Abstract:Considering the complexities of nonlinearity, uncertainties and different interested parties in irrigation water allocation optimization, two models of different decision levels were established: one (upper level) was interval linear fractional programming (ILFP) model with the objective of maximizing irrigation water productivity, and the other one (lower level) was interval quadratic programming (IQP) model with the objective of maximizing irrigation outputs. On this basis, a linear fractional-quadratic bi-level programming (LFQBP) model was developed by integrating the decisions of the upper and the lower levels as a whole, in order to coordinate the benefits of different decision levels. LFQBP model was advantageous to make grain outputs and irrigation productivity reach a relatively high level and thus promoting the sustainable development of irrigation districts. All the three models were solved by using specific method, among which the key to the solution of IQP model and ILFP model was to transform the uncertain models into deterministic ones, and the key to the solution of LFQBP model was to transform the two-level model into single-level model. Then the developed models were applied to irrigation water allocation for grain crops in Yingke Irrigation District. Comparison among ILFP model, IQP model and LFQBP model demonstrated the characters of each model, and the optimization results showed that total water allocation amounts of the IQP model, ILFP model and LFQBP model were 63.01 million m3, 55.01 million m3 and 60.34 million m3, respectively. Compared with IQP model, the crop output of LFQBP model was decreased by 0.44% while the irrigation productivity was increased by 4%, and compared with ILFP model, the crop output of LFQBP model was increased by 1.42% while the irrigation productivity was decreased by 7.64%. ILFP model and ILQBP model were more applicable in arid regions. The developed models reflected actual problems of irrigation allocation from different aspects, and the corresponding results were conducive to balance the benefits of decision-makers at different levels of an irrigation district.
