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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., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Graphical abstract Highlights • Structures of industrial sectors have significant impacts on energy intensity. • The energy intensity may be affected by uncertainties in industrial activities. • The randomness of energy intensity may lead to unexpected violation events. • Copula-based violation risk analysis can support decision-making in energy-intensity mitigation. Abstract An integrated approach was developed through incorporating a copula-based violation risk analysis into a programming model for optimizing industrial structures of urban clusters in uncertain conditions. Also, this approach can be used to support decision making about promoting advanced manufacturing sectors (AMSs) and mitigating industrial energy intensity. The advantages and the improvements of this approach lie in (a) reflecting the relationships between energy consumption and economic benefits in industrial sectors, and (b) incorporating the violation risk of the targets in energy-intensity mitigation into an optimizing model. A case study was conducted to illustrate the application of this approach in the Pearl River Delta of China, a highly urbanized area that includes the cities of Guangzhou, Shenzhen, Zhuhai, Dongguan, Huizhou, Zhaoqing, Foshan, and Jiangmen. The results indicated that under the desired industrial structures, violation risk of energy-intensity mitigation in the urban cluster of the Pearl River Delta would be indistinctive in the single-city perspective. Also, except Dongguan, Jiangmen and Zhaoqing, the cities of the urban cluster would achieve the goal for developing AMSs, based on the Industrial Plans for the 13th Five Year. [ABSTRACT FROM AUTHOR]

In this research, an export coefficient based inexact fuzzy bi-level multi-objective programming (EC-IFBLMOP) model was developed through integrating export coefficient model (ECM), interval parameter programming (IPP) and fuzzy parameter programming (FPP) within a bi-level multi-objective programming framework. The proposed EC-IFBLMOP model can effectively deal with the multiple uncertainties expressed as discrete intervals and fuzzy membership functions. Also, the complexities in agricultural systems, such as the cooperation and gaming relationship between the decision makers at different levels, can be fully considered in the model. The developed model was then applied to identify the optimal land use patterns and BMP implementing levels for agricultural nonpoint source (NPS) pollution management in a subcatchment in the upper stream watershed of the Miyun Reservoir in north China. The results of the model showed that the desired optimal land use patterns and implementing levels of best management of practices (BMPs) would be obtained. It is the gaming result between the upper- and lower-level decision makers, when the allowable discharge amounts of NPS pollutants were limited. Moreover, results corresponding to different decision scenarios could provide a set of decision alternatives for the upper- and lower-level decision makers to identify the most appropriate management strategy. The model has a good applicability and can be effectively utilized for agricultural NPS pollution management. [ABSTRACT FROM AUTHOR]

An enhanced radial interval programming approach was developed for supporting the identification of sound agricultural production plans. It was designed to tackle dual uncertainties in both the economic and environmental subsystems as well as reflect differential aspiration levels for 'immunity' against such uncertainty. By adding protection functions to both the objective functions and constraints susceptible to dual uncertainties without any distributions, it improved upon previous methods through simultaneously measuring and manipulating expected return risk and resource-environmental compliance risk. Moreover, this study made novel attempts to explore system-wide optimal levels of robustness based on proposed performance evaluation criteria and investigations over the interactive effects of varied robustness aspirations for different model components. Based on analyzed tradeoffs among system optimality, robustness and uncertainty degree of solutions pertaining to the study case, a unified protection level of 13 (or 10) was recommended for risk-averse (or risk-neutral) decision making. The model outputs were compared to those from three alternatives, revealing that it could achieve a high level of system reliability at a minor price of economic return. This approach could be generalized for wide-scale applications. [ABSTRACT FROM AUTHOR]

In this research, an export coefficient based dual inexact two-stage stochastic credibility constrained programming (ECDITSCCP) model was developed through integrating an improved export coefficient model (ECM), interval linear programming (ILP), fuzzy credibility constrained programming (FCCP) and a fuzzy expected value equation within a general two stage programming (TSP) framework. The proposed ECDITSCCP model can effectively address multiple uncertainties expressed as random variables, fuzzy numbers, pure and dual intervals. Also, the model can provide a direct linkage between pre-regulated management policies and the associated economic implications. Moreover, the solutions under multiple credibility levels can be obtained for providing potential decision alternatives for decision makers. The proposed model was then applied to identify optimal land use structures for agricultural NPS pollution mitigation in a representative upstream subcatchment of the Miyun Reservoir watershed in north China. Optimal solutions of the model were successfully obtained, indicating desired land use patterns and nutrient discharge schemes to get a maximum agricultural system benefits under a limited discharge permit. Also, numerous results under multiple credibility levels could provide policy makers with several options, which could help get an appropriate balance between system benefits and pollution mitigation. The developed ECDITSCCP model can be effectively applied to addressing the uncertain information in agricultural systems and shows great applicability to the land use adjustment for agricultural NPS pollution mitigation. [ABSTRACT FROM AUTHOR]

In this research, an interval-parameter two-stage stochastic programming approach was developed for supporting the identification of low-carbon strategies and the post-earthquake reconstruction in the city of Gugangyuan, Sichuan province of China. The approach can effectively deal with uncertainties that can be expressed as both probability density functions and interval numbers without any distribution information. Also, the approach can provide useful decision alternatives for supporting long-term corrections for any plans associated with carbon dioxide emission limits within a city context. The developed approach was applied in the city of Guangyuan. Three scenarios were established including the baseline (i.e., regional planning) as scenario 1, zero carbon emission as scenario 2, and carbon sink as scenario 3. Also, based on practical information and the collected data, three projection values (i.e., low, medium and high levels) for the carbon emission of the entire city were generated and analyzed under varying probability levels (i.e., 20, 60, and 20%). The results indicated that in order to achieve low-carbon post-earthquake development in the city, the priority areas and industries for carbon emission reduction would be Chaotian (the secondary industry) > Wangcang (the secondary industry) > Lizhou (the secondary industry) = Qingchuan (the tertiary industry) > Cangxi (the secondary industry) = Chaotian (the tertiary industry). [ABSTRACT FROM AUTHOR]

In this study, a feasibility-analysis-based inexact fuzzy multistage model (FA-IFMSM) was developed for supporting the planning of energy and environmental systems under multiform uncertainties. In FA-IFMSM, methods of feasibility-analysis-based fuzzy linear programming (FA-FLP) and inexact multistage stochastic programming (IMSP) with recourse were integrated into a general mixed-integer linear programming framework, such that the developed model could tackle uncertainties described in terms of probability distributions, interval values, fuzzy sets, and their hybrid and mixture. Moreover, it could reflect dynamic features of facility-capacity expansions and energy supplies over a multistage context. It could also quantify constraint violation degrees through the adoption of various acceptable degree levels. Then the proposed model was applied to a regional energy and environmental system to illustrate its applicability, where conventional and renewable energy resources and their economic and environmental implications were considered. The results indicated that reasonable solutions were generated. They were helpful for supporting (1) adjustment or justification of allocation patterns of regional energy resources and services; (2) formulation of local policies regarding energy consumption, economic development, and environmental protection; and (3) in-depth analysis of trade-offs among system cost and satisfaction degree, and environmental requirements under multiple uncertainties. [ABSTRACT FROM AUTHOR]

SUMMARY A regional energy system consists of diverse forms of energy. Energy-related issues such as utilization of renewable energy and reduction of greenhouse gas (GHG) emission are confronting decision makers. Meanwhile, various uncertainties and dynamics of the energy system are posing difficulties for the energy system planning, especially for those under multiple stages. In this study, an interval multi-stage stochastic programming regional energy systems planning model (IMSP-REM) was developed to support regional energy systems management and GHG control under uncertainty. The IMSP-REM is a hybrid methodology of inexact optimization and multi-stage stochastic programming. Not only can it handle uncertainties presented as intervals and probability density functions but also reflect dynamics of system conditions over multiple planning stages. The developed IMSP-REM was applied to a hypothetical regional energy system. The results indicate that the IMSP-REM can effectively reflect issues of GHG reduction and renewable energy utilization within an energy system planning framework. In addition, the model has advantages in incorporating multiple uncertainties and dynamics within energy management systems. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Multiple correlated risks caused by uncertain information pose great challenges to the coordinated regulation of water-energy-food nexus (WEFN). In this study, a Copula-based radial interval chance-constrained programming (CRICP) was developed. CRICP can not only quantify composite risk induced by multiple risks with nonlinear correlations, but also tackle dual uncertainty expressed as redial intervals with adjustable protection levels. CRICP was applied to an irrigated agricultural management problem constrained by water, energy, and land resource in Bayan Nur City in northern China. Results indicate that system benefit would increase with the incline of composite risk or the decline of protection level. Monte Carlo simulation verified that the different definitions of composite risk could lead to significant differences in the combination of subsystem risks. The composite risk induced by the simultaneous shortage of multiple resources would have greater impacts on system benefits compared against composite risk caused by shortage of at least one resources, with an increase of [24.65%, 25.95%] in the minimum value of system benefits. Comparisons against two alternative models further verified that CRICP outweighs previous methods by modeling the correlation structure of multiple risks and tackling dual uncertainties without distribution information. • The complex interactions and inherent uncertainty affect the security of Water-Energy-Food Nexus. • A Copula-based radial interval chance-constrained programming method was developed. • It can tackle composite risk induced by random variables with unknown correlations. • It can also address dual uncertainties without detailed distributions. • The bias in decision making process triggered different composite risks were clarified. [ABSTRACT FROM AUTHOR]

Effective water allocation among multiple jurisdictions is a key instrument to improve water use efficiency within the basin scale. To achieve equitable and reasonable water allocation, natural, socio-economic, and ecological conditions within a specific basin need to be systematically considered. Based on the main principles of equitable and reasonable water allocation that were defined by UN Watercourses Convention, an integrated multi-criteria decision making (MCDM) with bankruptcy rules (IMCDM-BR) under multiple hydrological constraints were proposed to allocate trans-jurisdiction water resources in Guanting reservoir basin (GRB), a shared basin between Zhangjiakou and Beijing in China. Projection pursuit (PP), as one of an effective MCDM approach, was employed to synthesize values of the related principles, which were ranked as weights for the corresponding water claims by relevant agents. Then, the weighted bankruptcy rules (BR) with multiple hydrological constraints were applied to allocate water among the related agents of the studying basin. The results of ordinary bankruptcy rules, bankruptcy rules with regular and hydrological constraints, and the proposed methods were compared and discussed. Among them, the proposed IMCDM-BR was recommended as an effective tool to support practical water allocation. Moreover, factors of equitable and reasonable water allocation were comprehensively considered. The results can thus be used for facilitating negotiation in trans-jurisdiction water allocation among agents within basins. [ABSTRACT FROM AUTHOR]

Due to insufficiency and ineffectiveness of monitoring facilities, variations in natural conditions and changes of human behaviors, watershed planning is interwoven with imprecise data, resulting in a multitude of complexities. A robust interval fuzzy programming approach with superiority–inferiority and risk-aversion analyses (RIFP-SIRA) was developed for identifying sustainable agricultural and industrial production strategies at the watershed scale in a highly uncertain environment. RIFP-SIRA represented a novel attempt to tackle synergies of uncertain information in the forms of intervals with non-statistical bounds and conventional intervals. The developed method was applied to a Chinese watershed. A RIFP-SIRA model was formulated and analyzed under three scenarios to investigate the effects of different policies and standards on watershed development plans. Sensitivity of the model's solutions to varied risk-aversion and input-fluctuation levels were analyzed, verifying the superiority of RIFP-SIRA over the existing inexact approaches. This research revealed that RIFP-SIRA could provide local authorities with robust, yet flexible decision plans. It could enable a quantitative analysis over the trade-offs between the economic benefits and environmental risks in the absence of probabilistic information. [ABSTRACT FROM AUTHOR]

In this study, an environmental-friendly modeling system was developed and applied to an agriculture nonpoint source (AGNPS) management in Ulansuhai Nur watershed. In this system, water environmental capacity, credibility-based chance-constrained programming (CCCP), and AGNPS optimization models were integrated into a general modeling framework. It could be used to calculate water environmental capacity of total nitrogen and total phosphorus in Ulansuhai Nur watershed, which could consequentially provide input data for the developed AGNPS optimization model. Also, the inherent uncertainties in estimating water environmental capacities that can be expressed as possibilistic distributions were reflected and addressed based on computational results of three widely used methods. Such uncertainties were consequentially transferred to the proposed CCCP model based on the adoption of multiple credibility satisfactory levels, significantly facilitating objectivity reflection of decision alternatives. The developed modeling system was then applied to Ulansuhai Nur watershed of Inner Mongolia, a semi-arid river basin in northwestern China. Optimal strategies for AGNPS management in Ulansuhai Nur watershed were generated with consideration of the maximum total agricultural income under multiple policy scenarios. The results showed that the total agricultural income would increase with point source pollution being cut down, and would decrease with rising credibility levels, representing decreasing system violation risks. It was indicated that the higher of total nitrogen/phosphorus discharge being less than water environmental capacity of Ulansuhai Nur, the lower the total agriculture incomes. The proposed methods could help decision makers establish various production patterns with cost-effective agriculture nonpoint source management schemes in the basin of Ulansuhai Nur, and gain in-depth insights into the trade-offs between total agricultural incomes and system reliabilities. [ABSTRACT FROM AUTHOR]

Abstract: In this study, a feasibility based inexact fuzzy programming approach (FBIFP) was developed and applied to the planning of a regional electric power generation system (REPGS). As an extension of existing interval linear programming and fuzzy linear programming, FBIFP could tackle uncertainties expressed as intervals, fuzzy sets as well as their combination in both of the objective function and constraints. Through introducing the index of feasibility degree, FBIFP could be used to facilitate the efficient reflection of constraint violation, and thus allow decision makers to have a complete view of the relationships between uncertain inputs and the related solutions. A hypothetic regional electric power generation system was provided for demonstrating applicability of the developed model. Useful solutions for the planning of REPGS were generated. Interval solutions under different feasibility degrees were obtained. They could be used for helping decision makers identify desired alternatives under various reliability risks of the system. The solutions could also help identify optimal patterns for energy resources allocation, electricity generation and facility capacity expansion with a minimized system cost. Tradeoffs between system costs and system security could be successfully addressed through the analysis of the feasibility degrees of constraints, i.e., a higher feasibility degree would correspond to a higher system cost, while a lower system cost would run into a higher risk of potential instability of the study system. [Copyright &y& Elsevier]

Site selection is one of the most significant decision making activities for development of wind energy resource. In this study, a novel method integrating Geographic Information System (GIS), interval Analytic Hierarchy Process (IAHP) and stochastic VIKOR was proposed to tackle site selection issue of wind farms in the Wafangdian region, China. Two major factors, i.e. biodiversity conservation and production safety, were utilized to determine feasible areas. Afterwards, the weight of evaluation criteria, including the social impact, economic benefit, terrain and eco-environment protection, were identified by using IAHP. Finally, the suitability indexes of various alternatives were calculated by stochastic VIKOR and their ranking was used to determine high-suitability areas for wind farm locations. The obtained results indicated that 30.2% of studied region were suitable for installing the wind-power facilities, but only 3.36% were determined to be highly suitable. By comparing the optimized results to the actual locations of existing wind farms, it was revealed that the ideological framework of this study were practical and effective in guiding site selection of wind farms, and they were also useful for applications in site selection of other renewable energy forms involving complex spatial analysis and multiple criteria evaluation, including solar, hydroelectric, geothermal and biomass. • A novel integrated method of IAHP and stochastic VIKOR was developed. • A typical Chinese onshore wind farm site selection case was investigated. • Social impact, economic benefit, terrain and eco-environment were considered. • The suitability evaluation of candidate region for wind farm was conducted. • Evaluated results shows 30.2% area favorable for wind farm arrangement. [ABSTRACT FROM AUTHOR]