Multi-stage stochastic fuzzy random programming for food-water-energy nexus management under uncertainties

A hybrid inexact optimization model is developed for food-water-energy nexus system management with the consideration of complex uncertainties and decision makers’ risk tolerance. A multi-stage stochastic fuzzy random programming (MSFRP) model is tailored to tackle variables with deeper uncertainties, a mixture of fuzzy and random fuzzy characteristics. Allowing to reflect decision makers’ subjective opinion and risk preference, it can provide decision makers the tradeoff information between system benefit and risk attitude. The proposed model was applied to an agricultural area Shandong Province, China with the aim of maximum total system benefits. The valuable managerial insights on optimal cultivated land distribution, water resource allocation, and energy supply strategies are provided for decision makers under uncertainties. Meanwhile, the pesticide and fertilizer consumption for crop planting, and the carbon emission embodied in per unit crop supply are also quantitatively estimated. Moreover, by setting different water resource availability scenarios, the impacts of future water resource conditions on optimal management strategies under climate change are evaluated and discussed. The results suggested that rice would be the critical crop with the largest planting area for food security during the planning horizon. Under scarcer water resource conditions, the system benefits would reduce due to more desalination water consumption and planting strategy adjustment. However, it would lead to less carbon emission embodied in per unit crop supply and relieve local carbon emission control pressure. Compared to the conventional multi-stage stochastic programming, the developed MSFRP can be more effective to reflect the optimistic and pessimistic attitude of decision makers and deal with future scenario information with deeper uncertainties.