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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 837919, 9 pages
http://dx.doi.org/10.1155/2013/837919
Research Article

Bilevel Multiobjective Programming Applied to Water Resources Allocation

1Centre for Agricultural Water Research in China, China Agricultural University, Beijing 100083, China
2Environmental Science and Engineering Program, University of Northern British Columbia, Prince George, BC, Canada V2N 4Z9
3College of Water Conservancy, Hydropower and Architecture Engineering, Yunnan Agricultural University, Kunming 650201, China

Received 28 November 2012; Accepted 3 February 2013

Academic Editor: Yongping Li

Copyright © 2013 Shiqi Fang et al. 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. D. Prinz and A. K. Singh, “Water resources in arid regions and their sustainable management,” Annals of Arid Zone, vol. 39, no. 3, pp. 251–271, 2000. View at Google Scholar · View at Scopus
  2. D. P. Loucks, E. van Beek, J. R. Stedinger et al., Water Resources Systems Planning and Management: An Introduction to Methods, Models and Applications, UNESCO, Paris, France, 2005.
  3. A. K. Biswas, “Integrated water resources management: a reassessment,” Water International, vol. 29, no. 2, pp. 248–256, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. W. O. Maddaus and J. M. McGill, “Development and application of a water resource allocation model.,” Water Resources Research, vol. 12, no. 4, pp. 767–774, 1976. View at Publisher · View at Google Scholar · View at Scopus
  5. R. P. Lejano and C. A. Davos, “Cost allocation of multiagency water resource projects: game theoretic approaches and case study,” Water Resources Research, vol. 31, no. 5, pp. 1387–1393, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. E. F. Y. Gakpo, L. A. D. Plessis, and M. F. Viljoen, “Towards institutional arrangements to ensure optimal allocation and security of South Africa's water resources,” Agrekon, vol. 40, no. 1, pp. 87–103, 2001. View at Publisher · View at Google Scholar
  7. H. Lévite, H. Sally, and J. Cour, “Testing water demand management scenarios in a water-stressed basin in South Africa: application of the WEAP model,” Physics and Chemistry of the Earth, vol. 28, no. 20-27, pp. 779–786, 2003. View at Publisher · View at Google Scholar · View at Scopus
  8. I. Fischhendler, “Institutional conditions for IWRM: the Israeli case,” Ground Water, vol. 46, no. 1, pp. 91–102, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. G. N. Paudyal and H. B. Manguerra, “Two-step dynamic programming approach for optimal irrigation water allocation,” Water Resources Management, vol. 4, no. 3, pp. 187–204, 1990. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Wardlaw and K. Bhaktikul, “Application of a genetic algorithm for water allocation in an irrigation system,” Irrigation and Drainage, vol. 50, no. 2, pp. 159–170, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Z. Wang, L. Fang, and K. W. Hipel, “Water resources allocation: a cooperative game theoretic approach,” Journal of Environmental Informatics, vol. 2, no. 2, pp. 11–22, 2003. View at Google Scholar
  12. F. Messner, O. Zwirner, and M. Karkuschke, “Participation in multi-criteria decision support for the resolution of a water allocation problem in the Spree River basin,” Land Use Policy, vol. 23, no. 1, pp. 63–75, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. P. Li, G. H. Huang, Y. F. Huang, and H. D. Zhou, “A multistage fuzzy-stochastic programming model for supporting sustainable water-resources allocation and management,” Environmental Modelling and Software, vol. 24, no. 7, pp. 786–797, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Sadegh, N. Mahjouri, and R. Kerachian, “Optimal inter-basin water allocation using crisp and fuzzy Shapley games,” Water Resources Management, vol. 24, no. 10, pp. 2291–2310, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Sadegh and R. Kerachian, “Water resources allocation using solution concepts of fuzzy cooperative games: fuzzy least core and fuzzy weak least core,” Water Resources Management, vol. 25, no. 10, pp. 2543–2573, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. L. G. Shao, X. S. Qin, and Y. Xu, “A conditional value-at-risk based inexact water allocation model,” Water Resources Management, vol. 25, no. 9, pp. 2125–2145, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. L. Jin, G. H. Huang, Y. R. Fan et al., “A hybrid dynamic dual interval programming for irrigation water allocation under uncertainty,” Water Resources Management, vol. 26, no. 5, pp. 1183–1200, 2012. View at Publisher · View at Google Scholar
  18. E. Xevi and S. Khan, “A multi-objective optimisation approach to water management,” Journal of Environmental Management, vol. 77, no. 4, pp. 269–277, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. A. P. Singh, S. K. Ghosh, and P. Sharma, “Water quality management of a stretch of river Yamuna: an interactive fuzzy multi-objective approach,” Water Resources Management, vol. 21, no. 2, pp. 515–532, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. A. A. Fasakhodi, S. H. Nouri, and M. Amini, “Water resources sustainability and optimal cropping pattern in farming systems; a multi-objective fractional goal programming approach,” Water Resources Management, vol. 24, no. 15, pp. 4639–4657, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. W. Candler and R. D. Norton, “Multi-level programming,” World Bank, 1977.
  22. H. S. Shih, Y. J. Lai, and E. S. Lee, “Fuzzy approach for multi-level programming problems,” Computers & Operations Research, vol. 23, no. 1, pp. 73–91, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. K. B. Aviso, R. R. Tan, A. B. Culaba, and J. B. Cruz, “Bi-level fuzzy optimization approach for water exchange in eco-industrial parks,” Process Safety and Environmental Protection, vol. 88, no. 1, pp. 31–40, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. A. N. Sadigh, M. Mozafari, and B. Karimi, “Manufacturer-retailer supply chain coordination: a bi-level programming approach,” Advances in Engineering Software, vol. 45, no. 1, pp. 144–152, 2012. View at Publisher · View at Google Scholar
  25. J. Wonga, C. Su, and C. Wang, “Stochastic dynamic lot-sizing problem using bi-level programming base on artificial intelligence techniques,” Applied Mathematical Modelling, vol. 36, no. 5, pp. 2003–2016, 2012. View at Publisher · View at Google Scholar
  26. Y. Lv, G. H. Huang, Y. P. Li, Z. F. Yang, Y. Liu, and G. H. Cheng, “Planning regional water resources system using an interval fuzzy bi-level programming method,” Journal of Environmental Informatics, vol. 16, no. 2, pp. 43–56, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. B. Colson, P. Marcotte, and G. Savard, “Bilevel programming: a survey,” 4OR, vol. 3, no. 2, pp. 87–107, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. W. Candler and R. Townsley, “A linear two-level programming problem,” Computers & Operations Research, vol. 9, no. 1, pp. 59–76, 1982. View at Publisher · View at Google Scholar · View at Scopus
  29. C. Shi, J. Lu, and G. Zhang, “An extended Kth-best approach for linear bilevel programming,” Applied Mathematics and Computation, vol. 164, no. 3, pp. 843–855, 2005. View at Publisher · View at Google Scholar · View at Scopus
  30. W. F. Bialas and M. H. Karwan, “Two-level linear programming,” Management Science, vol. 30, no. 8, pp. 1004–1020, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  31. J. F. Bard and J. T. Moore, “A branch and bound algorithm for the bilevel programming problem,” Siam Journal on Scientific and Statistical Computing, vol. 11, no. 2, pp. 281–292, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. A. Charnes and W. W. Cooper, “Management models and industrial applications of linear programming,” Management Science, vol. 4, no. 1, pp. 38–91, 1957. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  33. B. Moitra and B. Pal, “A fuzzy goal programming approach for solving bilevel programming problems,” Advances in Soft Computing-Afss, vol. 2275, pp. 415–421, 2002. View at Google Scholar · View at Zentralblatt MATH
  34. B. B. Pal and B. N. Moitra, “A fuzzy goal programming procedure for solving quadratic bilevel programming problems,” International Journal of Intelligent Systems, vol. 18, no. 5, pp. 529–540, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  35. S. Pramanik and T. K. Roy, “Fuzzy goal programming approach to multilevel programming problems,” European Journal of Operational Research, vol. 176, no. 2, pp. 1151–1166, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  36. S. R. Arora and R. Gupta, “Interactive fuzzy goal programming approach for bilevel programming problem,” European Journal of Operational Research, vol. 194, no. 2, pp. 368–376, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  37. I. A. Baky, “Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach,” Applied Mathematical Modelling, vol. 34, no. 9, pp. 2377–2387, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  38. R. H. Mohamed, “The relationship between goal programming and fuzzy programming,” Fuzzy Sets and Systems, vol. 89, no. 2, pp. 215–222, 1997. View at Publisher · View at Google Scholar · View at Scopus
  39. F. You, Y. Li, and S. C. Dong, “Environmental sustainability and scenarios of urbanization in arid area: a case study in Wuwei City of Gansu Province,” Chinese Geographical Science, vol. 15, no. 2, pp. 120–130, 2005. View at Publisher · View at Google Scholar · View at Scopus
  40. J. Ma, Z. Ding, G. Wei, H. Zhao, and T. Huang, “Sources of water pollution and evolution of water quality in the Wuwei basin of Shiyang river, Northwest China,” Journal of Environmental Management, vol. 90, no. 2, pp. 1168–1177, 2009. View at Publisher · View at Google Scholar · View at Scopus