Annals of Operations Research

, Volume 181, Issue 1, pp 337–358 | Cite as

A new mixed integer linear model for a rich vehicle routing problem with docking constraints

  • Julia RieckEmail author
  • Jürgen Zimmermann


In this paper we address a rich vehicle routing problem that arises in real-life applications. Among other aspects we consider time windows, simultaneous delivery and pick-up at customer locations and multiple use of vehicles. To guarantee a coordinated material flow at the depot, we include the timed allocation of vehicles to loading bays at which the loading and unloading activities can occur. The resulting vehicle routing problem is formulated as a two-index vehicle-flow model which integrates the routing under real-life conditions and the assignment of vehicles to loading bays at the depot. We use CPLEX 11.0 to solve medium-sized instances that are derived from the extended Solomon test set. The selective implementation of preprocessing techniques and cutting planes improves the solver performance significantly.


Vehicle routing Simultaneous delivery and pick-up Docking constraints Mixed integer linear programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bräysy, O., & Gendreau, M. (2005a). Vehicle routing with time windows, part I: route construction and local search algorithms. Transportation Science, 39, 104–118. CrossRefGoogle Scholar
  2. Bräysy, O., & Gendreau, M. (2005b). Vehicle routing with time windows, part II: metaheuristics. Transportation Science, 39, 119–139. CrossRefGoogle Scholar
  3. Choi, E., & Tcha, D.-W. (2007). A column generation approach to the heterogeneous fleet vehicle routing problem. Computers and Operations Research, 34, 2080–2095. CrossRefGoogle Scholar
  4. Desrosiers, J., Soumis, F., & Desrochers, M. (1984). Routing with time windows by column generation. Networks, 14, 545–565. CrossRefGoogle Scholar
  5. Dethloff, J. (2001). Vehicle routing and reverse logistics: the vehicle routing problem with simultaneous delivery and pick-up. OR Spektrum, 23, 79–96. CrossRefGoogle Scholar
  6. Dror, M. (1994). Note on the complexity of the shortest path models for column generation in VRPTW. Operations Research, 42, 977–978. CrossRefGoogle Scholar
  7. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of NP completeness. New York: Freeman. Google Scholar
  8. Goel, A., & Gruhn, V. (2008). A general vehicle routing problem. European Journal of Operational Research, 191, 650–660. CrossRefGoogle Scholar
  9. Hajri-Gabouj, S., & Darmoul, S. (2003). A hybrid evolutionary approach for a vehicle routing problem with double time windows for the depot and multiple use of vehicles. Studies in Informatics and Control, 12, 253–268. Google Scholar
  10. Homberger, J., & Gehring, H. (2002). Parallelization of a two-phase metaheuristic for routing problems with time windows. Journal of Heuristics, 8, 251–276. CrossRefGoogle Scholar
  11. Kallehauge, B., Larsen, J., Madsen, O. B. G., & Solomon, M. M. (2005). Vehicle routing problem with time windows. In G. Desaulniers, J. Desrosiers, & M. M. Solomon (Eds.), Column Generation (pp. 67–98). New York: Springer. CrossRefGoogle Scholar
  12. Laporte, G., & Nobert, Y. (1983). A branch and bound algorithm for the capacitated vehicle routing problem. OR Spektrum, 5, 77–85. CrossRefGoogle Scholar
  13. Letchford, A. N., & Salazar-Gonzales, J.-J. (2006). Projection results for vehicle routing. Mathematical Programming, Series B, 105, 251–274. CrossRefGoogle Scholar
  14. Lysgaard, J. (2004). CVRPSEP: a package of separation routines for the capacitated vehicle routing problem. Working paper 03–04, Department of Business Studies, Aarhus School of Business, University of Aarhus, Denmark. Google Scholar
  15. Lysgaard, J., Letchford, A. N., & Eglese, R. W. (2004). A new branch-and-cut algorithm for the capacitated vehicle routing problem. Mathematical Programming, Series A, 100, 423–445. CrossRefGoogle Scholar
  16. Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2008). A survey on pickup and delivery problems, part I: transportation between customers and depot. Journal für Betriebswirtschaft, 58, 21–51. CrossRefGoogle Scholar
  17. Rieck, J., & Zimmermann, J. (2009). A hybrid algorithm for vehicle routing of less-than-truckload carriers. In M.-J. Geiger, W. Habenicht, M. Sevaux, & K. Sörensen (Eds.), Lecture notes in economics and mathematical systems (LNEMS) : Vol. 624. Metaheuristics in the service industry (pp. 155–172). Berlin: Springer. CrossRefGoogle Scholar
  18. Taillard, E. (1999). A heuristic column generation method for the heterogeneous fleet VRP. Rairo Operations Research, 33, 1–14. CrossRefGoogle Scholar
  19. Toth, P., & Vigo, D. (2002). An overview of vehicle routing problems. In P. Toth & D. Vigo (Eds.), The vehicle routing problem (pp. 1–26). Philadelphia: Siam. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Operations ResearchClausthal University of TechnologyClausthal-ZellerfeldGermany

Personalised recommendations