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Lifted polynomial size formulations for the homogeneous and heterogeneous vehicle routing problems

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  • Leggieri, Valeria
  • Haouari, Mohamed

Abstract

We propose compact formulations for the symmetric and asymmetric capacitated vehicle routing problems. These formulations are obtained by lifting, using the Reformulation–Linearization Technique, a novel polynomial size ordered path-based formulation. We show that the strongest proposed formulation is equivalent to the strongest multi-commodity flow formulation presented so far. In addition, we propose polynomial size valid inequalities that aim at further tightening the proposed formulations. Also, the tightest formulation is extended to model the fleet size and mix vehicle routing problem with fixed costs. We show that the new derived model is not comparable with a state-of-the-art polynomial length formulation. We present the results of computational experiments that demonstrate the tightness of the proposed formulations and the impact of the valid inequalities.

Suggested Citation

  • Leggieri, Valeria & Haouari, Mohamed, 2017. "Lifted polynomial size formulations for the homogeneous and heterogeneous vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 263(3), pages 755-767.
    • Handle: RePEc:eee:ejores:v:263:y:2017:i:3:p:755-767
    DOI: 10.1016/j.ejor.2017.05.039
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    1. M. L. Balinski & R. E. Quandt, 1964. "On an Integer Program for a Delivery Problem," Operations Research, INFORMS, vol. 12(2), pages 300-304, April.
    2. G. B. Dantzig & J. H. Ramser, 1959. "The Truck Dispatching Problem," Management Science, INFORMS, vol. 6(1), pages 80-91, October.
    3. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
    4. Matteo Fischetti & Paolo Toth & Daniele Vigo, 1994. "A Branch-and-Bound Algorithm for the Capacitated Vehicle Routing Problem on Directed Graphs," Operations Research, INFORMS, vol. 42(5), pages 846-859, October.
    5. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "Thirty years of heterogeneous vehicle routing," European Journal of Operational Research, Elsevier, vol. 249(1), pages 1-21.
    6. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
    7. Letchford, Adam N. & Salazar-González, Juan-José, 2015. "Stronger multi-commodity flow formulations of the Capacitated Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 730-738.
    8. François Clautiaux & Cláudio Alves & José Valério de Carvalho, 2010. "A survey of dual-feasible and superadditive functions," Annals of Operations Research, Springer, vol. 179(1), pages 317-342, September.
    9. Gouveia, Luis & Pires, Jose Manuel, 1999. "The asymmetric travelling salesman problem and a reformulation of the Miller-Tucker-Zemlin constraints," European Journal of Operational Research, Elsevier, vol. 112(1), pages 134-146, January.
    10. N. R. Achuthan & L. Caccetta & S. P. Hill, 2003. "An Improved Branch-and-Cut Algorithm for the Capacitated Vehicle Routing Problem," Transportation Science, INFORMS, vol. 37(2), pages 153-169, May.
    11. Kara, Imdat & Laporte, Gilbert & Bektas, Tolga, 2004. "A note on the lifted Miller-Tucker-Zemlin subtour elimination constraints for the capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(3), pages 793-795, November.
    12. R. Baldacci & E. Hadjiconstantinou & A. Mingozzi, 2004. "An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation," Operations Research, INFORMS, vol. 52(5), pages 723-738, October.
    13. Gilbert Laporte & Yves Nobert & Martin Desrochers, 1985. "Optimal Routing under Capacity and Distance Restrictions," Operations Research, INFORMS, vol. 33(5), pages 1050-1073, October.
    14. Baldacci, Roberto & Mingozzi, Aristide & Roberti, Roberto, 2012. "Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints," European Journal of Operational Research, Elsevier, vol. 218(1), pages 1-6.
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    Cited by:

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    2. Qiuping Ni & Yuanxiang Tang, 2023. "A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research," Sustainability, MDPI, vol. 15(9), pages 1-37, April.
    3. Letchford, Adam N. & Salazar-González, Juan-José, 2019. "The Capacitated Vehicle Routing Problem: Stronger bounds in pseudo-polynomial time," European Journal of Operational Research, Elsevier, vol. 272(1), pages 24-31.
    4. Khalid Mekamcha & Mehdi Souier & Hakim Nadhir Bessenouci & Mohammed Bennekrouf, 2021. "Two metaheuristics approaches for solving the traveling salesman problem: an Algerian waste collection case," Operational Research, Springer, vol. 21(3), pages 1641-1661, September.

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