Research Article: An inexact fractional programming model for irrigation water resources optimal allocation under multiple uncertainties

Date Published: June 13, 2019

Publisher: Public Library of Science

Author(s): Chongfeng Ren, Jiantao Yang, Hongbo Zhang, Baogui Xin.

http://doi.org/10.1371/journal.pone.0217783

Abstract

In reality, severe water shortage crisis has made bad impact on the sustainable development of a region. In addition, uncertainties are inevitable in the irrigation system. Therefore, a fully fuzzy fractional programming model for optimization allocation of irrigation water resources, which aimed at not only irrigation water optimization but also improving water use efficiency. And then the developed model applied to a case study in Minqin County, Gansu Province, China, which selected maximum economic benefit of per unit water resources as planning objective. Moreover, surface and underground water are main water sources for irrigation. Thus, conjunctive use of surface and underground water was taken under consideration in this study. By solving the developed model, a series of optimal crop area and planting schemes, which were under different α-cut levels, were offered to the decision makers. The obtained results could be helpful for decision makers to make decision on the optimal use of irrigation water resources under multiple uncertainties.

Partial Text

Today, water resources scarcity, which has great negative influence on the development of society and economy, becomes more and more serious [1–3]. Moreover, the demand for water resources is growing rapidly because of the rapid growth of economy and society [4–6]. Thus, there is great conflict between the growing demand for water resources and limited water resources. However, irrigation consumes approximately 70% of the world’s freshwater resources [7]. Especially in the arid and semi-arid regions of Northwest China, characterized with high evaporation and low rainfall, approximately 90% of freshwater resources has been used to irrigation [7–10]. Therefore, optimization allocation of irrigation water resources has great positive influence on the sustainable development of a region.

In reality, a large amount of parameter in irrigation system has characteristics of fuzzy uncertainty. And the parameters with fuzzy uncertainty exist not only in constraints but also in objective functions. The form of FFFPM is as following:
MaxZ˜=∑j=1nc˜j·x˜j+p˜∑j=1nd˜j·x˜j+q˜(10)

In this paper, eleven α-cut levels were chosen by the developed model, including 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. Fig 3 represents the optimized objective value of lower and upper level under different α-cut levels, respectively. From the Fig 3, the optimized objective value would vary under multiple uncertainties. As α-cut levels increase, the objective value of upper level would decrease; while, as α-cut levels increase, the objective value of lower level would increase. For example, the optimized objective value of upper level would vary from 14.95 (α = 0) to 8.51 (α = 1); while, the optimized value of lower level would vary from 5.91 (α = 0) to 8.51 (α = 1). In addition, it also represents the irrigation water use efficiency would vary as α-cut level changed because objective function means maximizing the economic benefit of per unit irrigation water resources.

In this paper, a FFFPM was developed to optimization allocation of irrigation water resources under multiple fuzzy uncertainties, which existed not only in constraints but also in objective function. The proposed model has the ability to deal with uncertainties expressed as fuzzy sets, and could offer a range of optimization schemes under different α-cut levels.

 

Source:

http://doi.org/10.1371/journal.pone.0217783