IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v181y2024ics0191261524000286.html
   My bibliography  Save this article

Average minimum distance to visit a subset of random points in a compact region

Author

Listed:
  • Lei, Chao
  • Ouyang, Yanfeng

Abstract

This paper seeks an analytical estimate of the expected distance for visiting an arbitrary subset of independently and uniformly distributed random points within a compact region. This problem has many real-world application contexts such as the emerging on-demand transportation and logistics services (e.g., ridesharing, customized buses). The lower bounds of the expected optimal tour length are analytically derived by considering a so-called “trapping effect”, which explicitly addresses probabilistically the situation that some of the tour legs must connect points that are not neighbors. A parametric approach is developed to estimate the expected optimal tour length for both Euclidean and rectilinear metrics. Numerical experiments demonstrate the validity of these bounds, as well as the closeness of the proposed estimator to simulated results.

Suggested Citation

  • Lei, Chao & Ouyang, Yanfeng, 2024. "Average minimum distance to visit a subset of random points in a compact region," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
  • Handle: RePEc:eee:transb:v:181:y:2024:i:c:s0191261524000286
    DOI: 10.1016/j.trb.2024.102904
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261524000286
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.trb.2024.102904?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Figliozzi, Miguel Andres, 2009. "Planning approximations to the average length of vehicle routing problems with time window constraints," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 438-447, May.
    2. Merrill M. Flood, 1956. "The Traveling-Salesman Problem," Operations Research, INFORMS, vol. 4(1), pages 61-75, 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. Liu, Yining & Ouyang, Yanfeng, 2023. "Planning ride-pooling services with detour restrictions for spatially heterogeneous demand: A multi-zone queuing network approach," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    5. Max Shen, Zuo-Jun & Qi, Lian, 2007. "Incorporating inventory and routing costs in strategic location models," European Journal of Operational Research, Elsevier, vol. 179(2), pages 372-389, June.
    6. Ouyang, Yanfeng & Yang, Haolin & Daganzo, Carlos F., 2021. "Performance of reservation-based carpooling services under detour and waiting time restrictions," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 370-385.
    7. Carlos F. Daganzo, 2005. "Logistics Systems Analysis," Springer Books, Springer, edition 0, number 978-3-540-27516-9, June.
    8. Yining Liu & Yanfeng Ouyang, 2022. "Planning ride-pooling services with detour restrictions for spatially heterogeneous demand: A multi-zone queuing network approach," Papers 2208.02219, arXiv.org, revised Jun 2023.
    9. Jiang, Zhoutong & Lei, Chao & Ouyang, Yanfeng, 2020. "Optimal investment and management of shared bikes in a competitive market," Transportation Research Part B: Methodological, Elsevier, vol. 135(C), pages 143-155.
    10. Luo, Sida & Nie, Yu (Marco), 2019. "Impact of ride-pooling on the nature of transit network design," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 175-192.
    11. Furuhata, Masabumi & Dessouky, Maged & Ordóñez, Fernando & Brunet, Marc-Etienne & Wang, Xiaoqing & Koenig, Sven, 2013. "Ridesharing: The state-of-the-art and future directions," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 28-46.
    12. Liu, Tao & Ceder, Avishai (Avi), 2015. "Analysis of a new public-transport-service concept: Customized bus in China," Transport Policy, Elsevier, vol. 39(C), pages 63-76.
    13. Lei, Chao & Jiang, Zhoutong & Ouyang, Yanfeng, 2020. "Path-based dynamic pricing for vehicle allocation in ridesharing systems with fully compliant drivers," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 60-75.
    14. Daganzo, Carlos F., 2010. "Public Transportation Systems:Basic Principles of System Design,Operations Planning and Real-TimeControl," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt46f4x3zf, Institute of Transportation Studies, UC Berkeley.
    15. 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.
    16. Dell'Amico, Mauro & Hadjicostantinou, Eleni & Iori, Manuel & Novellani, Stefano, 2014. "The bike sharing rebalancing problem: Mathematical formulations and benchmark instances," Omega, Elsevier, vol. 45(C), pages 7-19.
    17. Jean-François Cordeau & Gilbert Laporte, 2007. "The dial-a-ride problem: models and algorithms," Annals of Operations Research, Springer, vol. 153(1), pages 29-46, September.
    18. Agatz, Niels & Erera, Alan & Savelsbergh, Martin & Wang, Xing, 2012. "Optimization for dynamic ride-sharing: A review," European Journal of Operational Research, Elsevier, vol. 223(2), pages 295-303.
    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. Ouyang, Yanfeng & Yang, Haolin, 2023. "Measurement and mitigation of the “wild goose chase” phenomenon in taxi services," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 217-234.
    2. Liu, Yining & Ouyang, Yanfeng, 2023. "Planning ride-pooling services with detour restrictions for spatially heterogeneous demand: A multi-zone queuing network approach," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    3. Daganzo, Carlos F. & Ouyang, Yanfeng & Yang, Haolin, 2020. "Analysis of ride-sharing with service time and detour guarantees," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 130-150.
    4. Yining Liu & Yanfeng Ouyang, 2022. "Planning ride-pooling services with detour restrictions for spatially heterogeneous demand: A multi-zone queuing network approach," Papers 2208.02219, arXiv.org, revised Jun 2023.
    5. Behrend, Moritz & Meisel, Frank & Fagerholt, Kjetil & Andersson, Henrik, 2019. "An exact solution method for the capacitated item-sharing and crowdshipping problem," European Journal of Operational Research, Elsevier, vol. 279(2), pages 589-604.
    6. Mourad, Abood & Puchinger, Jakob & Chu, Chengbin, 2019. "A survey of models and algorithms for optimizing shared mobility," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 323-346.
    7. Ke, Jintao & Yang, Hai & Li, Xinwei & Wang, Hai & Ye, Jieping, 2020. "Pricing and equilibrium in on-demand ride-pooling markets," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 411-431.
    8. Zhang, Ruolin & Masoud, Neda, 2021. "A distributed algorithm for operating large-scale ridesourcing systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).
    9. Liu, Yining & Ouyang, Yanfeng, 2021. "Mobility service design via joint optimization of transit networks and demand-responsive services," Transportation Research Part B: Methodological, Elsevier, vol. 151(C), pages 22-41.
    10. Si, Jinhua & He, Fang & Lin, Xi & Tang, Xindi, 2024. "Vehicle dispatching and routing of on-demand intercity ride-pooling services: A multi-agent hierarchical reinforcement learning approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 186(C).
    11. Dessouky, Maged M & Hu, Shichun, 2021. "Dynamic Routing for Ride-Sharing," Institute of Transportation Studies, Working Paper Series qt6qq8r7hz, Institute of Transportation Studies, UC Davis.
    12. 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.
    13. Bhoopalam, Anirudh Kishore & Agatz, Niels & Zuidwijk, Rob, 2018. "Planning of truck platoons: A literature review and directions for future research," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 212-228.
    14. Masoud, Neda & Jayakrishnan, R., 2017. "A decomposition algorithm to solve the multi-hop Peer-to-Peer ride-matching problem," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 1-29.
    15. Li, Yuanyuan & Liu, Yang, 2021. "Optimizing flexible one-to-two matching in ride-hailing systems with boundedly rational users," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).
    16. Beojone, Caio Vitor & Geroliminis, Nikolas, 2023. "A dynamic multi-region MFD model for ride-sourcing with ridesplitting," Transportation Research Part B: Methodological, Elsevier, vol. 177(C).
    17. Stumpe, Miriam & Dieter, Peter & Schryen, Guido & Müller, Oliver & Beverungen, Daniel, 2024. "Designing taxi ridesharing systems with shared pick-up and drop-off locations: Insights from a computational study," Transportation Research Part A: Policy and Practice, Elsevier, vol. 183(C).
    18. Ke, Jintao & Yang, Hai & Zheng, Zhengfei, 2020. "On ride-pooling and traffic congestion," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 213-231.
    19. Guo, Jiaqi & Long, Jiancheng & Xu, Xiaoming & Yu, Miao & Yuan, Kai, 2022. "The vehicle routing problem of intercity ride-sharing between two cities," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 113-139.
    20. Mohammad Asghari & Seyed Mohammad Javad Mirzapour Al-E-Hashem & Yacine Rekik, 2022. "Environmental and social implications of incorporating carpooling service on a customized bus system," Post-Print hal-03598768, HAL.

    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:eee:transb:v:181:y:2024:i:c:s0191261524000286. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    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.