Identification of optimal placements of best management practices through an interval-fuzzy possibilistic programming model

• An interval-fuzzy possibilistic programming (IFPP) method is developed.
• It can handle multiple uncertainties and enhance the traditional FPP model.
• IFPP is applied to identify the placements for BMPs to control nutrient loading.
• The results show implementation levels for BMPs under multiple credibility levels.
• Setting a global discharge permit may shift BMPs among sub-basins at a lower cost.

In this research, an interval-fuzzy possibilistic programming (IFPP) method was developed by integrating interval parameter programming (IPP), fuzzy possibilistic programming (FPP), and a fuzzy expected value equation within a general optimization framework. The developed IFPP method can not only effectively address uncertainties presented in terms of crisp intervals and fuzzy-boundary intervals in both the objective function and constraints, but it can also improve the traditional fuzzy mathematical programming by choosing the credibility degree of constraints based on the decision maker’s preference and avoiding complicated intermediate models with high computational efficiency. The developed method was applied to identify optimal placements for best management practices (BMPs) to control nutrient pollution in the Baoxianghe River watershed in China, in which a GIS-aided export coefficient model (ECM) was employed to estimate the phosphorus loads from a nonpoint source (NPS). The optimization results showed that the hybrid approach could be used to generate a series of implementation levels for BMPs under multiple credibility levels, ensuring that the NPS phosphorus loads discharged into rivers reduce to an allowable level and considering a proper balance between expected system costs and risks of violating the constraints. Relaxing the sub-basin discharge permits suggests a global discharge permit for the entire watershed, which may allow managers to shift BMP implementation among sub-basins to meet the overall discharge permit at a lower cost.