Inexact fuzzy-flexible left-hand-side chance-constrained programming for agricultural nonpoint-source water quality management

In this study, an inexact fuzzy-flexible left-hand-side chance-constrained programming (IFLCCP) method is proposed for optimizing an agricultural nonpoint-source water quality management problem under uncertainty. The developed method can address complex uncertainties resulted from system fuzzy flexible under various level of decision-making requirements and randomness parameters appeared on the left-hand side of the constraints, and deal with the conflict between water quality protection and agricultural system economic development. The IFLCCP model is formulated through incorporating inexact left-hand-sided chance-constrained programming into interval fuzzy flexible programming framework. The decision schemes obtained by the IFLCCP are analyzed under scenarios at different confidence level of environmental constraint. The results demonstrate that the scale of crop planting and breeding industries reduces as the confidence coefficient of environmental constraint (1-p_i) increases, in order to satisfy pollutant discharge constraints, which results in the reduction of the system net benefit from scenarios 1 to 3. Meanwhile, the interval control variables λ^± are introduced for quantifying the degrees of overall satisfaction for the objective function and the constraints, which get optimal adjustment to guarantee the net benefit to be as close as possible to the upper bound. The IFLCCP is able to provide management schemes with high system benefits under different levels of acceptable environmental risk, taking full consideration of decision makers' environmental management requirements. This study is a new application of the IFLCCP model to agricultural water quality management problem, demonstrating its applicability to practical environmental problems with high complexity and uncertainty.