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In this study, a new concept concerning comprehensive characteristics of water resources utilization as an index for risk modeling within the water allocation management model is proposed to explore the tolerance of unbalanced allocation problem under the water–energy nexus. The model is integrated with interval two-stage stochastic programming for reflecting system uncertainties. These uncertainties are associated with the industrial production feature and the decision-making process. With respect to the water–energy nexus, energy proposed is mainly focused on the consumption intensity of water purification and transportation from different water sources. The developed model is applied for industrial water resources allocation management in Henan province, China. Multiple scenarios related to disparate energy consumption control and the comprehensive risk levels are simulated to obtain a reasonable trade-off among system profit, comprehensive risk, and energy consumption. The results indicated that the strict comprehensive risk management or energy consumption control measures could cause damage to system benefit owing to decreasing the flexibility of industrial water resources distributions, and the preliminary energy consumption or the comprehensive risk control would be beneficial to moderate the conflict between industrial sectors and water resources, and accelerate industrial structure transformation in the future. HIGHLIGHTS A comprehensive risk-oriented industrial water resources management model is proposed.; Uncertainties are reflected as stochastic and interval information.; Energy–water nexus is a constraint index for water purification and transportation.; The tolerance of unbalanced allocation problem is explored.; Trade-off among system profit, comprehensive risk, and energy consumption is analyzed.

A clear understanding of regional water supply and demand trend is crucial for proper water resources planning and management in water-deficient areas, especially for Northwest China. In this study, three hybrid stochastic models (Markov chain model, unbiased Grey-Markov model and Markov model based on quadratic programming) were developed separately for predicating the available water resources, water demand, and water utilization structure in Urumqi. The novelty of this study arises from the following aspects: (1) compared with other models, the developed models would provide ideal forecasting results with small samples and poor information; (2) this study synthetically took into account water supply and demand, water utilization structure trend; (3) the prediction results were expressed as interval values for reducing the forecasting risk when carrying out water resources system planning and operational decisions. Analysis of water supply and demand in Urumqi under different reuse ratios was also conducted based on the forecasting results. The results would help managers and policy-makers to have a clear understanding of regional water supply and demand trend as well as the water utilization structure in the future.

In recent years, Binhai New Area of Tianjin has been suffering severe water shortage due to climate change and industrial activities. Integrated and effective water resources management approaches are urgent for the sustainable development of industrial parks in Binhai New Area. However, uncertainties exist in many aspects of the water resources system and are inevitably problematic for water resources planning and policy-making. To address these uncertainties, an interval multiple-objective programming model was developed here to support the long-term planning of industrial water resources management in Binhai New Area, Tianjin, China. The model incorporated both multiple-objective programming and interval linear programming into a general programming framework. The developed model could handle the uncertainties and complexities of the water management system, and also allowed decision makers to adjust fuzzy objective control decision variables to satisfy multiple holistic and interactive objectives. The solutions are useful for planning adjustments of the existing water allocation patterns in Binhai New Area.

In this study, a fuzzy credibility constrained programming (FCCP) model is developed for water quantity and quality management with uncertainties in water quality parameters. The proposed method could reflect not only inexact uncertainties in the objective function, variables and parameters, but also fuzzy uncertainties in the right-hand side. Credibility levels which represent satisfaction degrees of the constraints can be analysed. The developed model is applied to a case study of water resources management within one river basin, three subareas and three water users regarding water environment security. According to the different confidence levels and sewage recovery, scenario analysis is conducted to analyse possible events in water allocation and water quality control. The resulting solutions obtained show that the proposed method can help decision-makers to provide scientific bases for water quantity and quality management and energy system planning, solid waste management and other environmental system problems.