A simulation-based interval stochastic bi-level multi-objective programming (SISBLMOP) model was proposed in this research, through integrating the global nutrient export from watersheds model, intervalparameter prog...
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A simulation-based interval stochastic bi-level multi-objective programming (SISBLMOP) model was proposed in this research, through integrating the global nutrient export from watersheds model, interval parameter programming and stochastic chance-constrained programming into a general bi-level multi-objective programming framework. The SISBLMOP model can handle multiple uncertainties expressed as discrete intervals and probability density functions in both the simulation and optimization processes. System complexities, including the hierarchy structure of upper- and lower-level decision makers, can also be addressed in the model. The proposed model is applied to a real-world case study of the Xinfengjiang Reservoir Watershed in South China to identify the satisfactory implementation levels of multiple best management practices (BMPs). The model results show that multiple BMP schemes for water quality management can be obtained under different upper- and lower level decision-making and risk-violation scenarios, reflecting the cooperation and gaming results of the two-level decision makers. Consequently, the corresponding BMP implementation costs are acceptable to both the upper and lower-level decision makers. The model is widely applicable and can be effectively used for water quality management under multiple uncertainties and complexities.
Achieving optimal water allocation in an inter-basin water diversion project is a challenge that involves multilevel stakeholders, and the uncertainty and disequilibrium of water allocation further intensify competiti...
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Achieving optimal water allocation in an inter-basin water diversion project is a challenge that involves multilevel stakeholders, and the uncertainty and disequilibrium of water allocation further intensify competition among different stakeholders. This study proposes a bi-level multiobjective programming model for water allocation in inter-basin water diversions that considers equilibrium sustainability. The model integrates interval parameter programming, fuzzy credibility-constrained programming, bi-level multiobjective programming, and the Gini coefficient into a general framework. The model not only balances the stakeholders at different levels to ensure water allocation equity but also comprehensively considers the fuzzy uncertainty of parameters and constraints to obtain the interrelationship among water diversion, water allocation satisfaction, and efficiency objectives. The developed model was applied to allocate water for the Hanjiang-to-Weihe Water Diversion Project in Shaanxi Province, China. The results showed that 1) the model derived a feasible tradeoff between upper basin manager and lower regional managers under different water diversion scenarios;2) water allocations and objectives at each level are sensitive to changes in the credibility of water diversion;3) the new model improves the equity of water allocation and ensures the efficient allocation to various stakeholders at each level based on a comparison of the proposed model with a model that does not consider equilibrium. The proposed model can help decision makers choose the optimal scheme based on their acceptable risk level to achieve a more efficient and sustainable water allocation for inter-basin water diversions.
In this research, a dual-randomness bi-level interval multi-objective programming (DR-BIMP) model was developed for supporting water resources management among multiple water sectors under complexities and uncertainti...
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In this research, a dual-randomness bi-level interval multi-objective programming (DR-BIMP) model was developed for supporting water resources management among multiple water sectors under complexities and uncertainties. Techniques of bi-level multi-objective programming (BMOP), double-sided stochastic chance constrained programming (DSCCP), and interval parameter programming (IPP) were incorporated into an integrated modeling framework to achieve comprehensive consideration of the complexities and uncertainties of water resources management systems. The DR-BIMP model can not only effectively deal with the interactive effects between multiple decision-makers in complex water management systems through the bi-level hierarchical strategies, but also can characterize the multiple uncertainties information expressed as interval format and probability density functions. It could thus improve upon the existing bi-level multi-objective programming through addressing discrete intervalparameters and dual-randomness problems in optimization processes simultaneously. Then, the developed model was applied to a real-world case to optimally allocate water resources among three different water sectors in five sub-regions in the Dongjiang River basin, south China. The results of the model include determining values, interval values, and stochastic distribution information, which can assist bi-level decision-makers to plan future resources effectively to some extent. After comparing the variations of results, it is found that an increasing probability level can lead to higher system benefits, which is increased from [20,786.00, 26,425.92] x 10(8) CNY to [22,290.84, 27,492.57] x 10(8) CNY, while the Gini value is reduced from [0.365, 0.446] to [0.345, 0.405]. A set of increased probability levels gives rise to the lower-level objectives. Furthermore, the advantages of the DR-BIMP model were highlighted by comparing with the other models originated from the developed model. The compa
Nutrient export from diffuse sources poses a significant threat to watersheds, and methods to support the effective management of these watersheds is essential. However, real-world nutrient flows and watershed managem...
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Nutrient export from diffuse sources poses a significant threat to watersheds, and methods to support the effective management of these watersheds is essential. However, real-world nutrient flows and watershed management systems are highly complex, with a high degree of uncertainty in their descriptive information. Thus, an effective optimization method for watershed management must be developed to deal with this uncertainty, which is crucial for formulating and implementing appropriate management practices. This research presents an inexact simulation-based left-hand-side chance-constrained mixed-integer programming (ISLCCMIP) model to determine nutrient export characteristics and optimal management strategies. By introducing interval and stochastic parameters into the simulation process, the uncertain characteristics of nutrient export loads can be considered. Uncertainties and complexities in management processes can also be handled through incorporating interval parameter programming and mixed-integer programming within a left-hand-side chance-constrained programming framework. The proposed ISLCCMIP model can correlate the randomness in the simulation process and the optimization results. The East River basin in South China was selected as the case study area to apply the proposed model. The results indicated that inorganic nitrogen (N) and phosphorus (P) were the main forms for the nutrient export from diffuse sources in this basin. Five of the nine subbasins were identified as critical source areas for nutrient export. Planting areas of different crops, application amounts of chemical fertilizers, and quantities of livestock types can be optimized to achieve the maximum economic benefit under limited N and P discharge permits. Particularly, planting areas of vegetable and soybean (Glycine max L.) would be first decreased, while rice (Oryza sativa L.) and tubers would be retained, as the pollution emission standards become stricter. Decrease in the planting are
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