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Mathematical Problems in Engineering
Volume 2013, Article ID 837919, 9 pages
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.


Water allocation is an essential programming to support the sustainable development of Wuwei Basin, Gansu Province, China. To satisfy the demands of the decision makers (DMs) of each subarea and the total area, a bilevel multiobjective linear programming (BLMOLP) model is proposed. In the BLMOLP, DMs have a hierarchy of two levels—the upper level and the lower level DMs. In this paper, a fuzzy goal programming (FGP) approach is applied to solve the BLMOLP. Firstly, the upper level is solved and used as the tolerance for the lower level. Then the weights of each objective function in the lower level are evaluated. Finally, a satisfied optimization solution of the problem was calculated. The result suggests that the FGP is a simple and feasible approach to BLMOLP problems. The proposed method was applied to a case study for water resources allocation in Wuwei Basin. For four scenarios under consideration, the model can effectively balance the benefits among all regions and sections according to the priority of the upper level decision makers. The results indicate that comprehensive solutions have been obtained.