, Kim Allan, 2005. "Applying the minimax criterion in stochastic recourse programs," European Journal of Operational Research, Elsevier, vol. 165(3), pages 569-584, September.
    6. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    7. Prasad Parab & Lewis Ntaimo & Bernardo Pagnoncelli, 2025. "Stochastic decomposition for risk-averse two-stage stochastic linear programs," Journal of Global Optimization, Springer, vol. 91(1), pages 59-93, January.
    8. Cosmin Petra & Mihai Anitescu, 2012. "A preconditioning technique for Schur complement systems arising in stochastic optimization," Computational Optimization and Applications, Springer, vol. 52(2), pages 315-344, June.
    9. Julia Higle & Suvrajeet Sen, 2006. "Multistage stochastic convex programs: Duality and its implications," Annals of Operations Research, Springer, vol. 142(1), pages 129-146, February.
    10. Z. L. Chen & W. B. Powell, 1999. "Convergent Cutting-Plane and Partial-Sampling Algorithm for Multistage Stochastic Linear Programs with Recourse," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 497-524, September.
    11. Lee, Yu-Ching & Chen, Yu-Shih & Chen, Albert Y., 2022. "Lagrangian dual decomposition for the ambulance relocation and routing considering stochastic demand with the truncated Poisson," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 1-23.
    12. Wu, Weitiao & Zhu, Yanchen & Liu, Ronghui, 2024. "Dynamic scheduling of flexible bus services with hybrid requests and fairness: Heuristics-guided multi-agent reinforcement learning with imitation learning," Transportation Research Part B: Methodological, Elsevier, vol. 190(C).
    13. Sodhi, ManMohan S. & Tang, Christopher S., 2009. "Modeling supply-chain planning under demand uncertainty using stochastic programming: A survey motivated by asset-liability management," International Journal of Production Economics, Elsevier, vol. 121(2), pages 728-738, October.
    14. Adarsh Vaderobli & Dev Parikh & Urmila Diwekar, 2020. "Optimization under Uncertainty to Reduce the Cost of Energy for Parabolic Trough Solar Power Plants for Different Weather Conditions," Energies, MDPI, vol. 13(12), pages 1-17, June.
    15. Jie Sun & Xinwei Liu, 2006. "Scenario Formulation of Stochastic Linear Programs and the Homogeneous Self-Dual Interior-Point Method," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 444-454, November.
    16. Trukhanov, Svyatoslav & Ntaimo, Lewis & Schaefer, Andrew, 2010. "Adaptive multicut aggregation for two-stage stochastic linear programs with recourse," European Journal of Operational Research, Elsevier, vol. 206(2), pages 395-406, October.
    17. Rich, Jeppe & Seshadri, Ravi & Jomeh, Ali Jamal & Clausen, Sofus Rasmus, 2023. "Fixed routing or demand-responsive? Agent-based modelling of autonomous first and last mile services in light-rail systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 173(C).
    18. Postek, Krzysztof & Romeijnders, Ward & den Hertog, Dick & van der Vlerk, Maartne H., 2016. "Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems under Mean-MAD Information," Other publications TiSEM a03f895f-b941-41a9-84e0-b, Tilburg University, School of Economics and Management.
    19. Dimitris Bertsimas & Omid Nohadani & Kwong Meng Teo, 2010. "Robust Optimization for Unconstrained Simulation-Based Problems," Operations Research, INFORMS, vol. 58(1), pages 161-178, February.
    20. Konrad Steiner & Stefan Irnich, 2018. "Strategic Planning for Integrated Mobility-on-Demand and Urban Public Bus Networks," Working Papers 1819, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3048-:d:1488336. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.