An improved bi-level programming model for water resources allocation under multiple uncertainties

Nowadays, with the scarcity of water resources, competition for water resources among different levels and water sectors is growing increasingly fierce. Furthermore, uncertainties are unavoidable in the water resources system. To address the aforementioned issues, a fuzzy max-min decision bi-level multi-objective interval programming model was proposed, which can not only focus on water conflicts at the same level or between different levels, but also pay attention to optimal allocation of water resources under uncertainty. The developed model was then applied to a case study in Wuwei City, Gansu Province, China, which selected fairness of water distribution and agricultural economic benefits as planning objectives. Based on the developed model, different water resources optimal allocation schemes under different representative hydrological years were provided. From the result, as representative hydrological years changed from wet (P = 25%) to dry (P = 75%), agricultural economic benefit and Gini coefficient of agriculture would vary from [35.19, 37.78] × 10⁸ yuan to [31.12, 31.99] × 10⁸ yuan and from [0.468, 0.429] to [0.505, 0.503], which indicates that as available water resources decrease, agricultural economic benefit would decrease and fairness of water distribution would also decrease. And the water distribution fairness of the upper bound water allocation scheme is higher than that of the lower bound water allocation scheme when in the same representative hydrological year. In addition, no matter what representative hydrological year, the results of the established bi-level programming model are always in the middle of the results of the upper and lower level individual objective, which means that the developed bi-level programming model has great advantage to deal with water competing conflict among different levels. Furthermore, based on the results of developed model, the reasonable water resources optimization schemes can be determined by the decision-makers when faced with multi-objective, bi-level and multiple uncertainties problems.