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Split delivery routing

Author

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  • Moshe Dror
  • Pierre Trudeau

Abstract

This article examines a relaxed version of the generic vehicle routing problem. In this version, a delivery to a demand point can be split between any number of vehicles. In spite of this relaxation the problem remains computationally hard. Since only small instances of the vehicle routing problem are known to be solved using exact methods, the vehicle route construction for this problem version is approached using heuristic rules. The main contribution of this article to the existing body of literature on vehicle routing issues in (a) is presenting a new vehicle routing problem amenable to practical applications, and (b) demonstrating the potential for cost savings over similar “traditional” vehicle routing when implementing the model and solutions presented here. The solution scheme allowing for split deliveries is compared with a solution in which no split deliveries are allowed. The comparison is conducted on six sets of 30 problems each for problems of size 75, 115, and 150 demand points (all together 540 problems). For very small demands (up to 10% of vehicle's capacity) no significant difference in solutions is evident for both solution schemes. For the other five problem sets for which point demand exceeds 10% of vehicle's capacity, very significant cost savings are realized when allowing split deliveries. The savings are significant both in the total distance and the number of vehicles required. The vehicles' routes constructed by our procedure tend to cover cohesive geographical zones and retain some properties of optimal solutions.

Suggested Citation

  • Moshe Dror & Pierre Trudeau, 1990. "Split delivery routing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 383-402, June.
    • Handle: RePEc:wly:navres:v:37:y:1990:i:3:p:383-402
    DOI: 10.1002/nav.3800370304
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    References listed on IDEAS

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    1. Dror, Moshe & Trudeau, Pierre, 1986. "Stochastic vehicle routing with modified savings algorithm," European Journal of Operational Research, Elsevier, vol. 23(2), pages 228-235, February.
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    Cited by:

    1. Nicola Bianchessi & Michael Drexl & Stefan Irnich, 2019. "The Split Delivery Vehicle Routing Problem with Time Windows and Customer Inconvenience Constraints," Transportation Science, INFORMS, vol. 53(4), pages 1067-1084, March.
    2. Puca Huachi Vaz Penna & Anand Subramanian & Luiz Satoru Ochi & Thibaut Vidal & Christian Prins, 2019. "A hybrid heuristic for a broad class of vehicle routing problems with heterogeneous fleet," Annals of Operations Research, Springer, vol. 273(1), pages 5-74, February.
    3. Fatemeh Sabouhi & Ali Bozorgi-Amiri & Mohammad Moshref-Javadi & Mehdi Heydari, 2019. "An integrated routing and scheduling model for evacuation and commodity distribution in large-scale disaster relief operations: a case study," Annals of Operations Research, Springer, vol. 283(1), pages 643-677, December.
    4. Zhixing Luo & Hu Qin & Wenbin Zhu & Andrew Lim, 2017. "Branch and Price and Cut for the Split-Delivery Vehicle Routing Problem with Time Windows and Linear Weight-Related Cost," Transportation Science, INFORMS, vol. 51(2), pages 668-687, May.
    5. Burcu B. Keskin & İbrahim Çapar & Charles R. Sox & Nickolas K. Freeman, 2014. "An Integrated Load-Planning Algorithm for Outbound Logistics at Webb Wheel," Interfaces, INFORMS, vol. 44(5), pages 480-497, October.
    6. Wang, Wei & Wang, Shuaian & Zhen, Lu & Laporte, Gilbert, 2023. "The impact of autonomous ships in regional waterways," Transportation Research Part B: Methodological, Elsevier, vol. 178(C).
    7. Bortfeldt, Andreas & Yi, Junmin, 2020. "The Split Delivery Vehicle Routing Problem with three-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 282(2), pages 545-558.
    8. Saman Eskandarzadeh & Reza Tavakkoli-Moghaddam & Amir Azaron, 2009. "An extension of the relaxation algorithm for solving a special case of capacitated arc routing problems," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 214-234, February.
    9. Jie, Wanchen & Yang, Jun & Zhang, Min & Huang, Yongxi, 2019. "The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology," European Journal of Operational Research, Elsevier, vol. 272(3), pages 879-904.
    10. 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.
    11. Jianli Shi & Jin Zhang & Kun Wang & Xin Fang, 2018. "Particle Swarm Optimization for Split Delivery Vehicle Routing Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(02), pages 1-42, April.
    12. Kai Huang & Michael Xu, 2023. "Optimization Models for the Vehicle Routing Problem under Disruptions," Mathematics, MDPI, vol. 11(16), pages 1-21, August.
    13. Zhang, Yuankai & Sun, Lijun & Hu, Xiangpei & Zhao, Chen, 2019. "Order consolidation for the last-mile split delivery in online retailing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 309-327.
    14. Cortes, Juan David & Suzuki, Yoshinori, 2020. "Vehicle Routing with Shipment Consolidation," International Journal of Production Economics, Elsevier, vol. 227(C).
    15. Casazza, Marco & Ceselli, Alberto & Wolfler Calvo, Roberto, 2021. "A route decomposition approach for the single commodity Split Pickup and Split Delivery Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 289(3), pages 897-911.
    16. Zongyi Chen & Mingkang Yang & Yijun Guo & Yu Liang & Yifan Ding & Li Wang, 2020. "The Split Delivery Vehicle Routing Problem with Three-Dimensional Loading and Time Windows Constraints," Sustainability, MDPI, vol. 12(17), pages 1-21, August.
    17. Lavigne, Carolien & Inghels, Dirk & Dullaert, Wout & Dewil, Reginald, 2023. "A memetic algorithm for solving rich waste collection problems," European Journal of Operational Research, Elsevier, vol. 308(2), pages 581-604.
    18. Zhixing Luo & Hu Qin & Wenbin Zhu & Andrew Lim, 2016. "Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 138-171, March.
    19. Tröster, Michael, 2017. "Bildung Einer Kostenfunktion Für Die Ausbringung Von Düngemitteln Unter Berücksichtigung Einer Tourenplanungsroutine Mit Teillieferungen (Sdvrp)," 57th Annual Conference, Weihenstephan, Germany, September 13-15, 2017 262155, German Association of Agricultural Economists (GEWISOLA).
    20. Leonardo Berbotto & Sergio García & Francisco Nogales, 2014. "A Randomized Granular Tabu Search heuristic for the split delivery vehicle routing problem," Annals of Operations Research, Springer, vol. 222(1), pages 153-173, November.
    21. Daqing Wu & Chenxiang Wu, 2022. "Research on the Time-Dependent Split Delivery Green Vehicle Routing Problem for Fresh Agricultural Products with Multiple Time Windows," Agriculture, MDPI, vol. 12(6), pages 1-28, May.
    22. Yugang Yu & Chengbin Chu & Haoxun Chen & Feng Chu, 2012. "Large scale stochastic inventory routing problems with split delivery and service level constraints," Annals of Operations Research, Springer, vol. 197(1), pages 135-158, August.
    23. Li, Jiliu & Qin, Hu & Baldacci, Roberto & Zhu, Wenbin, 2020. "Branch-and-price-and-cut for the synchronized vehicle routing problem with split delivery, proportional service time and multiple time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    24. Nicola Bianchessi & Stefan Irnich, 2019. "Branch-and-Cut for the Split Delivery Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 53(2), pages 442-462, March.
    25. Rui Xu & Yumiao Huang & Wei Xiao, 2023. "A Two-Level Variable Neighborhood Descent for a Split Delivery Clustered Vehicle Routing Problem with Soft Cluster Conflicts and Customer-Related Costs," Sustainability, MDPI, vol. 15(9), pages 1-22, May.

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