Distributed ANN-bi level two-stage stochastic fuzzy possibilistic programming with Bayesian model for irrigation scheduling management

•The distributed ANNs model was built to simulate spatial yield.•The BLTSFPPSNE model was proposed.•The distributed ANN- BLTSFPPSNE was established.•Water allocation target, irrigation amounts and dates were optimized simultaneously.•The developed model was applied to a case study to verify its application. To optimize irrigation amount and date, and water allocation target across spatially distributed crops under uncertainties and risks, the framework of the distributed ANN-bi level two-stage stochastic fuzzy possibilistic programming with Bayesian (distributed ANN-BLTSFPPB) model was established by integrating bi-level programming, two stochastic programming (TSP), fuzzy possibilistic programming, Bayesian, downside risk with the distributed ANN model. Decisions making of distributed crops were conducted by building distributed model to optimize decisions at several spatially heterogeneous units. The risks of economic benefit and water productivity were considered and measured by the downside risk approach, and uncertainties of runoff were presented as fuzzy normal distribution numbers to reduce uncertainties and improve robustness of decisions. Besides, tradeoffs between economic benefit and risks in the upper layers, and contradictory relationships across objectives at the upper and lower layers were balanced by the BLTSFPPB model. Moreover, effects of water right trading on economic benefit with considerations of subjectivities of managers under different hydrological years were quantified by Bayesian approach. Calculation efficiencies of the distributed AquaCrop-optimization model were effectively improved by establishing the distributed ANN-BLTSFPPB, making it easy-to-use and expanding its applications. The developed model was applied to Yingke district to verify its application. The results disclosed that economic benefit and yield enlarged, and water productivity and risks lessened when the water right trading was considered. The results could offer insight into how to establish the distributed ANN model to replace distributed simulation model and further couple with optimization model to conduct spatially distributed decisions and improve calculation efficiencies for managers. They can reach key tradeoffs across economic benefit, yield and risks, and support in-depth analysis about how water right trading affects system outcomes.