Planning of best management practices for watershed-scale pollution control: A simulation-based inexact fractional programming approach.

[Display omitted] • A simulation-based inexact fractional programming model was proposed to control pollution. • This model can tackle ratio optimization problems with mixed-integer variables and uncertain parameters. • Placement plans for best management practices were optimized for both pollution abatement and cost saving. • The dual-objective model outperformed the single-objective one in cost efficiency. The implementation of best management practices (BMPs) is crucial for protecting and restoring watersheds from nonpoint source (NPS) pollution. BMP placement plans with a high pollution reduction to cost ratio are highly desired by decision makers. Nevertheless, few studies tackled such a ratio optimization problem in their efforts to identify BMP placement plans. BMP planning also faces challenges in handling inherent uncertainties and estimating NPS pollution loads. To address these gaps, a simulation-based inexact credibility-constrained mixed-integer fractional programming (SICMFP) model was proposed for supporting the placement of BMPs. This model was developed by integrating the export coefficient model (ECM), compound topographic index (CTI), inexact programming, and mixed-integer programming within a fractional programming framework. SICMFP extends the capability of previous BMP placement models by optimizing the ratio of conflicting objectives and handling uncertain parameters based on interval theory and credibility measure. It can also conveniently simulate the spatiotemporal distribution of pollution loads through the ECM, and efficiently identify potential wetland sites using CTI. SICMFP was applied to plan BMP placement in the Luan River Basin, located in northern China. The results showed that SICMFP could provide BMP placement plans with the optimal system efficiency between pollution reductions and cost savings under different credibility levels. These plans could help decision makers gain in-depth insights into the tradeoffs between expected system efficiency and the risk of constraint violation. As the credibility level rises from 0.6 to 0.9, the optimal ratio between pollution reduction and cost declined from [0.88, 1.66] kg/103 yuan to [0.70, 1.15] kg/103yuan, whereas the costs and pollution reductions increased. Compared with the least-cost single-objective model, SICMFP could lead to more pollution reductions and higher system efficiency. The developed SICMFP approach can also be extended to address the ratio optimization problems of water pollution management in other watersheds. [ABSTRACT FROM AUTHOR]