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A nested decomposition approach for solving the paratransit vehicle scheduling problem

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  • Karabuk, Suleyman

Abstract

The paratransit vehicle scheduling problem involves scheduling a fleet of specially equipped vehicles for serving transportation needs of disabled and elderly people. It is also referred to as a dial-a-ride problem, and it can be classified as a multi-depot pickup and delivery problem with time windows and side constraints. The column generation approach constitutes one of the effective methodologies to solve this problem. However, in order to cope with the complexity of the problem, it is commonly applied in two consecutive stages: clustering and routing. First, clusters of customers are formed who will receive service together; next, vehicle routing decisions are made subject to the clustering decisions. This paper develops a nested column generation method, which integrates clustering and routing decisions, thus extending the applicability of the column generation approach in the context of the subject problem. The proposed method is implemented and applied to solve a problem faced by the transit authority of a mid size US city. A detailed account of implementation experience is provided. The computational results, based on actual data, indicate that problem instances with up to 680 requests and 48 vehicles can be solved within 2% of optimality under mild assumptions, and a 12% performance improvement over a well-established manual planning system can be achieved.

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  • Karabuk, Suleyman, 2009. "A nested decomposition approach for solving the paratransit vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 448-465, May.
    • Handle: RePEc:eee:transb:v:43:y:2009:i:4:p:448-465
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    4. 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.
    5. Sapan Tiwari & Neema Nassir & Patricia Sauri Lavieri, 2024. "Review and Classification of Objectives in Dynamic Dial-a-Ride Systems: A Triple Bottom Line Approach of Sustainability," Sustainability, MDPI, vol. 16(13), pages 1-31, July.
    6. Masmoudi, Mohamed Amine & Hosny, Manar & Braekers, Kris & Dammak, Abdelaziz, 2016. "Three effective metaheuristics to solve the multi-depot multi-trip heterogeneous dial-a-ride problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 60-80.
    7. Xie, J. & Wong, S.C. & Zhan, S. & Lo, S.M. & Chen, Anthony, 2020. "Train schedule optimization based on schedule-based stochastic passenger assignment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    8. Christian Tilk & Michael Drexl & Stefan Irnich, 2018. "Nested Branch-and-Price-and-Cut for Vehicle Routing Problems with Multiple Resource Interdependencies," Working Papers 1801, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    9. Ibrahim Muter & Jean-François Cordeau & Gilbert Laporte, 2014. "A Branch-and-Price Algorithm for the Multidepot Vehicle Routing Problem with Interdepot Routes," Transportation Science, INFORMS, vol. 48(3), pages 425-441, August.
    10. Yves Molenbruch & Kris Braekers & An Caris, 2017. "Typology and literature review for dial-a-ride problems," Annals of Operations Research, Springer, vol. 259(1), pages 295-325, December.
    11. Dikas, G. & Minis, I., 2014. "Scheduled paratransit transport systems," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 18-34.
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