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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 803135, 7 pages
http://dx.doi.org/10.1155/2015/803135
Research Article

A Multiple-Starting-Path Approach to the Resource-Constrained th Elementary Shortest Path Problem

Department of Industrial and Management Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea

Received 12 September 2014; Accepted 9 March 2015

Academic Editor: Dong Ngoduy

Copyright © 2015 Hyunchul Tae and Byung-In Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Dror, “Note on the complexity of the shortest path models for column generation in VRPTW,” Operations Research, vol. 42, no. 5, pp. 977–978, 1994. View at Publisher · View at Google Scholar
  2. D. Feillet, P. Dejax, M. Gendreau, and C. Gueguen, “An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems,” Networks, vol. 44, no. 3, pp. 216–229, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. G. Righini and M. Salani, “Symmetry helps: bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints,” Discrete Optimization, vol. 3, no. 3, pp. 255–273, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. Baldacci, N. Christofides, and A. Mingozzi, “An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts,” Mathematical Programming, vol. 115, no. 2, pp. 351–385, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. G. Righini and M. Salani, “New dynamic programming algorithms for the resource constrained elementary shortest path problem,” Networks, vol. 51, no. 3, pp. 155–170, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. Desrochers, J. Desrosiers, and M. Solomon, “A new optimization algorithm for the vehicle routing problem with time windows,” Operations Research, vol. 40, no. 2, pp. 342–354, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  7. G. Desaulniers, F. Lessard, and A. Hadjar, “Tabu search, partial elementarity, and generalized k-path inequalities for the vehicle routing problem with time windows,” Transportation Science, vol. 42, no. 3, pp. 387–404, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Chabrier, “Vehicle routing problem with elementary shortest path based column generation,” Computers & Operations Research, vol. 33, no. 10, pp. 2972–2990, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Baldacci, A. Mingozzi, and R. Roberti, “New route relaxation and pricing strategies for the vehicle routing problem,” Operations Research, vol. 59, no. 5, pp. 1269–1283, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. H. Tae and B.-I. Kim, “A branch-and-price approach for the team orienteering problem with time windows,” International Journal of Industrial Engineering: Theory, Applications and Practice. In press.
  11. S. Boussier, D. Feillet, and M. Gendreau, “An exact algorithm for team orienteering problems,” 4OR, vol. 5, no. 3, pp. 211–230, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. M. Göthe-Lundgren, K. Jörnsten, and P. Värbrand, “On the nucleolus of the basic vehicle routing game,” Mathematical Programming, vol. 72, no. 1, pp. 83–100, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  13. G. Liu and K. G. Ramakrishnan, “A* prune: an algorithm for finding K shortest paths subject to multiple constraints,” in Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 743–749, Anchorage, Alaska, USA, April 2001. View at Scopus
  14. N. J. van der Zijpp and S. F. Catalano, “Path enumeration by finding the constrained K-shortest paths,” Transportation Research Part B: Methodological, vol. 39, no. 6, pp. 545–563, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. N. Shi, “K constrained shortest path problem,” IEEE Transactions on Automation Science and Engineering, vol. 7, no. 1, pp. 15–23, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. E. L. Lawler, “A procedure for computing the K best solutions to discrete optimization problems and its application to the shortest path problem,” Management Science, vol. 18, no. 7, pp. 401–405, 1972. View at Google Scholar · View at MathSciNet
  17. H. Tae and B.-I. Kim, “Dynamic programming approach for prize colleting travelling salesman problem with time windows,” IE Interfaces, vol. 24, no. 2, pp. 112–118, 2011. View at Publisher · View at Google Scholar
  18. M. M. Solomon, “Algorithms for the vehicle routing and scheduling problems with time window constraints,” Operations Research, vol. 35, no. 2, pp. 254–265, 1987. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus