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The Dial-a-Ride Problem with Split Requests and Profits

Author

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  • Sophie N. Parragh

    (Department of Business Administration, University of Vienna, 1090 Vienna, Austria; and INESC Porto/IBM CAS Portugal, 4200-465 Porto, Portugal)

  • Jorge Pinho de Sousa

    (INESC TEC/Faculdade de Engenharia da Universidade do Porto, 4200-465 Porto, Portugal)

  • Bernardo Almada-Lobo

    (INESC TEC/Faculdade de Engenharia da Universidade do Porto, 4200-465 Porto, Portugal)

Abstract

In this paper we introduce the dial-a-ride problem with split requests and profits (DARPSRP). Users place transportation requests, specifying a pickup location, a delivery location, and a time window for either of the two. Based on maximum user ride time considerations, the second time window is generated. A given fleet of vehicles, each with a certain capacity, is available to serve these requests, and maximum route duration constraints have to be respected. Each request is associated with a revenue and the objective is to maximize the total profit, that is, the total revenue minus the total costs. Transportation requests involving several persons may be split if it is beneficial to do so. We formulate the DARPSRP as a mixed-integer program using position variables and in terms of a path-based formulation. For the solution of the latter, we design a branch-and-price algorithm. The largest instance solved to optimality, when applied to available instances from the literature, has 40 requests; when applied to newly generated instances, the largest instance solved to optimality consists of 24 requests. To solve larger instances a variable neighborhood search algorithm is developed. We investigate the impact of request splitting under different geographical settings, assuming favorable settings for request splitting in terms of the number of people per request. The largest benefits from request splitting are obtained for problem settings exhibiting clustered customer locations.

Suggested Citation

  • Sophie N. Parragh & Jorge Pinho de Sousa & Bernardo Almada-Lobo, 2015. "The Dial-a-Ride Problem with Split Requests and Profits," Transportation Science, INFORMS, vol. 49(2), pages 311-334, May.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:2:p:311-334
    DOI: 10.1287/trsc.2014.0520
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    6. Wolfinger, David & Salazar-González, Juan-José, 2021. "The Pickup and Delivery Problem with Split Loads and Transshipments: A Branch-and-Cut Solution Approach," European Journal of Operational Research, Elsevier, vol. 289(2), pages 470-484.
    7. Christiaens, Jan & Çalik, Hatice & Wauters, Tony & Chirayil Chandrasekharan, Reshma & Vanden Berghe, Greet, 2020. "The prisoner transportation problem," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1058-1073.
    8. Johnsen, Lennart C. & Meisel, Frank, 2022. "Interrelated trips in the rural dial-a-ride problem with autonomous vehicles," European Journal of Operational Research, Elsevier, vol. 303(1), pages 201-219.
    9. 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.
    10. Bolor Jargalsaikhan & Ward Romeijnders & Kees Jan Roodbergen, 2021. "A Compact Arc-Based ILP Formulation for the Pickup and Delivery Problem with Divisible Pickups and Deliveries," Transportation Science, INFORMS, vol. 55(2), pages 336-352, March.
    11. 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.
    12. Jörn Schönberger, 2017. "Scheduling constraints in dial-a-ride problems with transfers: a metaheuristic approach incorporating a cross-route scheduling procedure with postponement opportunities," Public Transport, Springer, vol. 9(1), pages 243-272, July.
    13. 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.
    14. Dong, Xiaotong & Chow, Joseph Y.J. & Waller, S. Travis & Rey, David, 2022. "A chance-constrained dial-a-ride problem with utility-maximising demand and multiple pricing structures," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    15. Irawan, Chandra Ade & Ouelhadj, Djamila & Jones, Dylan & Stålhane, Magnus & Sperstad, Iver Bakken, 2017. "Optimisation of maintenance routing and scheduling for offshore wind farms," European Journal of Operational Research, Elsevier, vol. 256(1), pages 76-89.
    16. Schulz, Arne & Pfeiffer, Christian, 2024. "A Branch-and-Cut algorithm for the dial-a-ride problem with incompatible customer types," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 181(C).
    17. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    18. Sharif Azadeh, Sh. & Atasoy, Bilge & Ben-Akiva, Moshe E. & Bierlaire, M. & Maknoon, M.Y., 2022. "Choice-driven dial-a-ride problem for demand responsive mobility service," Transportation Research Part B: Methodological, Elsevier, vol. 161(C), pages 128-149.

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