The rational allocation of water resources in the basin/region can be better assisted and performed using a suitable water resources allocation model. Rule-based and optimization-based simulation methods are utilized to solve medium-and long-term water resources allocation problems. Since rule-based allocation methods requires more experience from expert practice than optimization-based allocation methods, it may not be utilized by users that lack experience. Although the optimal solution can be obtained via the optimization-based allocation method, the highly skilled expert experience is not taken into account. To overcome this deficiency and employ the advantages of both rule-based and optimization-based simulation methods, this paper proposes the optimal allocation model of water resources where the highly skilled expert experience has been considered therein. The "prospect theory" is employed to analyze highly skilled expert behavior when decision-making events occur. The cumulative prospect theory value is employed to express the highly skilled expert experience. Then, the various elements of the cumulative prospect theory value can be taken as the variables or parameters in the allocation model. Moreover, the optimal water allocation model developed by the general algebraic modeling system (GAMS) has been improved by adding the decision reversal control point and defining the inverse objective function and other constraints. The case study was carried out in the Wuyur River Basin, northeast of China, and shows that the expert experience considered as the decision maker's preference can be expressed in the improved optimal allocation model. Accordingly, the improved allocation model will contribute to improving the rationality of decision-making results and helping decision-makers better address the problem of water shortage.2 of 17 establish a water resources allocation and management decision-making tool. Abolpour et al. [7] adopted an adaptive neuro-fuzzy reinforcement learning method to enhance the accuracy of optimized parameters in the water resources allocation model. Prasad et al. [8] proposed a linear programming method for finding the optimal irrigation-planning model by considering various growth stages of crops in the water resources allocation. An inaccurate two-stage water allocation model was utilized by Li et al. [9] to simulate the irrigation water requirements of multiple crops in the large-scale areas. Dai and Li [10] constructed a multi-stage irrigation water allocation model for different season water allocation policies. An inaccurate multi-stage stochastic optimization model was proposed by Li and Guo [11] to solve the mesoscale agricultural water resources planning problem. Recently, the rational allocation of water resources has been devoted to solving many difficulties encountered in practice. Kralisch et al. [12] proposed a neural network method to solve the allocation problem between urban living water and agricultural water. Wang et al. [13] proposed a water rights allocation m...

A major objective of the optimization of water resources allocation is to ensure the supply an adequate amount of water to users at the right time and maximize the utilization of water resources. However, in case of insufficient water supply, water shortage is likely to occur intensively for specific water users or in specific periods, referred to as a “concentrated water shortage”. The risk of a concentrated water shortage should be shared across a wider range of users and periods, so that it would have a less severe impact on each calculation unit in each period, which we refer to as the “wide-mild water shortage”. In this study, the nonlinear weight of the water supply objective function can be converted into a piecewise linear weight based on the law of diminishing marginal utility, making it possible to reduce or even eliminate the concentrated water shortage and thus making the allocation of water resources more reasonable. The case study in the Nen River basin in northeast China shows that the improved method results in a significant increase in water shortage units but a significant reduction in water shortage range. As a consequence, water shortage is more uniformly distributed from April to June, which contributes to solving the concentrated water shortage problem in May. However, it should be noted that to what extent the wide-mild water shortage can be realized depends not only on the marginal utility of water demand, but also on the available water supply and the regulative capacity of water supply projects. In spite of this, the improved method enables water to be supplied more suitably for users at the appropriate time, which contributes to improving the utilization of water resources and helping decision-makers better address the problem of concentrated water shortage.

Water pricing is the key to maximize the economic and social benefits of the water transfer project. In this study, we propose the extended linear expenditure system-water price tolerance index (ELES-WPTI) model that combines the ELES model and the WPTI method for water pricing, Firstly, the ELES model is used to estimate the price elasticity of water demand and the basic demand for farmers of different income levels. Secondly, the WPTI method is used to simulate and analyze the affordability of farmers of different income levels for agricultural water under the dynamic change of water price standards. Finally, the ELES-WPTI model is applied to the Yinda-Jihuang (YJ) Project, China, to determine the appropriate agricultural water price. The results reveal that the farmers in the DH district have is slightly higher affordability for water price than that in HL District. As water consumption should account for less than 15% of the total production cost and 10% of the net income, the affordable water price is determined to be 237 $/hm² in the DH district and 205 $/hm² in the HL district, respectively.