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An Algorithm For The Generalized Vehicle Routing Problem With Backhauling

Author

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  • SUBRATA MITRA

    (Indian Institute of Management Calcutta, Joka, Diamond Harbour Road, Kolkata – 700 104, India)

Abstract

The Vehicle Routing Problem with Backhauling deals with the supply of finished goods from a depot to a number of delivery points, and picking up returnable items and bringing them back to the depot using a fleet of trucks. Traditionally, the objective of the problem has been to determine the truck routes such that the total number of trucks and/or the total distance traveled/total route cost are minimized. Most of the papers available in the literature in this connection deal with problems where the linehaul (having a demand for finished goods) and backhaul (having items to be returned to the depot) customers are different, and a customer may be visited by at most one truck limiting demand and returns at a location by the capacity of the truck. In this paper, we allow the linehaul and backhaul customers to be the same leading to simultaneous delivery and pickup at a customer location, and also there is no restriction on the quantity demanded at (to be returned from) a customer location. As such a customer may be visited by more than one truck and more than once by the same truck. We developed a Mixed Integer Linear programming (MILP) formulation of the problem and a route construction heuristic. The heuristic averaged 80 ms for 110 problems tested, and in 78 of them the heuristic costs were either equal to the optimal costs or at most equal to the upper bounds on the optimal costs obtained after running the optimization package for 30 min. Optimal solutions were obtained for 28 problems at an average time of 295 ms. The heuristic could match the optimal solutions for 22 of these problems at an average time of 71 ms.

Suggested Citation

  • Subrata Mitra, 2005. "An Algorithm For The Generalized Vehicle Routing Problem With Backhauling," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 153-169.
    • Handle: RePEc:wsi:apjorx:v:22:y:2005:i:02:n:s0217595905000522
    DOI: 10.1142/S0217595905000522
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    Citations

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    Cited by:

    1. Gábor Nagy & Niaz A. Wassan & M. Grazia Speranza & Claudia Archetti, 2015. "The Vehicle Routing Problem with Divisible Deliveries and Pickups," Transportation Science, INFORMS, vol. 49(2), pages 271-294, May.
    2. Fazi, Stefano & Fransoo, Jan C. & Van Woensel, Tom & Dong, Jing-Xin, 2020. "A variant of the split vehicle routing problem with simultaneous deliveries and pickups for inland container shipping in dry-port based systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    3. S Mitra, 2008. "A parallel clustering technique for the vehicle routing problem with split deliveries and pickups," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1532-1546, November.
    4. Lai, Michela & Crainic, Teodor Gabriel & Di Francesco, Massimo & Zuddas, Paola, 2013. "An heuristic search for the routing of heterogeneous trucks with single and double container loads," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 56(C), pages 108-118.
    5. Santos, Maria João & Jorge, Diana & Ramos, Tânia & Barbosa-Póvoa, Ana, 2023. "Green reverse logistics: Exploring the vehicle routing problem with deliveries and pickups," Omega, Elsevier, vol. 118(C).

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