A Regional Water Optimal Allocation Model Based on the Cobb-Douglas Production Function under Multiple Uncertainties

To optimize the water distribution of three industries based on the water demand prediction under multiple uncertainties, a fuzzy credibility-constrained interval two-stage stochastic programming (FCITSP) model base on the Cobb-Douglas production (CD) function was developed. The CD-FCITSP model integrated fuzzy credibility-constrained programming (FCP), an interval two-stage stochastic programming (ITSP) method and CD function. The developed model could deal with uncertainties with interval, random, and fuzzy features, reflect tradeoffs between different water use sectors, and provide water managers in arid regions with sustainable and reasonable water-allocation schemes under different credibility scenarios of local policies. Moreover, the relationships between economic benefits and water consumption were taken into consideration via the Cobb-Douglas production function. The developed model was applied to support the optimal allocation of limited water resources in Minqin County, northwest China. The obtained solution demonstrated that the developed method could help local water managers to effectively allocate limited water under multiple uncertainties and different credibility scenarios. In addition, water use efficiency could be promoted and the emissions of major pollutants could be reduced. The developed method could be extended to water management practices in other arid regions.