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Exact algorithms for routing problems under vehicle capacity constraints

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  • Roberto Baldacci
  • Paolo Toth
  • Daniele Vigo

Abstract

The solution of a vehicle routing problem calls for the determination of a set of routes, each performed by a single vehicle which starts and ends at its own depot, such that all the requirements of the customers are fulfilled and the global transportation cost is minimized. The routes have to satisfy several operational constraints which depend on the nature of the transported goods, on the quality of the service level, and on the characteristics of the customers and of the vehicles. One of the most common operational constraint addressed in the scientific literature is that the vehicle fleet is capacitated and the total load transported by a vehicle cannot exceed its capacity. This paper provides a review of the most recent developments that had a major impact in the current state-of-the-art of exact algorithms for vehicle routing problems under capacity constraints, with a focus on the basic Capacitated Vehicle Routing Problem (CVRP) and on heterogeneous vehicle routing problems. The most important mathematical formulations for the problem together with various relaxations are reviewed. The paper also describes the recent exact methods and reports a comparison of their computational performances. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Roberto Baldacci & Paolo Toth & Daniele Vigo, 2010. "Exact algorithms for routing problems under vehicle capacity constraints," Annals of Operations Research, Springer, vol. 175(1), pages 213-245, March.
  • Handle: RePEc:spr:annopr:v:175:y:2010:i:1:p:213-245:10.1007/s10479-009-0650-0
    DOI: 10.1007/s10479-009-0650-0
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    References listed on IDEAS

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    1. Marshall L. Fisher, 1994. "Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees," Operations Research, INFORMS, vol. 42(4), pages 626-642, August.
    2. 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.
    3. G. B. Dantzig & J. H. Ramser, 1959. "The Truck Dispatching Problem," Management Science, INFORMS, vol. 6(1), pages 80-91, October.
    4. Araque, J. & Hall, L. & Magnanti, T., 1990. "Capacitated trees, capacitated routing, and associated polyhedra," LIDAM Discussion Papers CORE 1990061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. Matteo Fischetti & Paolo Toth, 1989. "An Additive Bounding Procedure for Combinatorial Optimization Problems," Operations Research, INFORMS, vol. 37(2), pages 319-328, April.
    7. 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.
    8. 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.
    9. Gilbert Laporte & Yves Nobert & Martin Desrochers, 1985. "Optimal Routing under Capacity and Distance Restrictions," Operations Research, INFORMS, vol. 33(5), pages 1050-1073, October.
    10. Augerat, P. & Belenguer, J. M. & Benavent, E. & Corberan, A. & Naddef, D., 1998. "Separating capacity constraints in the CVRP using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 546-557, April.
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