Research on Bi-Level Objective Programming Model of Water Resources Uncertainty Based on Water Rights Trading—A Case Study of the Yehe Irrigation District in Hebei Province, China

Water resource allocation systems typically involve multi-level decision-making, with each level having distinct goals and interests, while being influenced by various factors such as social, economic, environmental, and policy planning. The decision-making in water resource allocation systems is characterized by complex uncertainty factors and dynamic changes. In light of this, this study integrates stochastic chance-constrained programming, dynamic programming, bi-level programming, goal programming, and water rights trading to construct a bi-level objective programming model of water resource uncertainty based on water rights trading. The model not only effectively represents the random uncertainty, dynamic characteristics, interests of decision-making levels, and planning requirements of policies in water resource allocation systems but also utilizes market mechanisms to enable compensated transfer of water rights, fully leveraging the role of water rights marketization in water resource allocation. Taking the Yehe River Irrigation District in Hebei Province of China as an illustrative case study, the specific allocation scheme of each stage under the guaranteed rate of 50% in 2025 and the water rights trading results of each sub-region are obtained. Compared with the bi-level objective programming model of water resources uncertainty without water rights trading, the results show that the water consumption per CNY ten thousand GDP(WG)of the irrigation district decreased by 3.42%, and the economic benefits of Luquan District, Jingxing County, Pingshan County, and Yuanshi County in each sub-region increased by 19.17%, 7.19%, 15.11%, and 4.94%, respectively. This improves regional water use efficiency and economic benefits and provides a scientific basis for regional water resource allocation.