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Continuous approximation for demand balancing in solving large-scale one-commodity pickup and delivery problems

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  • Lei, Chao
  • Ouyang, Yanfeng

Abstract

The one-commodity pickup and delivery problem (1-PDP) has a wide range of applications in the real world, e.g., for repositioning bikes in large cities to guarantee the sustainable operations of bike-sharing systems. It remains a challenge, however, to solve the problem for large-scale instances. This paper proposes a hybrid modeling framework for 1-PDP, where a continuum approximation (CA) approach is used to model internal pickup and delivery routing within each of multiple subregions, while matching of net surplus or deficit of the commodity out of these subregions is addressed in a discrete model with a reduced problem size. The interdependent local routing and system-level matching decisions are made simultaneously, and a Lagrangian relaxation based algorithm is developed to solve the hybrid model. A series of numerical experiments are conducted to show that the hybrid model is able to produce a good solution for large-scale instances in a short computation time.

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  • Lei, Chao & Ouyang, Yanfeng, 2018. "Continuous approximation for demand balancing in solving large-scale one-commodity pickup and delivery problems," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 90-109.
    • Handle: RePEc:eee:transb:v:109:y:2018:i:c:p:90-109
    DOI: 10.1016/j.trb.2018.01.009
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    1. Tingting Cui & Yanfeng Ouyang & Zuo-Jun Max Shen, 2010. "Reliable Facility Location Design Under the Risk of Disruptions," Operations Research, INFORMS, vol. 58(4-part-1), pages 998-1011, August.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. Xin Wang & Michael K. Lim & Yanfeng Ouyang, 2017. "A Continuum Approximation Approach to the Dynamic Facility Location Problem in a Growing Market," Transportation Science, INFORMS, vol. 51(1), pages 343-357, February.
    4. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    5. Rieck, Julia & Ehrenberg, Carsten & Zimmermann, Jürgen, 2014. "Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery," European Journal of Operational Research, Elsevier, vol. 236(3), pages 863-878.
    6. Newell, Gordon F. & Daganzo, Carlos F., 1986. "Design of multiple-vehicle delivery tours--I a ring-radial network," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 345-363, October.
    7. Daganzo, Carlos F., 1984. "The length of tours in zones of different shapes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 135-145, April.
    8. Newell, Gordon F. & Daganzo, Carlos F., 1986. "Design of multiple vehicle delivery tours--II other metrics," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 365-376, October.
    9. Carlos F. Daganzo, 2005. "Logistics Systems Analysis," Springer Books, Springer, edition 0, number 978-3-540-27516-9, December.
    10. Yanfeng Ouyang & Carlos F. Daganzo, 2006. "Discretization and Validation of the Continuum Approximation Scheme for Terminal System Design," Transportation Science, INFORMS, vol. 40(1), pages 89-98, February.
    11. Mladenović, Nenad & Urošević, Dragan & Hanafi, Saı¨d & Ilić, Aleksandar, 2012. "A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 220(1), pages 270-285.
    12. Ouyang, Yanfeng & Wang, Zhaodong & Yang, Hai, 2015. "Facility location design under continuous traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 18-33.
    13. Erdoğan, Güneş & Laporte, Gilbert & Wolfler Calvo, Roberto, 2014. "The static bicycle relocation problem with demand intervals," European Journal of Operational Research, Elsevier, vol. 238(2), pages 451-457.
    14. Ouyang, Yanfeng, 2007. "Design of vehicle routing zones for large-scale distribution systems," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1079-1093, December.
    15. Ho, Sin C. & Szeto, W.Y., 2017. "A hybrid large neighborhood search for the static multi-vehicle bike-repositioning problem," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 340-363.
    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. Newell, G. F., 1986. "Design of multiple-vehicle delivery tours--III valuable goods," Transportation Research Part B: Methodological, Elsevier, vol. 20(5), pages 377-390, October.
    18. Cui, Tingting & Ouyang, Yanfeng & Shen, Zuo-Jun Max J, 2010. "Reliable Facility Location Design under the Risk of Disruptions," University of California Transportation Center, Working Papers qt5sh2c7pw, University of California Transportation Center.
    19. Erdoğan, Güneş & Battarra, Maria & Wolfler Calvo, Roberto, 2015. "An exact algorithm for the static rebalancing problem arising in bicycle sharing systems," European Journal of Operational Research, Elsevier, vol. 245(3), pages 667-679.
    20. Younes Rahmani & Wahiba Ramdane Cherif-Khettaf & Ammar Oulamara, 2016. "The two-echelon multi-products location-routing problem with pickup and delivery: formulation and heuristic approaches," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 999-1019, February.
    21. Robuste, Francesc & Daganzo, Carlos F. & Souleyrette, Reginald R., 1990. "Implementing vehicle routing models," Transportation Research Part B: Methodological, Elsevier, vol. 24(4), pages 263-286, August.
    22. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.
    23. Carlos F. Daganzo, 1984. "The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application," Transportation Science, INFORMS, vol. 18(4), pages 331-350, November.
    24. Forma, Iris A. & Raviv, Tal & Tzur, Michal, 2015. "A 3-step math heuristic for the static repositioning problem in bike-sharing systems," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 230-247.
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    6. Fu, Chenyi & Zhu, Ning & Ma, Shoufeng & Liu, Ronghui, 2022. "A two-stage robust approach to integrated station location and rebalancing vehicle service design in bike-sharing systems," European Journal of Operational Research, Elsevier, vol. 298(3), pages 915-938.
    7. Chen, Zhiwei & Guo, Yujie & Stuart, Amy L. & Zhang, Yu & Li, Xiaopeng, 2019. "Exploring the equity performance of bike-sharing systems with disaggregated data: A story of southern Tampa," Transportation Research Part A: Policy and Practice, Elsevier, vol. 130(C), pages 529-545.
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