In this study, a joint-probabilistic interval multistage programming (JIMP) method is developed for planning water resources management under uncertainty. The JIMP method can tackle uncertainties presented in terms of interval parameters in objective function and constraints, in addition to random variables in the left and right-hand sides of constraints. It can also reflect the dynamics in terms of decisions for water resources allocation through transactions at discrete points of a complete scenario set over a multistage context. Moreover, the JIMP method can be used for analyzing various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The JIMP method is applied to a real case of planning water trading for supporting the regional sustainable development of the Kaidu-Qongque River basin, which is one of the most arid regions of China. Monte Carlo simulation is introduced into the JIMP framework for evalua...

This study proposes an interval semiinfinite De Novo programming (ISIDP) method for the planning of water resource management systems under uncertainty. The ISIDP problem is settled by dividing it into two interactive linear programming subproblems and solving it by using a conventional simplex method. To evaluate the applicability of the proposed model, the method is applied to a case study of the Yuecheng Reservoir in Zhangweinan River Basin, China. The results indicate that the strategies generated through ISIDP would not increase the complexity in decision-making processes. Compared with the conventional optimization method, ISIDP has the advantages of (1) better reflecting the association of the system benefits with water price, (2) generating more reliable solutions with a lower risk of system failure as a result of the possible violation of constraints, and (3) providing more flexible management planning because the availability of budgets can be adjusted with the variations in water price.

In this study, a two-stage interval-stochastic water trading (TIWT) model is developed for reallocating water resources under uncertainty, which integrates techniques of interval-parameter programing and two-stage stochastic programing into a general framework. The TIWT model can provide an effective linkage between system benefit and the associated economic penalty attributed to the violation of the pre-regulated water permit under uncertainties expressed as probabilistic distributions and interval values. The trading scheme is introduced to optimize water allocation of Kaidu-Kongque River in northwestern China. Results obtained suggest that trading program can effectively allocate limited water resources to competitive users by market approach in such an arid area, which improves economic efficiency in the mass (e.g., maximizing system benefits) and remedies water deficiency. A number of policies for water permits are analyzed and reveal that different water permits lead to different water shortages, system benefits, and system-failure risks. Tradeoffs between economic benefit and system-failure risk are also examined under different policies, which support generating an increased robustness in risk control for water resources allocation under uncertainty. The results are helpful for local decision-makers in adjusting the current water allocation pattern optimally.

In this study, an inexact chance-constrained waste-load allocation (ICWA) model is proposed for supporting river quality management under uncertainty that is capable of addressing uncertainties expressed as intervals and probability distributions as well as analyzing the reliability of satisfying (or the risk of violating) various constraints. The ICWA model is then applied to water quality management of the Xiangxihe River in the Three Gorges Reservoir Region, which faces severe water quality problems due to point and nonpoint source pollution. The results demonstrate that higher biological oxygen demand (BOD) discharge amounts are observed at the Baishahe chemical plant and Gufu wastewater treatment plant. Moreover, total phosphorus discharges into the river come mainly from point sources, particularly the chemical plants and phosphorus mining companies. For nonpoint sources, crop farming generates large amounts of total phosphorus and total nitrogen. Tradeoffs between economic benefits and system-failure risks are also examined. Alternatives can be obtained from different combinations of decision variables within their lower and upper bounds, which are valuable for decision makers, who need to develop the desired regional economic plans while satisfying environmental requirements.