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Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows

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  • Kohar, Amit
  • Jakhar, Suresh Kumar
  • Agarwal, Yogesh K.

Abstract

In this paper, we propose an improved 2-index mixed integer linear programming formulation for capacitated multi-pickup and delivery problems with time windows. We develop new families of valid inequalities, present some simple separation heuristics and solve the benchmark problems using a cutting plane approach. Specifically, we propose and demonstrate the effectiveness of incompatible request sets based valid inequalities, exploiting thereby the time window and capacity constraints. Further, we introduce two sub-families of these inequalities: node-based and request-based incompatible request set cuts, along with their separation heuristics. The computational results show that the incompatible request set cuts are highly useful as cutting planes for the benchmark instances. Overall, there is a marked improvement in solution performance vis-à-vis the different formulations and solution approaches used in extant literature. The approach in this paper is able to solve 12%, 37% and 43% more instances to optimality, improve the root gap by 18%, 33% and 36%, and final gap by 36%, 45% and 43% vis-à-vis the asymmetric representative formulation, three-index and the two-index formulations respectively.

Suggested Citation

  • Kohar, Amit & Jakhar, Suresh Kumar & Agarwal, Yogesh K., 2023. "Strong cutting planes for the capacitated multi-pickup and delivery problem with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:transb:v:176:y:2023:i:c:s0191261523001315
    DOI: 10.1016/j.trb.2023.102806
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    References listed on IDEAS

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    1. 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.
    2. Yogesh Agarwal, 2013. "Design of Survivable Networks Using Three- and Four-Partition Facets," Operations Research, INFORMS, vol. 61(1), pages 199-213, February.
    3. Naccache, Salma & Côté, Jean-François & Coelho, Leandro C., 2018. "The multi-pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 269(1), pages 353-362.
    4. 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.
    5. Aziez, Imadeddine & Côté, Jean-François & Coelho, Leandro C., 2020. "Exact algorithms for the multi-pickup and delivery problem with time windows," European Journal of Operational Research, Elsevier, vol. 284(3), pages 906-919.
    6. Stefan Ropke & Jean-François Cordeau, 2009. "Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows," Transportation Science, INFORMS, vol. 43(3), pages 267-286, August.
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