Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2016, Article ID 2804525, 12 pages
http://dx.doi.org/10.1155/2016/2804525
Research Article

An Inverse Robust Optimisation Approach for a Class of Vehicle Routing Problems under Uncertainty

1School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China
2School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 250049, China

Received 29 October 2015; Accepted 14 December 2015

Academic Editor: Seenith Sivasundaram

Copyright © 2016 Liang Sun and Bing Wang. 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. J. C. Goodson, J. W. Ohlmann, and B. W. Thomas, “Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand,” European Journal of Operational Research, vol. 217, no. 2, pp. 312–323, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. C. Novoa and R. Storer, “An approximate dynamic programming approach for the vehicle routing problem with stochastic demands,” European Journal of Operational Research, vol. 196, no. 2, pp. 509–515, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. D. Taş, N. Dellaert, T. Van Woensel, and T. De Kok, “Vehicle routing problem with stochastic travel times including soft time windows and service costs,” Computers & Operations Research, vol. 40, no. 1, pp. 214–224, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. D. Taş, M. Gendreau, N. Dellaert, T. van Woensel, and A. G. de Kok, “Vehicle routing with soft time windows and stochastic travel times: a column generation and branch-and-price solution approach,” European Journal of Operational Research, vol. 236, no. 3, pp. 789–799, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. M. Allahviranloo, J. Y. J. Chow, and W. W. Recker, “Selective vehicle routing problems under uncertainty without recourse,” Transportation Research Part E: Logistics and Transportation Review, vol. 62, pp. 68–88, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Zhang, W. H. Lam, and B. Y. Chen, “A stochastic vehicle routing problem with travel time uncertainty: trade-off between cost and customer service,” Networks and Spatial Economics, vol. 13, no. 4, pp. 471–496, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. D. Bertsimas and M. Sim, “The price of robustness,” Operations Research, vol. 52, no. 1, pp. 35–53, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. J. M. Mulvey and A. Ruszczyński, “A new scenario decomposition method for large-scale stochastic optimization,” Operations Research, vol. 43, no. 3, pp. 477–490, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. M. Mulvey, R. J. Vanderbei, and S. A. Zenios, “Robust optimization of large-scale systems,” Operations Research, vol. 43, no. 2, pp. 264–281, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  10. I. Sungur, F. Ordóñez, and M. Dessouky, “A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty,” IIE Transactions, vol. 40, no. 5, pp. 509–523, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. C. E. Gounaris, W. Wiesemann, and C. A. Floudas, “The robust capacitated vehicle routing problem under demand uncertainty,” Operations Research, vol. 61, no. 3, pp. 677–693, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. C. Lee, K. Lee, and S. Park, “Robust vehicle routing problem with deadlines and travel time/demand uncertainty,” Journal of the Operational Research Society, vol. 63, no. 9, pp. 1294–1306, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. A. Agra, M. Christiansen, R. Figueiredo, L. M. Hvattum, M. Poss, and C. Requejo, “The robust vehicle routing problem with time windows,” Computers & Operations Research, vol. 40, no. 3, pp. 856–866, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. Montemanni, J. Barta, M. Mastrolilli, and L. M. Gambardella, “The robust traveling salesman problem with interval data,” Transportation Science, vol. 41, no. 3, pp. 366–381, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. L. Zhang, J. Wang, and J. Huang, “Robust optimal resource allocation model for uncertain demands,” Journal of Systems Science and Mathematical Sciences, vol. 30, no. 10, pp. 1283–1292, 2010. View at Google Scholar
  16. T. Yao, S. R. Mandala, and B. D. Chung, “Evacuation transportation planning under uncertainty: a robust optimization approach,” Networks and Spatial Economics, vol. 9, no. 2, pp. 171–189, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. M. Jafari-Eskandari, A. R. Aliahmadi, and G. H. H. Khaleghi, “A robust optimisation approach for the milk run problem with time windows with inventory uncertainty: an auto industry supply chain case study,” International Journal of Rapid Manufacturing, vol. 1, no. 3, pp. 334–347, 2010. View at Google Scholar
  18. M. Najafi, K. Eshghi, and W. Dullaert, “A multi-objective robust optimization model for logistics planning in the earthquake response phase,” Transportation Research Part E: Logistics and Transportation Review, vol. 49, no. 1, pp. 217–249, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Markowitz, “Portfolio selection,” The Journal of Finance, vol. 7, no. 1, pp. 77–91, 1952. View at Publisher · View at Google Scholar
  20. G. F. List, B. Wood, L. K. Nozick et al., “Robust optimization for fleet planning under uncertainty,” Transportation Research Part E: Logistics and Transportation Review, vol. 39, no. 3, pp. 209–227, 2003. View at Publisher · View at Google Scholar · View at Scopus
  21. Y. Sun, R. Song, and S.-W. He, “Robust optimization for transit timetable design under stochastic demands,” System Engineering Theory and Practice, vol. 31, no. 5, pp. 986–992, 2011. View at Google Scholar · View at Scopus
  22. S. Y. Yan and C.-H. Tang, “An integrated framework for intercity bus scheduling under stochastic bus travel times,” Transportation Science, vol. 42, no. 3, pp. 318–335, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. Yan, Q. Meng, S. Wang, and X. Guo, “Robust optimization model of schedule design for a fixed bus route,” Transportation Research Part C: Emerging Technologies, vol. 25, pp. 113–121, 2012. View at Publisher · View at Google Scholar · View at Scopus
  24. Y. Yan, Z. Liu, Q. Meng, and Y. Jiang, “Robust optimization model of bus transit network design with stochastic travel time,” Journal of Transportation Engineering, vol. 139, no. 6, pp. 625–634, 2013. View at Publisher · View at Google Scholar · View at Scopus
  25. M. Naumann, L. Suhl, and S. Kramkowski, “A stochastic programming approach for robust vehicle scheduling in public bus transport,” Procedia—Social and Behavioral Sciences, vol. 20, pp. 826–835, 2011. View at Publisher · View at Google Scholar
  26. J. C. Qin, J. L. Zhang, and K. L. Wang, “Robust optimization approach to truck transport of hazardous material,” Statistics & Decisions, no. 20, pp. 25–26, 2009. View at Google Scholar
  27. L. Sun and B. Wang, “Robust optimisation approach for vehicle routing problems with demand and cost uncertainty,” International Journal of Computer Applications in Technology, vol. 50, no. 3, pp. 200–205, 2014. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Sun, “A new robust optimization model for the vehicle routing problem with stochastic demands,” Journal of Interdisciplinary Mathematics, vol. 17, no. 3, pp. 287–309, 2014. View at Publisher · View at Google Scholar · View at Scopus
  29. L. Sun and B. Wang, “Robust optimisation approach for vehicle routing problems with uncertainty,” Mathematical Problems in Engineering, vol. 2015, Article ID 901583, 8 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  30. A. Ben-Tal, B. D. Chung, S. R. Mandala, and T. Yao, “Robust optimization for emergency logistics planning: risk mitigation in humanitarian relief supply chains,” Transportation Research Part B: Methodological, vol. 45, no. 8, pp. 1177–1189, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. J. Z. Zhang, Z. F. Ma, and C. Yang, “A column generation method for inverse shortest path problems,” Zeitschrift für Operations Research, vol. 41, no. 3, pp. 347–358, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. 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
  33. P. W. Frizzell and J. W. Giffin, “The split delivery vehicle scheduling problem with time windows and grid network distances,” Computers and Operations Research, vol. 22, no. 6, pp. 655–667, 1995. View at Publisher · View at Google Scholar · View at Scopus