A Variable Neighborhood Search Approach for the Two-Echelon Location-Routing Problem

  • Martin Schwengerer
  • Sandro Pirkwieser
  • Günther R. Raidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7245)


We consider the two-echelon location-routing problem (2E-LRP), a well-known problem in freight distribution arising when establishing a two-level transport system with limited capacities. The problem is a generalization of the location routing problem (LRP), involving strategic (location), tactical (allocation) and operational (routing) decisions at the same time. We present a variable neighborhood search (VNS) based on a previous successful VNS for the LRP, accordingly adapted as well as extended. The proposed algorithm provides solutions of high quality in short time, making use of seven different basic neighborhood structures parameterized with different perturbation size leading to a total of 21 specific neighborhood structures. For intensification, two consecutive local search methods are applied, optimizing the transport costs efficiently by considering only recently changed solution parts. Experimental results clearly show that our method is at least competitive regarding runtime and solution quality to other leading approaches, also improving upon several best known solutions.


Variable Neighborhood Search Vehicle Route Problem Facility Location Problem Path Relinking Location Route Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jacobsen, S.K., Madsen, O.B.G.: A comparative study of heuristics for a two-level routing-location problem. European Journal of Operational Research 5(6), 378–387 (1980)zbMATHCrossRefGoogle Scholar
  2. 2.
    Salhi, S., Rand, G.K.: The effect of ignoring routes when locating depots. European Journal of Operational Research 39(2), 150–156 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Pirkwieser, S., Raidl, G.R.: Variable Neighborhood Search Coupled with ILP-Based Very Large Neighborhood Searches for the (Periodic) Location-Routing Problem. In: Blesa, M.J., Blum, C., Raidl, G., Roli, A., Sampels, M. (eds.) HM 2010. LNCS, vol. 6373, pp. 174–189. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Gonzalez-Feliu, J.: The n-echelon location routing problem: concepts and methods for tactical and operational planning. Working Papers halshs-00422492, HAL (2009)Google Scholar
  5. 5.
    Boccia, M., Crainic, T.G., Sforza, A., Sterle, C.: Location-routing models for designing a two-echelon freight distribution system. Technical Report CIRRELT-2011-06, University of Montreal (2011)Google Scholar
  6. 6.
    Boccia, M., Crainic, T., Sforza, A., Sterle, C.: A Metaheuristic for a Two Echelon Location-Routing Problem. In: Festa, P. (ed.) SEA 2010. LNCS, vol. 6049, pp. 288–301. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Nguyen, V.P., Prins, C., Prodhon, C.: Solving the two-echelon location routing problem by a GRASP reinforced by a learning process and path relinking. European Journal of Operational Research 216(1), 113–126 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Nguyen, V.P., Prins, C., Prodhon, C.: A multi-start iterated local search with tabu list and path relinking for the two-echelon location-routing problem. Engineering Applications of Artificial Intelligence 25(1), 56–71 (2011)CrossRefGoogle Scholar
  9. 9.
    Contardo, C., Hemmelmayr, V.C., Crainic, T.G.: Lower and upper bounds for the two-echelon capacitated location routing problem. Technical Report CIRRELT-2011-63, University of Montreal (2011)Google Scholar
  10. 10.
    Jin, L., Zhu, Y., Shen, H., Ku, T.: A hybrid genetic algorithm for two-layer location-routing problem. In: 2010 4th International Conference on New Trends in Information Science and Service Science (NISS), pp. 642–645 (2010)Google Scholar
  11. 11.
    Crainic, T.G., Mancini, S., Perboli, G., Tadei, R.: Multi-start heuristics for the two-echelon vehicle routing problem. Technical Report CIRRELT-2010-30, University of Montreal (2010)Google Scholar
  12. 12.
    Hemmelmayr, V.C., Cordeau, J.F., Crainic, T.G.: An adaptive large neighborhood search heuristic for two-echelon vehicle routing problems arising in city logistics. Technical Report CIRRELT-2011-42, University of Montreal (2011)Google Scholar
  13. 13.
    Tragantalerngsak, S., Holt, J., Rönnqvist, M.: Lagrangian heuristics for the two-echelon, single-source, capacitated facility location problem. European Journal of Operational Research 102(3), 611–625 (1997)zbMATHCrossRefGoogle Scholar
  14. 14.
    Gao, L.L., Robinson Jr., E.P.: A dual-based optimization procedure for the two-echelon uncapacitated facility location problem. Naval Research Logistics 39(2), 191–212 (1992)zbMATHCrossRefGoogle Scholar
  15. 15.
    Gonzalez-Feliu, J.: Two-echelon freight transport optimisation: unifying concepts via a systematic review. Post-Print halshs-00569980, HAL (2011)Google Scholar
  16. 16.
    Contardo, C., Cordeau, J.F., Gendron, B.: A grasp + ilp-based metaheuristic for the capacitated location-routing problem. Technical Report CIRRELT-2011-52, University of Montreal (2011)Google Scholar
  17. 17.
    Hansen, P., Mladenović, N., Brimberg, J., Moreno Pérez, J.A.: Variable neighborhood search. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, 2nd edn., pp. 61–86. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Clarke, G., Wright, J.W.: Scheduling of vehicles from a central depot to a number of delivery points. Operations Research 12(4), 568–581 (1964)CrossRefGoogle Scholar
  19. 19.
    Potvin, J.Y., Rousseau, J.M.: An exchange heuristic for routeing problems with time windows. Journal of the Operational Research Society 46, 1433–1446 (1995)zbMATHGoogle Scholar
  20. 20.
    Hemmelmayr, V.C., Doerner, K.F., Hartl, R.F.: A variable neighborhood search heuristic for periodic routing problems. European Journal of Operational Research 195(3), 791–802 (2009)zbMATHCrossRefGoogle Scholar
  21. 21.
    Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Prodhon, C.: (December 2011),
  23. 23.
    Sterle, C.: Private communication (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Martin Schwengerer
    • 1
  • Sandro Pirkwieser
    • 2
  • Günther R. Raidl
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria
  2. 2.Destion – IT Consulting OGViennaAustria

Personalised recommendations