Table of Contents Author Guidelines Submit a Manuscript
Journal of Optimization
Volume 2016, Article ID 8518921, 9 pages
http://dx.doi.org/10.1155/2016/8518921
Research Article

A Hybrid Dynamic Programming for Solving Fixed Cost Transportation with Discounted Mechanism

Sharif University of Technology, Azadi Avenue, P.O. Box 11155-9414, Tehran, Iran

Received 2 December 2015; Accepted 28 January 2016

Academic Editor: Manlio Gaudioso

Copyright © 2016 Farhad Ghassemi Tari. 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. R. Wilson, “26th Annual state of logistics report,” Tech. Rep., Penske Logistics Corporation CSCMP, Washington, DC, USA, 2015. View at Google Scholar
  2. M. R. Bartolacci, L. J. LeBlanc, Y. Kayikci, and T. A. Grossman, “Optimization modeling for logistics: options and implementations,” Journal of Business Logistics, vol. 33, no. 2, pp. 118–127, 2012. View at Publisher · View at Google Scholar · View at Scopus
  3. R. S. Tibben-Lembke and D. S. Rogers, “Real options: applications to logistics and transportation,” International Journal of Physical Distribution & Logistics Management, vol. 36, no. 4, pp. 252–270, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. M. Mourits and J. J. Evers, “Distribution network design: an integrated planning support framework,” Logistics Information Management, vol. 9, no. 1, pp. 45–54, 1996. View at Publisher · View at Google Scholar
  5. S. E. Griffis, J. E. Bell, and D. J. Closs, “Metaheuristics in logistics and supply chain management,” Journal of Business Logistics, vol. 33, no. 2, pp. 90–106, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. M. A. Waller and S. E. Fawcett, “The total cost concept of logistics: one of many fundamental logistics concepts begging for answers,” Journal of Business Logistics, vol. 33, no. 1, pp. 1–3, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Kowalski, B. Lev, W. Shen, and Y. Tu, “A fast and simple branching algorithm for solving small scale fixed-charge transportation problem,” Operations Research Perspectives, vol. 1, no. 1, pp. 1–5, 2014. View at Publisher · View at Google Scholar
  8. D. Goossens and F. C. R. Spieksma, “The transportation problem with exclusionary side constraints,” 4OR: A Quarterly Journal of Operations Research, vol. 7, no. 1, pp. 51–60, 2009. View at Publisher · View at Google Scholar
  9. S. Waldherr, J. Poppenborg, and S. Knust, “The bottleneck transportation problem with auxiliary resources,” 4OR: A Quarterly Journal of Operations Research, vol. 13, no. 3, pp. 279–292, 2015. View at Publisher · View at Google Scholar
  10. V. Adlakha and K. Kowalski, “On the quadratic transportation problem,” Open Journal of Optimization, vol. 2, no. 3, pp. 89–94, 2013. View at Publisher · View at Google Scholar
  11. V. Adlakha and K. Kowalski, “An alternative solution algorithm for certain transportation problems,” International Journal of Mathematical Education in Science and Technology, vol. 30, no. 5, pp. 719–728, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  12. K. M. Altassan, M. M. El-Sherbiny, and B. Sasidhar, “Near optimal solution for the step fixed charge transportation problem,” Applied Mathematics & Information Sciences, vol. 7, no. 2, pp. 661–669, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. A. Das, M. Basu, and D. Acharya, “Fixed charge capacitated non-linear transportation problem,” Journal of Engineering, Computers & Applied Sciences, vol. 2, no. 12, pp. 49–54, 2013. View at Google Scholar
  14. D. Acharya, M. Basu, and A. Das, “Discounted generalized transportation problem,” International Journal of Scientific and Research Publications, vol. 3, no. 7, pp. 1–6, 2013. View at Google Scholar
  15. J. Blazewicz, P. Bouvry, M. Y. Kovalyov, and J. Musial, “Internet shopping with price sensitive discounts,” 4OR: A Quarterly Journal of Operations Research, vol. 12, no. 1, pp. 35–48, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. G. A. Osuji, J. Ogbonna-Chukwudi, and O. Jude, “Transportation algorithm with volume discount on distribution cost (a case study of the Nigerian Bottling Company Plc Owerri Plant),” American Journal of Applied Mathematics and Statistics, vol. 2, no. 5, pp. 318–323, 2014. View at Publisher · View at Google Scholar
  17. K. V. Donselaar and G. Sharman, “An innovative survey in the transportation and distribution sector,” International Journal of Physical Distribution & Logistics Management, vol. 28, no. 8, pp. 617–629, 1998. View at Publisher · View at Google Scholar
  18. J. Bhadury, S. Khurana, H. S. Peng, and H. Zong, “Optimization modeling in acquisitions: a case study from the motor carrier industry,” Journal of Supply Chain Management, vol. 42, no. 4, pp. 41–53, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. R. C. M. Yam and E. P. Y. Tang, “Transportation systems in Hong Kong and Southern China: a manufacturing industries perspective,” International Journal of Physical Distribution & Logistics Management, vol. 26, no. 10, pp. 46–59, 1996. View at Publisher · View at Google Scholar
  20. P. F. Wanke, “Efficiency drivers in the Brazilian trucking industry: a longitudinal study from 2002–2010,” International Journal of Physical Distribution & Logistics Management, vol. 44, no. 7, pp. 540–558, 2014. View at Publisher · View at Google Scholar
  21. J. Olhager, S. Pashaei, and H. Sternberg, “Design of global production and distribution networks: a literature review and research agenda,” International Journal of Physical Distribution & Logistics Management, vol. 45, pp. 138–158, 2015. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Reimann, R. T. Neto, and E. Bogendorfer, “Joint optimization of production planning and vehicle routing problems: a review of existing strategies,” Pesquisa Operacional, vol. 34, no. 2, pp. 189–214, 2014. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Biellia, A. Biellib, and R. Rossic, “Trends in models and algorithms for fleet management,” Procedia—Social and Behavioral Sciences, vol. 20, pp. 4–18, 2011. View at Publisher · View at Google Scholar
  24. M. Kiani, J. Sayareh, and S. Nooramin, “A simulation framework for optimizing truck congestions in marine terminals,” Journal of Maritime Research, vol. 7, no. 1, pp. 55–70, 2010. View at Google Scholar · View at Scopus
  25. J. F. Netto and R. C. Botter, “Simulation model for container fleet sizing on dedicated route,” in Proceedings of the Winter Simulation Conference (WSC '13), pp. 3385–3394, Washington, DC, USA, December 2013. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Sebbah, A. Ghanmi, and A. Boukhtouta, “A column-and-cut generation algorithm for planning of Canadian armed forces tactical logistics distribution,” Computers & Operations Research, vol. 40, no. 12, pp. 3069–3079, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. M. L. Fisher, “The Lagrangian relaxation method for solving integer programming problems,” Management Science, vol. 27, no. 1, pp. 1–18, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  28. K. Mathur, H. M. Salkin, and S. Morito, “A branch and search algorithm for a class of nonlinear knapsack problems,” Operations Research Letters, vol. 2, no. 4, pp. 155–160, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. F. Glover, “Surrogate constraint duality in mathematical programming,” Operations Research, vol. 23, no. 3, pp. 434–451, 1975. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. H. J. Greenberg, “The generalized penalty-function/surrogate model,” Operations Research, vol. 21, no. 1, pp. 162–178, 1973. View at Publisher · View at Google Scholar · View at MathSciNet
  31. K. Mizukami and J. Sikrorski, “Three algorithms for calculating surrogate constraint in integer programming problem,” Control and Cybernetics, vol. 13, no. 4, pp. 375–397, 1984. View at Google Scholar
  32. T. L. Morin and A. M. O. Esogbue, “The imbedded state space approach to reducing dimensionality in dynamic programs of higher dimensions,” Journal of Mathematical Analysis and Applications, vol. 48, pp. 801–810, 1974. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. F. Ghassemi-Tari and E. Jahangiri, “Development of a hybrid dynamic programming approach for solving discrete nonlinear knapsack problems,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 1023–1030, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. G. Righini and M. Salani, “Decremental state space relaxation strategies and initialization heuristics for solving the orienteering problem with time windows with dynamic programming,” Computers & Operations Research, vol. 36, no. 4, pp. 1191–1203, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. J. Fang, L. Zhao, J. C. Fransoo, and T. V. Woensel, “Sourcing strategies in supply risk management: an approximate dynamic programming approach,” Computers & Operations Research, vol. 40, no. 5, pp. 1371–1382, 2013. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Russo, A. Sforza, and C. Sterle, “An exact dynamic programming algorithm for large-scale unconstrained two-dimensional guillotine cutting problems,” Computers & Operations Research, vol. 50, pp. 97–114, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. K. Chebil and M. Khemakhem, “A dynamic programming algorithm for the knapsack problem with setup,” Computers & Operations Research, vol. 64, pp. 40–50, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  38. W. M. Hirsch and G. B. Dantzig, “The fixed charge problem,” Naval Research Logistics Quarterly, vol. 15, pp. 413–424, 1968. View at Publisher · View at Google Scholar · View at MathSciNet