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Hybrid algorithms for the vehicle routing problem with clustered backhauls and 3D loading constraints

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  • Bortfeldt, Andreas
  • Hahn, Thomas
  • Männel, Dirk
  • Mönch, Lars

Abstract

In this paper, we extend the vehicle routing problem with clustered backhauls (VRPCB) to an integrated routing and three-dimensional loading problem, called VRPCB with 3D loading constraints (3L-VRPCB). In the VRPCB each customer is either a linehaul or a backhaul customer and in each route all linehaul customers must be visited before any backhaul customer. In the 3L-VRPCB, each customer demand is given as a set of 3D rectangular items (boxes) and the vehicle capacity is replaced by a 3D loading space. Moreover, some packing constraints, e.g. concerning stacking of boxes, are also integrated. A set of routes of minimum total length has to be determined such that each customer is visited once. For each route two packing plans have to be provided that stow all boxes of all visited linehaul and backhaul customers, respectively, taking into account the additional packing constraints. We propose two hybrid algorithms for solving the 3L-VRPCB, each of them consisting of a routing and a packing procedure. The routing procedures follow different metaheuristic strategies (large vs. variable neighborhood search) and in both algorithms a tree search heuristic is responsible for packing boxes. Extensive computational experiments were carried out using 95 3L-VRPCB benchmark instances that were derived from well-known VRPCB instances. Good results are also achieved for the capacitated vehicle routing problem with 3D loading constraints as a special case of the 3L-VRPCB.

Suggested Citation

  • Bortfeldt, Andreas & Hahn, Thomas & Männel, Dirk & Mönch, Lars, 2015. "Hybrid algorithms for the vehicle routing problem with clustered backhauls and 3D loading constraints," European Journal of Operational Research, Elsevier, vol. 243(1), pages 82-96.
  • Handle: RePEc:eee:ejores:v:243:y:2015:i:1:p:82-96
    DOI: 10.1016/j.ejor.2014.12.001
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    5. Sadati, Mir Ehsan Hesam & Çatay, Bülent, 2021. "A hybrid variable neighborhood search approach for the multi-depot green vehicle routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    6. Maria João Santos & Pedro Amorim & Alexandra Marques & Ana Carvalho & Ana Póvoa, 2020. "The vehicle routing problem with backhauls towards a sustainability perspective: a review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 358-401, July.
    7. Dirk Männel & Andreas Bortfeldt, 2015. "Solving the Pickup and Delivery Problem with 3D Loading Constraints and Reloading Ban," FEMM Working Papers 150016, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    8. Ana Moura & Telmo Pinto & Cláudio Alves & José Valério de Carvalho, 2023. "A Matheuristic Approach to the Integration of Three-Dimensional Bin Packing Problem and Vehicle Routing Problem with Simultaneous Delivery and Pickup," Mathematics, MDPI, vol. 11(3), pages 1-16, January.
    9. Yuan Shiyi & Fu Jianwen & Cui Feng & Zhang Xin, 2020. "Truck and Trailer Routing Problem Solving by a Backtracking Search Algorithm," Journal of Systems Science and Information, De Gruyter, vol. 8(3), pages 253-272, June.
    10. Männel, Dirk & Bortfeldt, Andreas, 2016. "A hybrid algorithm for the vehicle routing problem with pickup and delivery and three-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 254(3), pages 840-858.
    11. Henriette Koch & Maximilian Schlögell & Andreas Bortfeldt, 2020. "A hybrid algorithm for the vehicle routing problem with three-dimensional loading constraints and mixed backhauls," Journal of Scheduling, Springer, vol. 23(1), pages 71-93, February.
    12. Henriette Koch & Andreas Bortfeldt & Gerhard Wäscher, 2018. "A hybrid algorithm for the vehicle routing problem with backhauls, time windows and three-dimensional loading constraints," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 1029-1075, October.
    13. Shi, Yong & Boudouh, Toufik & Grunder, Olivier, 2019. "A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 52-95.
    14. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.
    15. Henriette Koch & Andreas Bortfeldt & Gerhard Wäscher, 2017. "A hybrid solution approach for the 3L-VRP with simultaneous delivery and pickups," FEMM Working Papers 170005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    16. 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.
    17. Dirk Männel & Andreas Bortfeldt, 2015. "A Hybrid Algorithm for the Vehicle Routing Problem with Pickup and Delivery and 3D Loading Constraints," FEMM Working Papers 150015, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.

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