Robust optimization with equity and efficiency framework for basin-wide water resources planning

This study proposes an equitable and effective water resource planning framework that handles competing regions and conflicting water departments within water-stressed watersheds under uncertainty. To cope with uncertainty, a robust optimization method based on an ellipsoidal uncertainty set is presented to keep the best solution viable and less conservative while attempting to find a balance between the reliability and optimum goals. The comprehensive framework consists of two predominant steps: equitable initial water allocation robust optimization programming, which employs the absolute difference between the supply and demand of water resources as the objective function and the Gini coefficient as the restricted condition, given that both surface water and groundwater are random, and subsequent effective water re-allocation robust modeling, which applies cooperative game theory to achieve maximum welfare in a river basin under uncertainty of the benefit coefficient. A realistic example of the Tuojiang River Basin was conducted, and the simulation experiments showed a significant increase (79.20%) in reliability with only an 11.44% increase in objective values and 2.76% and 15.17% decreases in the amount of surface water and groundwater, respectively. The findings of the analysis reveal that robust policies achieve adaptive optimal decision-making under uncertainty at a low cost.