Integrated model for optimal scheduling and allocation of water resources considering fairness and efficiency: A case study of the Yellow River Basin

•The effects of fairness and efficiency on water allocation are explored by constructing different of optimization models.•Welfare economics theory is introduced to balance the efficiency and fairness of water-resource regulations.•An integrated model of water-resource scheduling and allocation is constructed based on a proxy model, which significantly improves computational efficiency. Water is an important natural resource with economic and social attributes. The most important aspects of water resource regulations are fairness and efficiency. Achieving a balance between fairness and efficiency is a challenging but popular topic in related research. In this study, three optimal water-resource allocation models were constructed: efficiency priority (E-P), fairness priority (F-P), and stratified water supply (SWS). The three models were applied to the Yellow River Basin (YRB), and the results show that, compared with the E-P and F-P models, the SWS model is a more equilibrium model with significant advantages. Considering the impact of reservoirs on water allocation, an optimal operation model for cascade reservoirs groups, considering fairness and efficiency, was constructed based on the principle of welfare economics and coupled with the SWS model. Proxy modeling was used in the coupling process to enhance the computational efficiency of the integrated model. Compared with the SWS model, the integrated model can better satisfy the water supply demand outside a river while ensuring the ecological environment and sand flushing demand inside the river; its fairness and efficiency are also significantly improved. In addition, integrated models can effectively address hydrological uncertainty and reduce losses. The model proposed in this study has significant flexibility and application potential and can provide a reference for other governments and water-resource management institutions worldwide.