Interval Two-stage Stochastic Programming Research Articles

Different policies constrained agricultural non-point pollutants emission trading management for water system under interval, fuzzy, and stochastic information

Formulating suitable policies is essential for resources and environmental management. In this study, an agricultural pollutants emission trading management model driven by water resources and pollutants control is developed to search reasonable policies for agricultural water resources allocation under multiple uncertainties. Random-fuzzy and interval information in water resources system that have directly impact on the effectiveness of management schemes is reflected through interval two-stage stochastic fuzzy-probability programming. The model was root from regional agricultural water resources system in Jining City, China under considering the relationship among effective precipitation, crop water demand, and pollutants emission. Two types policies (water consumption-control and pollutants emission-control) are designed for searching the related interaction on water resources management and water quality improvement. The results indicated that water resources policies would be of water and environmental double benefits, and a large rainfall would reduce irrigation amount from water sources and lead to a larger pollutants emission trading. The results will help for defining scientific and effective water resources protection and management policies and analyzing the related interacted effects on water consumption, pollutants control and system benefit.

Interval two-stage stochastic programming model under uncertainty for planning emission rights trading in the Yellow River basin of China.

As a critical way to realize the optimal allocation of water environment capacity resources in the basin, emission rights trading faces multiple uncertainties, making it extremely hard and challenging to formulate appropriate decisions and plans. Therefore, this study uses interval two-stage stochastic programming (ITSP) method to model the emission rights trading process with multiple uncertainties. It can promote the secondary optimal allocation of the emission rights between the demander and the supplier after the initial allocation. Externalities caused by environmental problems are internalized through the form of emission rights trading, thereby reducing the transaction costs and promoting the coordination and integrity of water pollution control among governments in a basin. Finally, the Yellow River basin is taken as an example for case analysis. The results show that the net revenue of emission rights system in the transaction status is better than that in the non-transaction status, and the average gap of net income reaches [171.031, 193.056] billion yuan. Under different reduction policies, the average water pollutant emission reduction in transaction status is [451.15, 628.34] thousand tons, which is generally less than [516.57, 670.05] thousand tons in non-transaction status. As policies get stricter and assimilative capacity of water bodies dwindles, reduction shrinks, leading to higher risks and economic loss from being unable to meet the discharge demand. When reduction policies are relatively loose and assimilative capacity is high, emission rights trading volume peaks. At this time, the trading volume of COD reached [29.05, 40.76] thousand tons, and that of NH3-N reached [3.74, 4.31] thousand tons. All these findings will offer insights for decision-makers on how to strike a balance between economic benefits and emission rights trading plans in the Yellow River basin.

Optimization of Ecological Water Replenishment Scheme Based on the Interval Fuzzy Two-Stage Stochastic Programming Method: Boluo Lake National Nature Reserve, Jilin Province, China.

In this paper, a fuzzy mathematical programming method is introduced on the basis of the interval two-stage stochastic programming (ITSP) optimisation model for the wetland ecological water replenishment scheme in Boluo Lake National Nature Reserve. The minimum ecological water supply is taken as the objective function, and the lake bubble water diversion capacity, lake bubble water supply capacity, water diversion sequence, ecological service value, and minimum capacity of the wetland water supply are taken as constraints. The ecological water replenishment schemes of five lakes in the Boluo Lake National Nature Reserve are optimised at the levels of low flow years, normal flow years, and high flow years, and an optimised model for the wetland ecological water replenishment scheme in Boluo Lake National Nature Reserve based on the interval fuzzy two-stage stochastic programming (IFTSP) method is constructed. The model fully considers the waste of water resources and the protection of migratory bird habitat and makes rational allocation of water resources to make full use of flood resources. The IFTSP model proposed herein fully considers the fuzzy and uncertain characteristics of the planning area in the lake bubble area of Boluo Lake National Nature Reserve and improves the decision-making efficiency of decision-makers by providing technical support for smooth implementation of the ecological water replenishment project in nature reserves. The model can also be used as a theoretical guide for ecological recharge projects in other regions of the world.

A risk-based stochastic model for supporting resources allocation of agricultural water-energy-food system under uncertainty

The interactive water-energy relationship is a major restriction on food production in agricultural irrigation systems. Applying water-saving irrigation systems can further intensify the interrelationship between water and electricity and trigger a water-energy joint risk. Currently, there are no approaches capable of effectively assessing the various uncertainties and water-energy joint risks in irrigation districts. In this study, a novel mathematical programming method termed copula-based interval two-stage stochastic mixed-integer programming (CITSMIP) is proposed. CITSMIP quantifies water-energy joint risks in food production and provides an optimal resource allocation plan and water-saving irrigation application schemes under different joint risk levels. CITSMIP was applied to solve an irrigation resource management problem in northwest China. The results show that under a certain water-energy joint risk, planting sunflowers would be the first choice for water-saving irrigation applications. As water-saving applications have become increasingly common over time, the water-saving volume is expected to increase to [74.65, 84.46] × 107 m3 by 2035. Moreover, under a certain joint risk, compared with the water risk, fluctuations in energy risk would have a greater impact on the total benefit of the system and the total consumption of resources. Compared with single water risk or energy risk management, the joint risk management results would have a lower degree of uncertainty and higher lower-bound benefits. Establishing CITSMIP can provide valuable insights into informing stakeholders to allocate resources and maximize benefits under water-energy joint risk.

Ecological Service Value Tradeoffs: An Ecological Water Replenishment Model for the Jilin Momoge National Nature Reserve, China.

Wetlands as an important ecosystem type have been damaged in recent years and restoration of wetland ecosystem functions through ecological water replenishment is one of the important ways. The present study involved the construction of a novel ecological water replenishment model for Jilin Momoge National Nature Reserve (JMNNR) using the interval two-stage stochastic programming (ITSP) method. Breaking down traditional economic models that often sacrifice environmental benefits, the model aims to replenish the ecological water in JMNNR, allocate the ecological water resources scientifically, restore the wetland function of the reserve, improve the functional area of the reserve, enhance the net carbon sequestration capacity of the reserve, and complete the reconstruction of the ecosystem, while considering the ecological service value (ESV) of the reserve to achieve a joint increase in the ecological and economic benefits. The ITSP model constructed in the present study overcame the limitation that the original project recommendation was a single recommended value, and the results are presented in the form of intervals to improve flexibility in decision making to allow the individuals responsible for under-taking decisions to bring focused adjustments according to the actual decision-making conditions and increase the selectivity of the decision-making scheme. The present report discusses the construction of an ITSP model for the ecological water replenishment of JMNNR in an attempt to effectively improve both economic benefits and ecosystem restoration of the reserve, achieve the reconstruction of the JMNNR ecosystem, and provide a selective decision space for the key decision-makers to formulate and optimize the project operation and the management plan. The use of the ITSP model as a pre-procedural basis for the implementation of the project and the simulation of the effects of the implementation of the project can effectively avoid the decision limitations that exist when carrying out the project directly. The ITSP model constructed in this paper can also be used as a theoretical guide for water replenishment projects in different areas of the world, and the model parameters can be reasonably adjusted to achieve better results when used according to the actual local conditions.

How should water resources be allocated for shale gas development? An exploratory study in China

Water scarcity has emerged as one of the most important global challenges of the twenty-first century. With rising demand for energy, and water being a critical input in energy production, the availability of water resources has put energy sustainable production under growing strain. While unconventional natural gas (especially shale gas) is seen as an important bridge for promoting the transition of energy system from high to low carbon, water availability is a significant constraint on the development of energy resources owing to the massive quantity of water used by the hydraulic fracturing. Against this background, our study aims to optimize the allocation of regionally scarce water resources for fostering integrated economic, social, and environmental growth in shale gas development plays. In light of the uncertainty inherent in the water supply management system for shale gas development, this work employed the Interval Two-stage Stochastic Programming (ITSP) to establish an optimal allocation model for water resources between wells jointly dispatched by surface water, underground water and reused water. The model predicted water scarcity, optimal water allocation, and the total benefit of the shale gas development water supply system under various scenarios. Furthermore, when compared to the Two-stage Stochastic Programming (TSP) model results, it was found that the ITSP model's interval value may present decision makers with more ideas and options than the TSP model. In addition, since the ITSP model is oblivious to the system risk issue, it incorporated robust optimization into the original ITSP model to build the Interval Two-stage Robust Stochastic Programming (ITRSP) model. Our findings were expressed as intervals that more accurately represent the actual optimal allocation of water resources, which also provided a broader decision-making space for decision makers in managing shale gas development water supply management schemes.

An interval two-stage robust stochastic programming approach for steam power systems design and operation optimization under complex uncertainties

In this study, an interval two-stage robust stochastic programming approach is developed for the design and operation optimization of steam power systems under complex uncertainties by integrating interval-parameter programming and robust optimization into two-stage stochastic programming. The approach has the following advantages: (1) it extends the traditional two-stage stochastic programming method by enabling uncertainties presented as both probability distributions and discrete intervals to be effectively incorporated within the optimization framework, and could permit in-depth analyses of various policy scenarios when the promised policy targets are violated; (2) it could effectively reflect system risks generated by stochastic programming process, overcome the deficiency of uncontrollable risks in system and enhance the robustness of optimization, such that it is suitable for risk-aversion planners under high-variability conditions. One case of a refinery engineering project is provided for demonstrating the applicability and availability of the proposed approach. The numerical results provides ample decision-making space for decision makers to evaluate trade-offs between system economy and stability.

Simulation and optimization coupling model for soil salinization and waterlogging control in the Urad irrigation area, North China

How to rationally optimize the allocation of surface water and groundwater resources in saline-alkali areas is a difficult problem in current model optimization. Based on an interval two-stage stochastic programming (ITSP) method, this paper considers the system risk involved in saline-alkali land treatment, follows a robust optimization method, and constructs an interval two-stage data-driven subrobust optimization (ITDRO) model, which can optimize the distribution of groundwater and surface water for different crops and realize the combination of wells and canals through the joint dispatch of surface water and groundwater. This paper takes the Urad Irrigation Area as the research object, and the obtained results provide water distribution objectives under situations of multiple sources of water, multiple crops, and different robust coefficients. After the successful calibration and verification of the SaltMod model, the water distribution target is taken as the main input parameter and substituted into the simulation model based on the principle of water and salt balance. The output includes soil salinity, drainage salinity, groundwater salinity (GWS), groundwater table (GWT) depth, and drainage. The results show that the integrated ITDRO and SaltMod model can control the groundwater level below the critical depth under the premise of satisfying crop irrigation, reducing the groundwater level by approximately 0.75 m and the GWS in the irrigation area by approximately 0.68 g/L, which can provide a reference for the prevention and control of soil salinization and waterlogging. This approach is suitable for arid and semiarid regions that face similar problems.

Optimal Allocation of Water Resources and Eco-Compensation Mechanism Model Based on the Interval-Fuzzy Two-Stage Stochastic Programming Method for Tingjiang River.

In this work, based on the upper line of water resources utilization and the bottom line of water environmental quality of “Three Lines, Single Project”, a fuzzy optimization method was introduced into the Tingjiang River water resources optimal allocation and eco-compensation mechanism model, which is based on the interval two-stage (ITS) stochastic programming method. In addition, a Tingjiang River water resources allocation and eco-compensation mechanism model based on the interval fuzzy two-stage (IFTS) optimization method was also constructed. The objective functions of both models were to maximize the economic benefits of the Tingjiang River. The available water resources in the basin, the water environmental quality requirements, and regional development requirements were used as constraints, and under the five hydrological scenarios of extreme dryness, dryness, normal flow, abundance, and extreme abundance, the water resources allocation plan of various sectors (industry, municipal, agriculture, and ecology) in the Tingjiang River was optimized, and an eco-compensation mechanism was developed. In this work, the uncertainty of the maximum available water resources in each region and the whole basin was considered. If the maximum available water resources were too high, it would lead to a large waste of water resources, whereas if the maximum available water resources were too low, regional economic development would be limited. Therefore, the above two parameters were set as fuzzy parameters in the optimization model construction in this work. The simulation results from the IFTS model showed that the amount of water available in the river basin directly affects the water usage by various departments, thereby affecting the economic benefits of the river basin and the amount of eco-compensation paid by the downstream areas. The average economic benefit of the Tingjiang River after the optimization of the IFTS model simulation was [3868.51, 5748.99] × 108 CNY, which is an increase of [1.67%, 51.9%] compared to the economic benefit of the basin announced by the government in 2018. Compared to the ITS model, the economic benefit interval of the five hydrological scenarios of extreme dryness, dryness, normal flow, abundance, and extreme abundance was reduced by 28.54%, 44.9%, 31.49%, 40.37%, and 36.43%, respectively, which can improve the economic benefits of the basin and provide more accurate decision-making schemes. In addition, the IFTS simulation showed that the eco-compensation quota paid by downstream Guangdong Province to upstream Fujian Province is [28,116.4, 30,738.6] × 104 CNY, which is a reduction of [8461.404, 110,836] × 104 CNY compared to the 2018 compensation scheme of the government. Compared to the ITS model, the range of eco-compensation values was observed to increase by 9.94%, 54.81%, 15.85%, 50.31%, and 82.90%, respectively, under the five hydrological scenarios, which reduces the burden of ecological expenditure downstream and provides a broader decision-making space for decision-makers and thus enables improved decision-making efficiency. At the same time, after the optimization of the IFTS model, the additional water consumption of the second stage of the Tingjiang River during the extremely dry year decreased by 62.11% compared to the results of the ITS model. The additional water consumption of the industrial sector decreased by 68.39%, the municipal sector decreased by 59.27%, and in the first phase of water resources allocation for 14 districts and counties in the Tingjiang River, industrial and municipal sectors are the main two sectors. After introducing the fuzzy method into the IFTS model, the difference in the water consumption by these two sectors in the basin under different hydrological scenarios can be alleviated, and the waste of water resources caused by too low water allocation or excessive water allocation can be avoided. The national and local (the downstream region) eco-compensation quotas can be indirectly reduced, and the risk of water resources allocation and eco-compensation decision-making in the basin can be effectively reduced.

Water management for industrial development, energy conservation, and subjective attitudes: a comprehensive risk-oriented model to explore the tolerance of unbalanced allocation problem

Abstract 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.

Optimal allocation of agricultural water resources under the background of China's agricultural water price reform-a case study of Heilongjiang province

To improve the performance of agricultural water resources and food production against a background of China's agricultural water price reform, an interval two-stage stochastic programming model is established and applied to account for impacts of agricultural water price reform and a water-saving technology subsidy in Heilongjiang Province, China. A water price affordability constraint and a water-saving technology subsidy to support uptake of water-saving irrigation technology are both introduced. Results of model runs show that when the current agricultural water price is increased to reflect national water price reform without a technology subsidy, the total income of irrigation farming is reduced by 2%-8%, with potential negative impacts on food production. However when an irrigation water-saving technology subsidy is introduced to accompany the increased water price, farm income can be protected and overall food production can be maintained. The two part mechanism of increased water price and water-saving technology subsidy can be used to encourage farmer to reduce water application rates as well as reduce land in production of high-water-consuming crops. Such a two part program offers considerable hope for protecting unsustainable use of water in water scarce regions while protecting farm income and food security in the face of unknown future water supply fluctuations.

Optimization Model of the Ecological Water Replenishment Scheme for Boluo Lake National Nature Reserve Based on Interval Two-Stage Stochastic Programming

In the present paper, an optimization model of the ecological water replenishment quantity of Boluo Lake wetland was constructed for ecological water replenishment in the Boluo Lake National Nature Reserve based on the interval two-stage stochastic programming (ITSP) method, which scientifically allocates the ecological water resources and enhances the utilization of flood resources in order to meet the minimum ecological water replenishment quantity requirement to meet the local economic and social water demand, to restore the wetland function of the reserve, and to improve the ecological environment. In addition, it considers the ecological service value of the reserve in order to achieve a shared increase in the ecological and economic benefits. The optimization model of the ecological water replenishment of Boluo Lake wetland considered the minimum ecological water replenishment as the objective function, while the water diversion capacity, water supply capacity, water diversion sequence, functional area, and ecological service value of the Lake bubble were utilized as constraints in order to restore the ecosystem function of the Boluo Lake National Nature Reserve. The results from the model revealed that the amount of ecological water replenishment was significantly reduced after optimization simulation, with the maximum reduction range in the ecological water replenishment being −100.00% and −74.58%. In addition, the total amount of flood diversion was significantly increased, and the flood resources could be fully utilized. Moreover, the recovery effect on the lake and pond functional areas was significant and compared much better to that prior to the ecological water replenishment, which was up to 2300.00% and 1987.59%. The ecological service value also increased significantly, and the rate of this increase was as high as 23.90% and 21.58%. In the present study, an optimization model was constructed for the ecological water replenishment of the Boluo Lake wetland supplement project based on the interval two-stage stochastic programming method, which would achieve the entire scope of ecological and economic benefits of the ecological water replenishment project by realizing the ecological system reconstruction and providing a feasible and reliable plan to the decision-makers.

Economic and Flexible Design under Uncertainty for Steam Power Systems Based on Interval Two-Stage Stochastic Programming

Design and optimization of steam power systems (SPS) should not only optimize the economic target of the system but also ensure the safe and stable operation of the production process against compl...

Application of an Interval Two-Stage Robust (ITSR) Optimization Model for Optimization of Water Resource Distribution in the Yinma River Basin, Jilin Province, China

The present study is based on the application of an interval two-stage stochastic programming (ITSP) model in the Yinma River Basin. A robust method based on interval two-stage robust (ITSR) optimization is introduced to construct an optimization model of water resource distribution in order to solve the problems of water shortage in low-income and high-income areas caused by the unreasonable distribution of water resources. The model would help in reducing the system risk in the Yinma River Basin caused by an excessive pursuit of economic benefits. The model simulations show that the amount of water required for the water resource distribution is significantly reduced after balancing the risks and the water resource distribution of the water use departments is reduced by up to 20%. In addition, the situation of water scarcity of various water use departments shows a decreasing trend. There is no scarcity of water use in Panshi, Yongji, Shuangyang and Jiutai areas. The water shortage of water use departments in other areas is reduced by up to 97%. The allocation of reused water to ecological and environmental departments with higher water demand further solved the water shortage problem in low-income departments in the interval-two-stage planning model. In this study, after the introduction of the robust optimization method in the Yinma River Basin, the stability of the water resources distribution system is significantly improved. In addition, the risk of water use system in the interval-two-stage stochastic model can be avoided.

A New Interval Two-stage Stochastic Programming with CVaR for Water Resources Management

In area of water resources management, decision-makers usually need to make plans under various uncertainties in order to achieve the maximal total net benefits and prevent possible losses under risks arising from the indeterminacy. In this paper, we have incorporated the conditional value-at-risk, which has been widely used in portfolio selection problems for effective risk management, in the interval two-stage stochastic programming framework to perform trade-offs between economic objectives and associated risks. Moreover, based on the late progresses in Grey linear system, we have developed a new method to obtain a solution of the proposed model. In particular, this new approach can provide a number of decision alternatives under different coefficients, which help decision-makers make proper water supply plans according to their personal preferences. Finally, numerical experiments have been presented to demonstrate the validity and applicability of the proposed model for maintaining balance between profits and risks, as well as the efficiency of the new method for dealing with such model.

Planning electric power system under carbon-price mechanism considering multiple uncertainties – A case study of Tianjin

The carbon-price mechanism has been proved to be an effective measure for promoting energy revolution and mitigating climate change. It is of vital importance to develop optimal energy development strategy for electric power-dependent regions by considering the complex interaction among carbon price, carbon emission control, and carbon-responsibility transfer. In order to fill the research gap on the optimal choice of carbon-price mechanism at the urban level, this study is the first attempt to express uncertainties embodied in the carbon price mechanism as interval values, probability distribution and downside risks. The developed risk-aversion-based interval two-stage stochastic programming (RITSP) model is effective in analyzing the effect of internal and electric-transmission related carbon-tax on power system structure. It is discovered that carbon compensation policy for imported electricity is more suitable for Tianjin's power system development. Tianjin would primarily purchase electricity from Inner-Mongolia. With the increase of carbon emission tax, Tianjin would import increasing proportion of electricity from Gansu. Due to the limited endowment of renewable energy in Tianjin, the impact of carbon emission limitations on the renewable energy power generation structure of is trivial, and it has a greater impact on stimulating the development of CCS technology. What's more, Tianjin's future power system planning is more inclined to develop CCS rather than renewable energy.

A risk-based fuzzy boundary interval two-stage stochastic water resources management programming approach under uncertainty

Establishing an optimal water allocation scheme is a challenging yet crucial task for effective risk management of water resources. The dynamic and complex interaction among various risk-related components in a water resources management system cannot be easily modeled to characterize the system response under different risk control settings. In this study, a risk-based fuzzy boundary interval two-stage stochastic water resources management programming (RFITSWMP) model is developed for the optimization of water consumption. This model incorporates a series of risk control constraints, such as water availability, maximum allowable penalty, and allowable benefit violation constraints into a fuzzy boundary interval two-stage stochastic programming framework for water resources management. It can address the uncertainties presented as fuzzy boundary intervals and probability distributions. It can also tackle the recourse action to minimize penalties based on interactive influences of different risk control measures, further generating optimal water allocation alternatives and guiding water resources management. This developed model is applied to a case study of water consumption optimization in the middle reaches of the Heihe River Basin in China. Feasible water allocation schemes under given risk levels, as well as the associated economic benefit, actual benefit and penalty loss are generated. The results can help decision makers to gain an insight into the inherent conflicts and tradeoffs amid risk, benefit and water allocation. The performance of developed model is further demonstrated by comparing it with a fuzzy boundary interval two stage stochastic water resources management programming (FITSWMP) model. In addition, a multiple factorial analysis (MFA) approach is employed to analyze the impacts of interactive risk parameters on the optimal decisions. The result disclosed that (1) the higher individual risk-parameter levels correspond to higher water shortage, penalty loss and benefit value-at-risk but higher economic benefit. (2) The combination of risk parameters can achieve robust water allocation and economic benefit as the constraints concerned with risk parameters affect and limited by each other. (3) The condition that water violated probability (p) is 0.2, penalty violated risk level (β) is 1 and benefit violated risk level (γ) is 1 has the highest water allocation and biggest economic benefit.

A Stochastic Optimization Model for Carbon-Emission Reduction Investment and Sustainable Energy Planning under Cost-Risk Control

Restricted by conventional energy resources and environmental space, the sustainable development of urban power sector faces enormous challenges. Renewable energy generation and carbon capture and storage (CCS) are attractive technologies for reducing conventional energy resource consumption and improving CO2 emission mitigation. Considering the limitation of expensive investment cost on their wide application, a stochastic optimization model for the optimal design and operation strategy of regional electric power system is proposed to achieve conventional resource-consumption reduction and CO2 emission mitigation under cost-risk control. The hybrid method integrates interval two-stage stochastic programming with downside risk theory. It can not only effectively deal with the complex uncertainties expressed as discrete intervals and probability distribution, but also help decision-makers make cost-risk tradeoff under predetermined budget. The proposed model is applied in the electric power system planning of Zhejiang Province, an economically developed area with limited fossil energy resources. The influences of different resource and environmental policies on the investment portfolio and power system operation are analyzed and discussed under various scenarios. The results indicated that different policies would lead to different generation technology portfolios. The aggressive CO2 emission reduction policy could stimulate the development of CCS technology, and the electric power system would still heavily rely on coal resource, while the tough coal-consumption control policy could directly promote regional renewable energy development and electric power structure adjustment.

An improved intuitionistic fuzzy interval two-stage stochastic programming for resources planning management integrating recourse penalty from resources scarcity and surplus

Two-stage programming (TSP) is popular in resources planning management, especially for limited and precious resources. Remarkable study has been done to improve the model performance. However, one of the biggest obstacle is lack of objectivity when it comes to penalty quantification derived from recourse behavior. Besides, much attention has been paid in the resources deficiency penalty but little in resources residual, which may lead to wasting. In order to clarify the physical meaning of mathematical equation for recourse penalty from both resources scarcity and surplus, the production frontier was estimated and the technical efficiency and shadow prices of resources were introduced into TSP to characterize the resources deficiency and residual penalty, respectively. Then, an intuitionist fuzzy interval two-stage stochastic programming (IFITSP) was generated integrating the uncertainty of fuzzy membership and traditional TSP. An integrated solving approach was proposed coupling several previous uncertain programming methods and an improved robust interval TSP method. A case study was conducted in an arid area of northwest China to schedule agricultural cultivation scale based on limited water resources. The inefficiencies were [0.26, 0.49], [0.14, 0.37] and [0, 0.03] for GZ, LZ, and GT. The shadow prices of GZ, LZ, and GT in 2015 were 12.94, 2.61, 2.67 Yuan/m3 respectively, indicating the sever water crisis of GZ. The relatively unbiased and abundant decision could be generated by the developed IFITSP to help decision makers with various preferences make tradeoff between benefits and basic crop production requirement as well as balance resources deficiency and surplus. The results also show that the developed model could unveil the uncertainty influence of model inputs on decision strategies and trigger managers to deeply analyze subjective effect and associated risk. By comparison, the proposed methodology can not only clarify the physical meaning of penalty but deal with more complex uncertainty than previous methods. Therefore, the established model can provide reliable and scientific support for resources planning with recourse.

Industry-environment system management based on an uncertain Gaussian diffusion optimization model for coal-dependent cities in ecologically fragile areas

In this study, an industry-environment system management based on uncertain Gaussian diffusion optimization model (IEM-UGOM) was formulated to handle administrant issues of coal-dependent cities in ecologically fragile areas. The proposed model based on interval two-stage credibility-constrained full-infinite programming (ITFP) method and Gaussian diffusion model. The method was integrated by interval two-stage stochastic programming (ITSP), fuzzy credibility constrained programming (FCCP) and interval full-infinite programming (IFIP), which can tackle multiple uncertainties in terms of probability distribution, possibility distribution, crisp intervals and functional intervals. In addition, Gaussian diffusion model can be used to predict pollutant concentrations under different wind velocities. Then, IEM-UGOM was applied for the administration of industry-environment system (IES) in Yulin City, a typical ecologically vulnerable coal-dependent city in China, by considering 7 key industries, 3 pollutants, 5 periods, 7 credibility satisfaction levels and 4 wind velocity levels. Meanwhile, retreatment efficiency and transfer factors are considered as well. Results of system benefits, production reduction, pollutants excess emission amounts and penalties, pollutants retreatment amounts and costs under various credibility satisfaction levels and wind velocities are generated. Overall, IEM-UGOM is proved to be an efficient way on this study for reflecting the decision maker's attitude toward various adjustment scenarios of industrial production and environmental protection, and could help seek cost-effective management strategies under various credibility satisfaction levels and wind velocities.