Radial interval chance-constrained programming for agricultural non-point source water pollution control under uncertainty

Inherent uncertainties in agricultural non-point source water pollution control problems cause great difficulties in relevant modeling processes. A radial interval chance-constrained programming (RICCP) approach was developed in this study for supporting source-oriented non-point source pollution control under uncertainty. The proposed RICCP approach could tackle two-layer uncertainty resulting from temporal and spatial variability of many factors and their uncertain interactions. Based on the concept of radial intervals and chance-constrained programming, RICCP could reflect the randomness in the bounds of interval parameters, with or without known probability distributions. RICCP could also allow decision makers to adjust the conservativeness of solutions via protection and significance levels, helping satisfy environmental, economic and resource-conservation requirements in a holistic and interactive manner. The proposed methodology has been applied to an agricultural water pollution control case. The most-profit agricultural development strategies were explored while restricting environmental impacts to an acceptable level. A series of interval solutions for agricultural practices were generated corresponding to varied risk levels of constraint violations, which could help screen optimal alternatives according to decision makers’ profit and risk considerations as well as various system conditions. RICCP model was also compared to its alternatives. Significant differences in the solutions among the compared models further demonstrated the advantages of the proposed approach.