An ecological interval two-stage fuzzy shadow price model for environmental flow allocation in the Shaying River Basin

In recent years, social water is pressurizing ecological water, causing the environmental flow to not be guaranteed and destroying the ecological environment. This research aims to coordinate social and natural water use to bring about optimal economic benefits, while ensuring environmental flow requirements. In this study, an interval two-stage fuzzy shadow price model (ITS-SPM) has been developed, which combines two-stage programming (TSP) and system of water value to optimize environmental flow. The ITS-SPM is mainly characterized as system benefits constituted by expected water resource benefits and water shortage penalty. This model has removed the uncertainties of economic data and environmental water demand (expressed fuzzy and interval). It has been found that adjusting the social water structure can effectively solve the problem of insufficient ecological flow. The ITS-SPM can make the adjustment of social water use more reasonable, which will produce benefits, unlike the current agricultural water reduction policy. Under the premise of guaranteeing optimal economic benefits, the added value of environmental water use in different scenarios is (social water structure adjustment) as follows: in 2020, it was expected that Shaying River water would increase by at least 13.49%; in 2025, it is expected to increase by at least 33.35%; in 2030, the increase will be by at least 57.54%; and in 2035, it will be by at least 77.50%.