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A Branch-and-Price Algorithm for the Vehicle Routing Problem with 2-Dimensional Loading Constraints

  • Telmo PintoEmail author
  • Cláudio Alves
  • José Valério de Carvalho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9855)

Abstract

In this paper, we describe a branch-and-price algorithm for the capacitated vehicle routing problem with 2-dimensional loading constraints and a virtually unlimited number of vehicles. The column generation subproblem is solved heuristically through variable neighborhood search. Branch-and-price is used when it is not possible to add more attractive columns to the current restricted master problem, and the solution remains fractional. In order to accelerate the convergence of the algorithm, a family of valid dual inequalities is presented. Computational results are provided to evaluate the performance of the algorithm and to compare the different branching strategies proposed.

Keywords

Vehicle routing Loading constraints Branch-and-price Computational study 

References

  1. 1.
    Cordeau, J., Iori, M., Ropke, S., Vigo, D.: Branch-and-cut-and-price for the capacitated vehicle routing problem with two-dimensional loading constraints. In: ROUTE 2007, Jekyll Island (2007)Google Scholar
  2. 2.
    Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Oper. Res. 8(1), 101–111 (1960)CrossRefzbMATHGoogle Scholar
  3. 3.
    Feillet, D., Dejax, P., Gendreau, M., Gueguen, C.: An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Networks 44(3), 216–229 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Gendreau, M., Iori, M., Laporte, G., Martello, S.: A Tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints. Networks 51(1), 4–18 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Hokama, P., Miyazawa, F., Xavier, E.: A branch-and-cut approach for the vehicle routing problem with loading constraints. Expert Syst. Appl. 47, 1–13 (2016)CrossRefGoogle Scholar
  6. 6.
    Iori, M., Salazar-Gonzalez, J.-J., Vigo, D.: An exact approach for the vehicle routing problem with two-dimensional loading constraints. Transp. Sci. 41(2), 253–264 (2007)CrossRefGoogle Scholar
  7. 7.
    Junqueira, L., Oliveira, J., Carravilla, M.A., Morabito, R.: An optimization model for the vehicle routing problem with practical three-dimensional loading constraints. Int. Trans. Oper. Res. 20(5), 645–666 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Macedo, R., Alves, C., Valério de Carvalho, J.: Exact algorithms for vehicle routing problems with different service constraints. In: CTW09, France (2009)Google Scholar
  9. 9.
    Mahvash, B., Awasthi, A., Chauhan, S.: A column generation based heuristic for the capacitated vehicle routing problem with three-dimensional loading constraints. In: 15th IFAC Symposium on Information Control Problems in Manufacturing, vol. 48(3), pp. 448–453 (2015)Google Scholar
  10. 10.
    Pinto, T., Alves, C., de Carvalho, J.V.: Variable neighborhood search for the elementary shortest path problem with loading constraints. In: Gervasi, O., Murgante, B., Misra, S., Gavrilova, M.L., Rocha, A.M.A.C., Torre, C., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2015. LNCS, vol. 9156, pp. 474–489. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  11. 11.
    Souza, V.: Algoritmos para o problema de roteamento de veículos capacitado com restrições de carregamento bidimensional. Master’s thesis, Universidade Federal de Minas Gerais, Belo Horizonte, Brasil (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Telmo Pinto
    • 1
    Email author
  • Cláudio Alves
    • 1
  • José Valério de Carvalho
    • 1
  1. 1.Departamento de Produção e Sistemas, Escola de EngenhariaUniversidade do MinhoBragaPortugal

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