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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Altinkemer, K., Gavish, B.: Technical Note: Heuristics for Delivery Problems with Constant Error Guarantees. Transportation Science 24(4), 294–297 (1990)
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)
Balas, E.: New classes of efficiently solvable generalized traveling salesman problems. Annals of Operations Research (56), 529–558 (1999)
Balinski, M.L., Quandt, R.E.: On an integer program for a delivery problem. Operations Research 12, 300–304 (1964)
Bianco, L., Mingozzi, A., Ricciardelli, S.: The traveling salesman problem with cumulative costs. Networks 23(2), 81–91 (1993)
Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, W.R., Raghavan, P., Sudan, M.: The minimum latency problem. In: STOC, pp. 163–171 (1994)
Bramel, J., Simchi-Levi, D.: Probabilistic Analysis and Practical Algorithms for the Vehicle Routing Problem with Time Windows. Operations Research 44, 501–509 (1996)
Chabrier, A.: Vehicle Routing Problem with elementary shortest path based column generation. Computers & Operations Research 33(10), 2972–2990 (2006)
Christofides, N., Eilon, S.: An algorithm for the vehicle-dispatching problem. In: OR, pp. 309–318 (1969)
Cullen, F.H., Jarvis, J.J., Ratliff, H.D.: Set partitioning based heuristics for interactive routing. Networks 11(2), 125–143 (1981)
Gaur, D.R., Mudgal, A., Singh, R.R.: Routing vehicles to minimize fuel consumption. Operations Research Letters 41(6), 576–580 (2013)
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)
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)
Hassin, R.: Approximation schemes for the restricted shortest path problem. Mathematics of Operations Research 17(1), 36–42 (1992)
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)
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)
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)
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)
Raghavan, P., Thompson, C.D.: Randomized Rounding: A Technique for Provably Good Algorithms and Algorithmic Proofs. Combinatorica 7(4), 365–374 (1987)
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)
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)
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)
Toth, P., Vigo, D.: The Vehicle Routing Problem. SIAM (2001)
Vazirani, V.V.: Approximation Algorithms. Springer, New York (2001)
Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms, 1st edn. Cambridge University Press, New York (2011)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
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)