A robust multi-objective model for supporting agricultural water management with uncertain preferences

Abstract Sustainable management of agricultural water resources is essential for promoting regional development and restoring ecological environment. Due to the imperfection of knowledge and imprecision of expression, the preferences of objectives are uncertain in nature. However, the uncertain feature of objective preferences is often neglected in solving multi-objective water management problems. Also, stochastic information is prevalent in agricultural system. Recognizing the needs to tackle uncertainty existing in objective preferences and parameters during the optimization process of agricultural water resources, a new mathematical programming named multi-objective chance-constrained programming approach for planning problems with uncertain weights (MCUW) was proposed. It could handle uncertain weights of objectives without known distributions, and quantify the risks of objective unattainability arising from such uncertainty. It could also deal with uncertain parameters with known probability distributions, generating solutions with varied risks of constraint violation. The proposed MCUW method was applied to a case study of agricultural water resources management problem in Northwest China to demonstrate its applicability. Multiple sets of optimal solutions under different combinations of weights fluctuation ranges, protection levels, and surface water availabilities were obtained, providing management options for stakeholders with different risk appetites. Results indicate that the objective value would increase with higher risks of objective unattainability or water-shortage. The MCUW method was compared to two potential alternatives and deemed effective in balancing multiple objectives and tackling complex uncertainties. Monte Carlo simulation showed that the results of MCUW were more densely distributed than those obtained from the model with deterministic weights, verifying that the developed MCUW model could provide robust solutions when faced with uncertain weights.