Abstract:

The United Nations Sustainable Development Goal 6 puts forward to improve water use efficiency while implementing integrated water resources management from a multi-scale perspective. However， how to design effective water resource allocation scheme in the situation of （semi） drought consider the game behavior of decision-makers is a severe problem in China. Firstly， climate change， economic development， population growth and other factors lead to a significant increase in the uncertainty in water supply and demand， of which its statistical distribution are difficult to be determined directly. Secondly， when adding hydrological environment uncertainty， Stackelberg game and non-convex objective function into a water resource allocation model， it would be difficult to solve. Therefore， to allocate initial water rights and water use rights in （semi-） arid environment， a new bi-level robust optimization model is proposed in this paper， moreover， the global optimal solution method based on robust optimization， convex optimization theory and piecewise linear method is needed and deigned.In this study， a bi-level multi-followers robust programming model is proposed for water allocation problems under uncertainty， wherein hierarchical optimization， polyhedral uncertainty sets， and a non-convex objective function coexist. The proposed deciding framework can suitably address resources allocation problems under uncertainty with multiple kinds of decision-makers. It is believed that our study makes a significant contribution to the literature. To some extent， prior studies have applied heuristics to solve analogous decision-making problems that include more than one hierarchy. These studies often obtained local solutions. However， the quality of the allocation strategy directly affects social progress and economic development. This predicament requires a global solution， which our work addresses. To be specific， in our three-stage global approach， the first stage supports uncertain characterization and robust equivalent transformations. In the second stage， a single-level model is generated through the Karush–Kuhn–Tucker and big M methods. The last stage focuses on obtaining a global solution by applying the convexification and piecewise linear technique. In this way， the authors obtain a robust counterpart problem for solving the uncertainty embodied in the proposed model. In addition， convexification and piecewise techniques are uniquely used to get a global solution.Finally， a case study of Heihe River basin is given to verify the validity of the model and solution method. Based on the above results， it is suggested that adjusting strategies should be optimized for different regions based on resource endowments and development targets. In real-world practice， it is believed our findings have important implications for the mitigation of resources use conflicts among multiple participants in resources （semi）-scarce areas.

Key words: bi-level optimization, robust optimization, global optimization solution, water resources allocation