Optimal Water Allocation of Irrigation District Based on Interval-parameter Two-stage Stochastic Fuzzy Credibility Constrained Programming

Due to the rapid development of urbanization and industrialization, the consequent increasing conflict between limited water resources and increased water demands gradually led to unsustainability of water resources utilization in an irrigation district. Therefore, it is crucial to optimize the water allocation to alleviate water shortage and promote the sustainable development of irrigation district. Taking Zhanghe Irrigation District in Hubei Province as an example, an interval-parameter two-stage stochastic fuzzy credibility constrained programming was developed for optimal water allocation. In the model, the maximal system benefit was regarded as the objective function. To reflect the multiple uncertainties, fuzzy variables, discrete intervals and probability distributions were introduced into the model framework. To address the fuzzy risk problems associated with the violation constraints, fuzzy credibility constrained programming was integrated into the interval-parameter two-stage stochastic programming model. Meanwhile, several credibility significance levels were given to examine the system failure risk. Optimal allocation schemes were obtained in the combination of different credibility levels (λ), inflow levels and fuzzy membership levels (α). The results indicated that the water inflow was positively related to the water resources allocation and agricultural irrigation areas; water and irrigation area allocation to all divisions were increased with the decrease of credibility level, which resulted in system benefit's expansion coupled with high violation risk. When λ was 1.0, the system benefit range was [0.741, 1.147] billion CNY, and when λ was set as 0.8, the system benefit reached [1.026, 1.325] billion CNY; with the increase of the α level, the system fuzzy feature was weakened, consequently the upper limit of the system benefit was gradually decreased and the lower limit of the system benefit was increased conversely; and the proposed model preferred to avoid high violation risk rather than purse high economic benefit impractically to some extent. The corresponding optimal results were helpful for managers to coordinate the conflict-laden water use issues, formulate reasonable allocation schemes, and achieve efficient utilization of water resources. Compared with the other optimal allocation in Zhanghe Irrigation District, the research had advantages as following: multiple uncertainties were considered and represented by proper mathematical methods; the tradeoff of system benefit and violation risk was reflected; multiple allocation schemes were provided under different scenarios; several engineering and non-engineering measures were suggested for sustainable development of Zhanghe Irrigation District; the analysis method and the model framework can also be applied to other similar regions. © 2019, Chinese Society of Agricultural Machinery. All right reserved.