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Cumulative Vehicle Routing Problem: A Column Generation Approach

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8959)

Abstract

Cumulative vehicle routing problems are a simplified model of fuel consumption in vehicle routing problems. Here we study computationally, an approach for constructing approximate solutions to cumulative vehicle routing problems based on rounding solutions to a linear program. The linear program is based on the set cover formulation, and is solved using column generation. The pricing sub-problem is solved using dynamic programming. Simulation results show that the simple scalable strategy computes solutions with cost close to the lower bound given by the linear programming relaxation.

Keywords

  • Routing
  • Transportation
  • Linear programming
  • Traveling salesman
  • Column generation

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References

  1. Altinkemer, K., Gavish, B.: Technical Note: Heuristics for Delivery Problems with Constant Error Guarantees. Transportation Science 24(4), 294–297 (1990)

    CrossRef  MATH  Google Scholar 

  2. Augerat, P., Belenguer, J.M., Benavent, E., Corberan, A., Naddef, D., Rinaldi, G.: Computational results with a branch and cut code for the capacitated vehicle routing problem, Tech. Rep. 1 RR949-M, ARTEMIS-IMAG, Grenoble France (1995)

    Google Scholar 

  3. Balas, E.: New classes of efficiently solvable generalized traveling salesman problems. Annals of Operations Research (56), 529–558 (1999)

    Google Scholar 

  4. Balinski, M.L., Quandt, R.E.: On an integer program for a delivery problem. Operations Research 12, 300–304 (1964)

    CrossRef  Google Scholar 

  5. Bianco, L., Mingozzi, A., Ricciardelli, S.: The traveling salesman problem with cumulative costs. Networks 23(2), 81–91 (1993)

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, W.R., Raghavan, P., Sudan, M.: The minimum latency problem. In: STOC, pp. 163–171 (1994)

    Google Scholar 

  7. Bramel, J., Simchi-Levi, D.: Probabilistic Analysis and Practical Algorithms for the Vehicle Routing Problem with Time Windows. Operations Research 44, 501–509 (1996)

    CrossRef  MATH  Google Scholar 

  8. Chabrier, A.: Vehicle Routing Problem with elementary shortest path based column generation. Computers & Operations Research 33(10), 2972–2990 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. Christofides, N., Eilon, S.: An algorithm for the vehicle-dispatching problem. In: OR, pp. 309–318 (1969)

    Google Scholar 

  10. Cullen, F.H., Jarvis, J.J., Ratliff, H.D.: Set partitioning based heuristics for interactive routing. Networks 11(2), 125–143 (1981)

    CrossRef  MathSciNet  Google Scholar 

  11. Gaur, D.R., Mudgal, A., Singh, R.R.: Routing vehicles to minimize fuel consumption. Operations Research Letters 41(6), 576–580 (2013)

    CrossRef  MATH  MathSciNet  Google Scholar 

  12. Fakcharoenphol, J., Harrelson, C., Rao, S.: The k-traveling repairman problem. In: Proceedings of the fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 655–664. Society for Industrial and Applied Mathematics (January 2003)

    Google Scholar 

  13. 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)

    CrossRef  MATH  MathSciNet  Google Scholar 

  14. Hassin, R.: Approximation schemes for the restricted shortest path problem. Mathematics of Operations Research 17(1), 36–42 (1992)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. Irnich, S., Desaulniers, G.: Shortest path problems with resource constraints. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds.) Column generation, GERAD 25th Anniversary Series, ch. 2, pp. 33–65. Springer (2005)

    Google Scholar 

  16. Kara, İ., Kara, B.Y., Yetiş, M.K.: Cumulative Vehicle Routing Problems. In: Caric, T., Gold, H. (eds.) Vehicle Routing Problem, pp. 85–98. I-Tech Education and Publishing KG, Vienna (2008)

    Google Scholar 

  17. Kara, İ., Kara, B.Y., Yetis, M.K.: Energy Minimizing Vehicle Routing Problem. In: Dress, A., Xu, Y., Zhu, B. (eds.) COCOA. LNCS, vol. 4616, pp. 62–71. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  18. Lysgaard, J., Wohlk, S.: A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem. European Journal of Operational Research (August 2013)

    Google Scholar 

  19. Raghavan, P., Thompson, C.D.: Randomized Rounding: A Technique for Provably Good Algorithms and Algorithmic Proofs. Combinatorica 7(4), 365–374 (1987)

    CrossRef  MATH  MathSciNet  Google Scholar 

  20. Rinaldi, G., Yarrow, L.: Optimizing a 48-city traveling salesman problem: A case study in combinatorial problem solving, New York University, Graduate School of Business Administration (1985)

    Google Scholar 

  21. Rousseau, L.M., Gendreau, M., Pesant, G., Focacci, F.: Solving VRPTWs with constraint programming based column generation. Annals of Operations Research 130(1-4), 199–216 (2004)

    CrossRef  MATH  MathSciNet  Google Scholar 

  22. Sahin, B., Yilmaz, H., Ust, Y., Guneri, A.F., Gulsun, B.: An approach for analyzing transportation costs and a case study. European Journal of Operational Research 193, 1–11 (2009)

    CrossRef  MATH  Google Scholar 

  23. Toth, P., Vigo, D.: The Vehicle Routing Problem. SIAM (2001)

    Google Scholar 

  24. Vazirani, V.V.: Approximation Algorithms. Springer, New York (2001)

    Google Scholar 

  25. Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, 1st edn. Cambridge University Press, New York (2011)

    CrossRef  MATH  Google Scholar 

  26. Xiao, Y., Zhao, Q., Kaku, I., Xu, Y.: Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Computers & Operations Research 39(7), 1419–1431 (2012)

    CrossRef  MATH  MathSciNet  Google Scholar 

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Gaur, D.R., Singh, R.R. (2015). Cumulative Vehicle Routing Problem: A Column Generation Approach. In: Ganguly, S., Krishnamurti, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2015. Lecture Notes in Computer Science, vol 8959. Springer, Cham. https://doi.org/10.1007/978-3-319-14974-5_25

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  • DOI: https://doi.org/10.1007/978-3-319-14974-5_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14973-8

  • Online ISBN: 978-3-319-14974-5

  • eBook Packages: Computer ScienceComputer Science (R0)