Approximation Algorithms for Conflict-Free Vehicle Routing

  • Kaspar Schüpbach
  • Rico Zenklusen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

Abstract

We consider a natural basic model for conflict-free routing of a group of k vehicles, a problem frequently encountered in many applications in transportation and logistics. There is a large gap between currently employed routing schemes and the theoretical understanding of the problem. Previous approaches have either essentially no theoretical guarantees, or suffer from high running times, severely limiting their usability. So far, no efficient algorithm is known with a sub-linear (in k) approximation guarantee and without restrictions on the graph topology.

We show that the conflict-free vehicle routing problem is hard to solve to optimality, even on paths. Building on a sequential routing scheme, we present an algorithm for trees with makespan bounded by O(OPT) + k. Combining this result with ideas known from packet routing, we obtain a first efficient algorithm with sub-linear approximation guarantee, namely an \(O(\sqrt{k})\)-approximation. Additionally, a randomized algorithm leading to a makespan of O(polylog(k))·OPT + k is presented that relies on tree embedding techniques applied to a compacted version of the graph to obtain an approximation guarantee independent of the graph size.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atkin, J.A.D., Burke, E.K., Ravizza, S.: The airport ground movement problem: Past and current research and future directions. In: 4th International Conference on Research in Air Transportation, ICRAT(2010)Google Scholar
  2. 2.
    Busch, C., Magdon-Ismail, M., Mavronicolas, M., Spirakis, P.G.: Direct routing: Algorithms and complexity. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 134–145. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Dhamdhere, K., Gupta, A., Räcke, H.: Improved embeddings of graph metrics into random trees. In: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, SODA, pp. 61–69 (2006)Google Scholar
  4. 4.
    Freling, R., Lentink, R.M., Kroon, L.G., Huisman, D.: Shunting of passenger train units in a railway station. Transportation Science 39(2), 261–272 (2005)CrossRefGoogle Scholar
  5. 5.
    Galbiati, G., Rizzi, R., Amaldi, E.: On the approximability of the minimum strictly fundamental cycle basis problem. Discrete Applied Mathematics 159(4), 187–200 (2011)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Ganesharajah, T., Hall, N.G., Sriskandarajah, C.: Design and operational issues in AGV-served manufacturing systems. Annals of Operations Research 76, 109–154 (1998)CrossRefMATHGoogle Scholar
  7. 7.
    Garcia, J., Berlanga, A., Molina, J., Besada, J., Casar, J.: Planning techniques for airport ground operations. In: Proceedings of 21st Digital Avionics Systems Conference., vol. 1, pp. 1D5-1–1D5-12 (2002)Google Scholar
  8. 8.
    auf der Heide, F.M., Scheideler, C.: Routing with bounded buffers and hot-potato routing in vertex-symmetric networks. In: Spirakis, P.G. (ed.) ESA 1995. LNCS, vol. 979, pp. 341–354. Springer, Heidelberg (1995)Google Scholar
  9. 9.
    Kim, C.W., Tanchoco, J.M.A.: Conflict-free shortest-time bidirectional AGV routeing. International Journal of Production Research (1991)Google Scholar
  10. 10.
    Kim, K., Jeon, S., Ryu, K.: Deadlock prevention for automated guided vehicles in automated container terminals. In: Kim, K.H., Günther, H.-O. (eds.) Container Terminals and Cargo Systems, pp. 243–263. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Koch, R., Peis, B., Skutella, M., Wiese, A.: Real-time message routing and scheduling. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) APPROX 2009. LNCS, vol. 5687, pp. 217–230. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Krishnamurthy, N.N., Batta, R., Karwan, M.H.: Developing conflict-free routes for automated guided vehicles. Operations Research 41(6), 1077–1090 (1993)CrossRefMATHGoogle Scholar
  13. 13.
    Möhring, R.H., Köhler, E., Gawrilow, E., Stenzel, B.: Conflict-free real-time AGV routing. In: Proceedings of Operations Research, pp. 18–24 (2005)Google Scholar
  14. 14.
    Oellrich, M.: Minimum-Cost Disjoint Paths Under Arc Dependences - Algorithms for Practice. Ph.D. thesis, Technische Universität Berlin (2008)Google Scholar
  15. 15.
    Peis, B., Skutella, M., Wiese, A.: Packet routing: Complexity and algorithms. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 217–228. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Petersen, E.R., Taylor, A.J.: An optimal scheduling system for the welland canal. Transportation Science 22(3), 173 (1988)CrossRefMATHGoogle Scholar
  17. 17.
    Sanità, L.: Robust Network Design. Ph.D. thesis, Università Sapienza di Roma (January 2009)Google Scholar
  18. 18.
    Scheideler, C.: Universal Routing Strategies for Interconnection Networks. Springer-Verlag New York, Inc., Secaucus (1998)CrossRefMATHGoogle Scholar
  19. 19.
    Spenke, I.: Complexity and Approximation of Static k-splittable Flows and Dynamic Grid Flows. Ph.D. thesis, Technische Universität Berlin (2006)Google Scholar
  20. 20.
    Srinivasan, A., Teo, C.P.: A constant-factor approximation algorithm for packet routing, and balancing local vs. global criteria. In: Proceedings of the ACM Symposium on the Theory of Computing, STOC, pp. 636–643 (1997)Google Scholar
  21. 21.
    Stahlbock, R., Voß, S.: Operations research at container terminals: a literature update. OR Spectrum 30, 1–52 (2008)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Stenzel, B.: Online Disjoint Vehicle Routing with Application to AGV Routing. Ph.D. thesis, Technische Universität Berlin (2008)Google Scholar
  23. 23.
    Vis, I.F.: Survey of research in the design and control of automated guided vehicle systems. European Journal of Operational Research 170(3), 677–709 (2006)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kaspar Schüpbach
    • 1
  • Rico Zenklusen
    • 2
  1. 1.Institute For Operations ResearchETH ZürichZürichSwitzerland
  2. 2.Department of MathematicsMITCambridgeUSA

Personalised recommendations