A bi-level multi-objective linear fractional programming for water consumption structure optimization based on water shortage risk

Abstract

Abstract In this study, a framework of a bi-level multi-objective linear fractional programming (BMLFP) approach is developed for the optimization of water consumption structure based on water shortage risk. It incorporates linear fractional programming (LFP), multi-objective programming (MOP) into bi-level programming (BP). The model considers the water shortage risk measured by interior-outer-set risk assessment method, and integrates it into inexact water resources optimization model. The complicated model not only can enhance the conventional programming method through the interactive influence and mutual restriction between the upper- and lower-level decision processes, and multiple objectives, but also improve the robustness of conventional programming methods by integrating the water shortage risk. Besides, the model could achieve the tradeoff between equality and economic benefit of system and figure out the interaction amid water shortage risk, water allocation and objectives. It is applied to a case study to conduct water resources management among different water users including agricultural, industrial, domestic, and ecological sectors in the middle reaches of Heihe River Basin, northwest China. The water allocation schemes with ten water-shortage risk scenarios is formed to compare the influence of water shortage degree on water allocation and figure out the optimal water allocation schemes. Besides, the performance of the developed model is enhanced by comparing with the two-level linear fractional water management (TLFWM) model and actual condition. The results indicate that the water shortage belongs to general risk area, and the water-shortage risk has obvious effect on agricultural water allocations while has insensitive influence on that of the industrial, domestic and ecological sectors. Compared with the TLFWM model and actual condition, the developed BMLFP model could improve the equality and benefit of system and lessen the water allocation. The decision makers can find better water-allocation decision alternatives obtained from BMLFP model according to their risk attitude to support social harmony and economic development.