Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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A Branch-and-price Algorithm for the Vehicle Routing Problem with Time Dependent Travel Times

이동시간의 변화를 고려한 차량경로 문제의 분지평가법을 이용한 최적화 해법

  • Lee, Yong-Sik (Department of Industrial and Systems Engineering, KAIST) ;
  • Lee, Chung-Mok (Department of Industrial and Systems Engineering, KAIST) ;
  • Park, Sung-Soo (Department of Industrial and Systems Engineering, KAIST)
  • 이용식 (KAIST 산업 및 시스템 공학과) ;
  • 이충목 (KAIST 산업 및 시스템 공학과) ;
  • 박성수 (KAIST 산업 및 시스템 공학과)
  • Received : 2011.05.09
  • Accepted : 2011.05.19
  • Published : 2011.06.01
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Abstract

Most of the models for the vehicle routing problems studied in the literature assumed constant travel times. However, those approaches may give infeasible solutions when traffic congestion causes delays in travel time. To overcome such difficulty, there have been some researches considering the change of the travel time which is called the time dependent vehicle routing problem (TDVRP). TDVRP assumes that the travel time between two locations is not only affected by the distance traveled, but by many other factors including the time of the day. In this paper, we propose a branch-and-price algorithm to solve the TDVRP. The time dependent property of the travel time is dealt with an enumeration scheme with bounding procedures in the column generation procedure identifying a profitable route. The proposed algorithm guarantees the "Non-passing" property to be held in the solutions. The algorithm was tested on problems composed of the Solomon's benchmark instances for 25 and 50 nodes. Computational results are reported.

Keywords

References

  1. Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., and Vance, P. H. (1998), Branch-and-price: Column generation for solving huge integer programs, Operations Research, 46(3), 316-329. https://doi.org/10.1287/opre.46.3.316
  2. Chabrier, A. (2006), Vehicle Routing Problem with elementary shortest path based column generation, Computers and operations research, 33, 2972-2990. https://doi.org/10.1016/j.cor.2005.02.029
  3. Danzig, G. B. and Rameser, J. H. (1959), The truck dispatching Problem, Mgmt. Science, 6, 80-91. https://doi.org/10.1287/mnsc.6.1.80
  4. Desrochers, M., Desrosiers, J., and Solomon, M. (1992), A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows, Operations Research, 40(2), 342-354. https://doi.org/10.1287/opre.40.2.342
  5. Desrosiers, J., Dumas, Y., M. Solomon, M., and Soumis, F. (1995), Time constrained routing and scheduling, in : M. O. Ball, T. L. Magnanti, C. L. Monma, G. L. Nemhauser (eds.), Network routing, Handbooks in Operations Research and Management Science, 8, 35-139.
  6. Donati, A. V., Montemanni, R., Casagrande, N., Rizzoli, A. E., and Gambardella, L. M. (2008), Time Dependent Vehicle Routing Problem with a Multi Ant Colony System, European Journal of Operational Research, 185, 1174-1191. https://doi.org/10.1016/j.ejor.2006.06.047
  7. Gabali, O. (2010), Analysis of Travel Times and CO2 Emissions in Time Dependent Vehicle Routing, http://cms.ieis.tue.nl/Beta/Files/Abstra ct%20Gabali.pdf.
  8. Gelinas, S., Desrochers, M., Desrosiers, J., and Solomon, M. M. (1995), A New Branching Strategy for Time Constrained Routing Problems With Application to Backhauling, Annals of Operations Research, 61, 91-109. https://doi.org/10.1007/BF02098283
  9. Haghani, A. and Jung, S. (2005), A Dynamic Vehicle Routing Problem with Time Dependent Travel Times, Computers and Operations Research, 32, 2959-2986. https://doi.org/10.1016/j.cor.2004.04.013
  10. Hill, A. V. and Benton, W. C. (1992), Modeling Intra-City Time Depen Dependent Travel Speeds for Vehicle Scheduling Problems, J.Opl. Res. Soc, 43(4), 343- 351. https://doi.org/10.1057/jors.1992.49
  11. Ichoua, S., Gendreau, M., and Potvin, J. Y. (2003), Vehicle Dispatching with Time Dependent Travel Times, European Journal of Operational Research, 144, 379-396. https://doi.org/10.1016/S0377-2217(02)00147-9
  12. Irnich, S. and Desaulniers, G. (2004), Shortest Path Problems with Resource Constraints, Springer.
  13. Kuo, Y. (2010), Using Simulated Annealing to Minimize Fuel Consumption for the Time Dependent Vehicle Routing Problem, Computers and Industrial Engineering, 59, 157-165. https://doi.org/10.1016/j.cie.2010.03.012
  14. Lee, C. (2009), Robust Optimization Models and Algorithm for the Problems in Telecommunication and Logistics, Ph.D. Thesis, Korea Advanced Institute of Science and Technology, Daejon, Republic of Korea, 77-104.
  15. Lenstra, J. K. and RinnooyKan, A. H. G. (1981), Complexity of Vehicle Routing and Scheduling Problems, Networks, 11, 221-227. https://doi.org/10.1002/net.3230110211
  16. Malandraki, C. (1989), Time Dependent Vehicle Routing Problems : Formulations, Solution Algorithms and Computations Experiments, Ph.D. dissertation, North western University, Evanston, III.
  17. Malandraki, C. and Daskin, M. (1992), Time Dependent Vehicle Routing Problems : Formulations, Properties and Heuristic Algorithms, Transportation Science, 26(3), 185-200. https://doi.org/10.1287/trsc.26.3.185
  18. Solomon, M. M. (1987), Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints, Operations Research, 35(2), 354-265. https://doi.org/10.1287/opre.35.3.354
  19. Sung, K., Bell, M. G. H., Seong, M., and Park, S. (2000), Shortest Paths in a Network with Time Dependent Flow Speeds, European Journal of Operational Research, 121 , 32-39. https://doi.org/10.1016/S0377-2217(99)00035-1