Two-stage fuzzy-stochastic robust programming: a hybrid model for regional air quality management

In this study, a hybrid two-stage fuzzy-stochastic robust programming (TFSRP) model is developed and applied to the planning of an air-quality management system. As an extension of existing fuzzy-robust programming and two-stage stochastic programming methods, the TFSRP can explicitly address complexities and uncertainties of the study system without unrealistic simplifications. Uncertain parameters can be expressed as probability density and/or fuzzy membership functions, such that robustness of the optimization efforts can be enhanced. Moreover, economic penalties as corrective measures against any infeasibilities arising from the uncertainties are taken into account. This method can, thus, provide a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken. In its solution algorithm, the fuzzy decision space can be delimited through specification of the uncertainties using dimensional enlargement of the original fuzzy constraints. The developed model is applied to a case study of regional air quality management. The results indicate that reasonable solutions have been obtained. The solutions can be used for further generating pollution-mitigation alternatives with minimized system costs and for providing a more solid support for sound environmental decisions.     

81st APCA Annual Meeting & Exhibition

Abstract

This study introduces a two-stage interval-stochastic programming (TISP) model for the planning of solid-waste management systems under uncertainty. The model is derived by incorporating the concept of two-stage stochastic programming within an interval-parameter optimization framework. The approach has the advantage that policy determined by the authorities, and uncertain information expressed as intervals and probability distributions, can be effectively communicated into the optimization processes and resulting solutions. In the modeling formulation, penalties are imposed when policies expressed as allowable waste-loading levels are violated. In its solution algorithm, the TISP model is converted into two deterministic submodels, which correspond to the lower and upper bounds for the desired objective-function value. Interval solutions, which are stable in the given decision space with associated levels of system-failure risk, can then be obtained by solving the two submodels sequentially. Two special characteristics of the proposed approach make it unique compared with other optimization techniques that deal with uncertainties. First, the TISP model provides a linkage to prede?ned policies determined by authorities that have to be respected when a modeling effort is undertaken; second, it furnishes the reflection of uncertainties presented as both probabilities and intervals. The developed model is applied to a hypothetical case study of regional solid-waste management. The results indicate that reasonable solutions have been generated. They provide desired waste-flow patterns with minimized system costs and maximized system feasibility. The solutions present as stable interval solutions with different risk levels in violating the waste-loading criterion and can be used for generating decision alternatives.     

A two-stage interval-stochastic programming model for waste management under uncertainty

This study introduces a two-stage interval-stochastic programming (TISP) model for the planning of solid-waste management systems under uncertainty. The model is derived by incorporating the concept of two-stage stochastic programming within an interval-parameter optimization framework. The approach has the advantage that policy determined by the authorities, and uncertain information expressed as intervals and probability distributions, can be effectively communicated into the optimization processes and resulting solutions. In the modeling formulation, penalties are imposed when policies expressed as allowable waste-loading levels are violated. In its solution algorithm, the TISP model is converted into two deterministic submodels, which correspond to the lower and upper bounds for the desired objective-function value. Interval solutions, which are stable in the given decision space with associated levels of system-failure risk, can then be obtained by solving the two submodels sequentially. Two special characteristics of the proposed approach make it unique compared with other optimization techniques that deal with uncertainties. First, the TISP model provides a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken; second, it furnishes the reflection of uncertainties presented as both probabilities and intervals. The developed model is applied to a hypothetical case study of regional solid-waste management. The results indicate that reasonable solutions have been generated. They provide desired waste-flow patterns with minimized system costs and maximized system feasibility. The solutions present as stable interval solutions with different risk levels in violating the waste-loading criterion and can be used for generating decision alternatives.     

Minimax Regret Analysis for Municipal Solid Waste Management: An Interval-Stochastic Programming Approach

Abstract

In this study, an interval minimax regret programming (IMMRP) method is developed for the planning of municipal solid waste (MSW) management under uncertainty. It improves on the existing interval programming and minimax regret analysis methods by allowing uncertainties presented as both intervals and random variables to be effectively communicated into the optimization process. The IMMRP can account for economic consequences under all possible scenarios without any assumption on their probabilities. The developed method is applied to a case study of long-term MSW management planning under uncertainty. Multiple scenarios associated with different cost and risk levels are analyzed. Reasonable solutions are generated, demonstrating complex tradeoffs among system cost, regret level, and system-failure risk. The method can also facilitate examination of the difference between the cost incurred with identified strategy and the least cost under an ideal condition. The results can help determine desired plans and policies for waste management under a variety of uncertainties.     

A generalized fuzzy linear programming approach for environmental management problem under uncertainty

In this study, a generalized fuzzy linear programming (GFLP) method was developed to deal with uncertainties expressed as fuzzy sets that exist in the constraints and objective function. A stepwise interactive algorithm (SIA) was advanced to solve GFLP model and generate solutions expressed as fuzzy sets. To demonstrate its application, the developed GFLP method was applied to a regional sulfur dioxide (SO2) control planning model to identify effective SO2 mitigation polices with a minimized system performance cost under uncertainty. The results were obtained to represent the amount of SO2 allocated to different control measures from different sources. Compared with the conventional interval-parameter linear programming (ILP) approach, the solutions obtained through GFLP were expressed as fuzzy sets, which can provide intervals for the decision variables and objective function, as well as related possibilities. Therefore, the decision makers can make a tradeoff between model stability and the plausibility based on solutions obtained through GFLP and then identify desired policies for SO2-emission control under uncertainty.     

Minimax regret analysis for municipal solid waste management: an interval-stochastic programming approach

In this study, an interval minimax regret programming (IMMRP) method is developed for the planning of municipal solid waste (MSW) management under uncertainty. It improves on the existing interval programming and minimax regret analysis methods by allowing uncertainties presented as both intervals and random variables to be effectively communicated into the optimization process. The IMMRP can account for economic consequences under all possible scenarios without any assumption on their probabilities. The developed method is applied to a case study of long-term MSW management planning under uncertainty. Multiple scenarios associated with different cost and risk levels are analyzed. Reasonable solutions are generated, demonstrating complex tradeoffs among system cost, regret level, and system-failure risk. The method can also facilitate examination of the difference between the cost incurred with identified strategy and the least cost under an ideal condition. The results can help determine desired plans and policies for waste management under a variety of uncertainties.     

Greenhouse Gas Mitigation-Induced Rough-Interval Programming for Municipal Solid Waste Management

Abstract

A greenhouse gas (GHG) mitigation-induced rough-interval programming model is proposed in this study. Components of GHG emission and environmental pollution control are incorporated into the objective function and a series of relevant constraints. To explicitly examine more complexities existing in many parameters, rough intervals are also communicated into the modeling framework. The proposed model presents satisfactory capabilities in analyzing complicated interrelationships among municipal solid waste (MSW) management, climate-change impact, and environmental pollution control. It can also provide optimal allocation schemes and facilitate decision-makers regulating environmentally sustainable strategies. The developed model is then applied to a case study for demonstrating its applicability. Two representative scenarios (relatively representing two potential management policies that may be implemented in the future years) are considered. The results indicate that the developed model presents advantages in mitigating GHG emissions and the associated climate-change impact. The comparison between the GHG mitigation-induced model with and without rough-interval parameters is also investigated. Completely different solutions of the two models imply the significant impact of dual-uncertain information on the system, which can hardly be addressed through the existing optimization approaches.     

Modeling Municipal Solid Waste Management System under Uncertainty

Abstract

In this study, a dynamic inexact waste management (DIWM) model is developed for identifying optimal waste-flow-allocation and facility-capacity-expansion strategies under uncertainty and is based on an inexact scenario-based probabilistic programming (ISPP) approach. The DIWM model can handle uncertainties presented as interval values and probability distributions, and it can support assessing the risk of violating system constraints. Several violation levels for facility-capacity and waste-diversion constraints are examined. Solutions associated with different risks of constraint violation were generated. The modeling results are valuable for supporting the planning of the study city’s municipal solid waste (MSW) management practices, the long-term capacity expansion for waste management system, and the identification of desired policies regarding waste diversion. Sensitivity analyses are also undertaken to demonstrate that the violations of different constraints have varied effects on the planning of waste-flow allocation, facility expansion, and waste management cost.     

A fuzzy composting process model

Composting processes are normally complicated with a variety of uncertainties arising from incomplete or imprecise information obtained in real-world systems. Previously, there has been a lack of studies that focused on developing effective approaches to incorporate such uncertainties within composting process models. To fill this gap, a fuzzy composting process model (FCPM) for simulating composting process under uncertainty was developed. This model was mainly based on integration of a fractional fuzzy vertex method and a comprehensive composting model. Degrees of influence by projected uncertain factors were also examined. Two scenarios were investigated in applying the FCPM method. In the first scenario, model simulation under deterministic conditions was conducted. A pilot-scale experiment was provided for verifications. The result indicated that the proposed composting model could provide an excellent vehicle for demonstrating the complex interactions that occurred in the composting process. In the second scenario, application of the proposed FCPM was conducted under uncertainties. Six input parameters were considered to be of uncertain features that were reflected as fuzzy membership functions. The results indicated that the uncertainties projected in input parameters will result in significant derivations on system predictions; the proposed FCPM can generate satisfactory system outputs, with less computational efforts being required. Analyses on degree of influence of system inputs were also provided to describe the impacts of uncertainties on system responses. Thus, suitable measures can be adopted either to reduce system uncertainty by well-directed reduction of uncertainties of those high-influencing parameters or to reduce the computational requirement by neglecting those negligible factors.     

Identification of water quality management policy of watershed system with multiple uncertain interactions using a multi-level-factorial risk-inference-based possibilistic-probabilistic programming approach

In this study, a multi-level-factorial risk-inference-based possibilistic-probabilistic programming (MRPP) method is proposed for supporting water quality management under multiple uncertainties. The MRPP method can handle uncertainties expressed as fuzzy-random-boundary intervals, probability distributions, and interval numbers, and analyze the effects of uncertainties as well as their interactions on modeling outputs. It is applied to plan water quality management in the Xiangxihe watershed. Results reveal that a lower probability of satisfying the objective function (θ) as well as a higher probability of violating environmental constraints (q _i ) would correspond to a higher system benefit with an increased risk of violating system feasibility. Chemical plants are the major contributors to biological oxygen demand (BOD) and total phosphorus (TP) discharges; total nitrogen (TN) would be mainly discharged by crop farming. It is also discovered that optimistic decision makers should pay more attention to the interactions between chemical plant and water supply, while decision makers who possess a risk-averse attitude would focus on the interactive effect of q _i and benefit of water supply. The findings can help enhance the model’s applicability and identify a suitable water quality management policy for environmental sustainability according to the practical situations.

     

Fuzzy programming method for multi-objective optimal allocation of sediment resources and the cooperative bargaining: a case study in Weishan irrigation area,China

The optimal allocation of sediment resources needs to balance three objectives including ecological, economic, and social benefits so as to realize sustainable development of sediment resources. This study aims to apply fuzzy programming and bargaining approaches to solve the problem of optimal allocation of sediment resources. Firstly, Pareto-optimal solutions of multi-objective optimization were introduced, and the multi-objective optimal allocation model of sediment resources and fuzzy programming model was constructed. Then, from the perspective of multiplayer cooperation, the optimal allocation model of sediment resources was transformed into a game model by using Nash bargaining, and Nash bargaining solution was obtained as the optimal equilibrium strategy. Finally, the influence of different disagreement utility points and bargaining weights on the results was discussed, and the results of Nash bargaining and fuzzy programming methods were compared and analyzed. Results corroborate that Nash bargaining can achieve the cooperative optimization of multiple objectives with competitive relationship and obtain satisfactory scheme. Disagreement utility points and bargaining weights have a certain impact on the optimization results. The solution of fuzzy programming is close to that of Nash bargaining, which provides different ideas for multi-objective optimization problem.

     

Compromising economic cost and air pollutant emissions of municipal solid waste management strategies by fuzzy multiobjective optimization model

Municipal solid waste management (MSWM) is an important environmental challenge and subject in urban planning. A sustainable MSWM strategy should consider not only economic efficiency but also life-cycle assessment of environmental impact. This study employs the fuzzy multiobjective linear programming (FMOLP) technique to find the optimal compromise between economic optimization and pollutant emission reduction for the MSWM strategy. Taichung City in Taiwan is evaluated as a case study. The results indicate that the optimal compromise MSWM strategy can reduce significant amounts of pollutant emissions and still achieve positive net profits. Minimization of the sulfur oxide (SO_x) and nitrogen oxide (NO_x) emissions are the two major priorities in achieving this optimal compromise strategy when recyclables recovery rate is lower; however, minimization of the carbon monoxide (CO) and particulate matter (PM) emissions become priority factors when recovery rate is higher.

Implications: This paper applied the multiobjective optimization model to find the optimal compromise municipal solid waste management (MSWM) strategy, which minimizes both life-cycle operating cost and air pollutant emissions, and also to analyze the correlation between recyclables recovery rates and optimal compromise strategies. It is different from past studies, which only consider economic optimization or environmental impacts of the MSWM system. The result shows that optimal compromise MSWM strategy can achieve a net profit and reduce air pollution emission. In addition, scenario investigation of recyclables recovery rates indicates that resource recycling is beneficial for both economic optimization and air pollutant emission minimization.     

Planning of methane emission control from hoggery using an inexact two-stage optimization model

This study aims to develop an inexact two-stage optimization model to gather manure distributed over the southwest Taiwan and convert it into bioenergy. In the method, local optimization of each hauling zone is performed first using a gray mixed-integer programming model. Then, the hauling zones are prioritized by its performance on four gray scenarios. Although the biogas yield and the manure generation rate are ambiguous, one can easily evaluate his opportunity and risk by gray interval, which is a group of values within the lower and upper bounds. The analyses reveal that the biogas yield dominates the profit in this project, and it leads to the failure of the project when the biogas yield is below the level of 0.2 m³ kg^?1. With the goal of reducing 45% of methane emissions from pig farms, seven hauling zones are required to be developed. The farmers living in these zones from the project get carbon credits ranging from 478 to 3269 ton CO_2eq per year, and the investors own the carbon credits in the range of 3264–11820 ton CO_2eq per year. Through the carbon trading, both the investors and pig farmers are able to make profits by trading their carbon credits.

Implications:Biogas recovered from hoggery can be used as a bioenergy source and mitigate the atmospheric greenhouse effect and global warming. This research develops an inexact two-stage optimization model to evaluate the potential of gathering manure for biogas and converting it into bioenergy. The analyses reveal that the biogas yield dominates the profit in this project, and it leads to the failure of the project when the biogas yield is below the level of 0.2 m³ kg^?1. This study has provided a useful reference for the management of biogas production and carbon trading from hoggery for bioenergy.     

Evaluation of Solid Waste Management Strategies in the Taipei Metropolitan Area of Taiwan

Abstract

Chenfang Lin is with the Department of Soil and Environmental Science at National Chung Hsing University.Municipal solid waste (MSW) management is a major concern for highly urbanized societies. Among proposed MSW management systems, regionalization programs generally have received considerable attention. This study analyzes real-world operational data to assess different MSW management policies, especially regionalization strategies, and their impact on MSW management systems in the Taipei metropolitan area. Linear programming is also used to identify the minimum costs sustained by each policy. The linear programming results show that regionalization programs are more economical and also improve incinerator operation efficiency. Sensitivity analysis indicates that the minimum treatment requirement of incinerators is a very sensitive influence on the MSW flows distributed through the entire region. The MSW of several “sensitive” administrative districts will be allocated to different treatment facilities according to different management strategies. A list of preferential sequences of MSW treatment and disposal facilities can also be identified by the model presented in this study. The results of this study may provide a useful tool for aiding decision-making related to real-world MSW management problems.     

An integrated simulation and optimization approach for managing human health risks of atmospheric pollutants by coal-fired power plants

This research developed a simulation-aided nonlinear programming model (SNPM). This model incorporated the consideration of pollutant dispersion modeling, and the management of coal blending and the related human health risks within a general modeling framework. In SNPM, the simulation effort (i.e., California puff [CALPUFF]) was used to forecast the fate of air pollutants for quantifying the health risk under various conditions, while the optimization studies were to identify the optimal coal blending strategies from a number of alternatives. To solve the model, a surrogate-based indirect search approach was proposed, where the support vector regression (SVR) was used to create a set of easy-to-use and rapid-response surrogates for identifying the function relationships between coal-blending operating conditions and health risks. Through replacing the CALPUFF and the corresponding hazard quotient equation with the surrogates, the computation efficiency could be improved. The developed SNPM was applied to minimize the human health risk associated with air pollutants discharged from Gaojing and Shijingshan power plants in the west of Beijing. Solution results indicated that it could be used for reducing the health risk of the public in the vicinity of the two power plants, identifying desired coal blending strategies for decision makers, and considering a proper balance between coal purchase cost and human health risk.

Implications:A simulation-aided nonlinear programming model (SNPM) is developed. It integrates the advantages of CALPUFF and nonlinear programming model. To solve the model, a surrogate-based indirect search approach based on the combination of support vector regression and genetic algorithm is proposed. SNPM is applied to reduce the health risk caused by air pollutants discharged from Gaojing and Shijingshan power plants in the west of Beijing. Solution results indicate that it is useful for generating coal blending schemes, reducing the health risk of the public, reflecting the trade-off between coal purchase cost and health risk.     

Municipal solid waste management planning for Xiamen City,China: a stochastic fractional inventory-theory-based approach

In this study, a stochastic fractional inventory-theory-based waste management planning (SFIWP) model was developed and applied for supporting long-term planning of the municipal solid waste (MSW) management in Xiamen City, the special economic zone of Fujian Province, China. In the SFIWP model, the techniques of inventory model, stochastic linear fractional programming, and mixed-integer linear programming were integrated in a framework. Issues of waste inventory in MSW management system were solved, and the system efficiency was maximized through considering maximum net-diverted wastes under various constraint-violation risks. Decision alternatives for waste allocation and capacity expansion were also provided for MSW management planning in Xiamen. The obtained results showed that about 4.24 × 10⁶ t of waste would be diverted from landfills when p _i is 0.01, which accounted for 93% of waste in Xiamen City, and the waste diversion per unit of cost would be 26.327 × 10³ t per $10⁶. The capacities of MSW management facilities including incinerators, composting facility, and landfills would be expanded due to increasing waste generation rate.     

Adapting a geographical information system-based water resource management to the needs of the Romanian water authorities

Background, aim, and scope

The need for global and integrated approaches to water resources management, both from the quantitative and the qualitative point of view, has long been recognized. Water quality management is a major issue for sustainable development and a mandatory task with respect to the implementation of the European Water Framework Directive as well as the Swiss legislation. However, data modelling to develop relational databases and subsequent geographic information system (GIS)-based water management instruments are a rather recent and not that widespread trend. The publication of overall guidelines for data modelling along with the EU Water Framework Directive is an important milestone in this area. Improving overall water quality requires better and more easily accessible data, but also the possibility to link data to simulation models. Models are to be used to derive indicators that will in turn support decision-making processes. For this whole chain to become effective at a river basin scale, all its components have to become part of the current daily practice of the local water administration. Any system, tool, or instrument that is not designed to meet, first of all, the fundamental needs of its primary end-users has almost no chance to be successful in the longer term.

Materials and methods

Although based on a pre-existing water resources management system developed in Switzerland, the methodological approach applied to develop a GIS-based water quality management system adapted to the Romanian context followed a set of well-defined steps: the first and very important step is the assessment of needs (on the basis of a careful analysis of the various activities and missions of the water administration and other relevant stakeholders in water management related issues). On that basis, a conceptual data model (CDM) can be developed, to be later on turned into a physical database. Finally, the specifically requested additional functionalities (i.e. functionalities not provided by classical commercial GIS software), also identified during the assessment of needs, are developed. This methodology was applied, on an experimental basin, in the Ialomita River basin.

Results

The results obtained from this action-research project consist of a set of tangible elements, among which (1) a conceptual data model adapted to the Romanian specificities regarding water resources management (needs, data availability, etc.), (2) a related spatial relational database (objects and attributes in tables, links, etc.), that can be used to store the data collected, among others, by the water administration, and later on exploited with geographical information systems, (3) a toolbar (in the ESRI environment) offering the requested data processing and visualizing functionalities. Lessons learned from this whole process can be considered as additional, although less tangible, results.

Discussion

The applied methodology is fairly classical and did not come up with revolutionary results. Actually, the interesting aspects of this work are, on the one hand, and obviously, the fact that it produced tools matching the needs of the local (if not national) water administration (i.e. with a good chance of being effectively used in the day-to-day practice), and, on the other hand, the adaptations and adjustments that were needed both at the staff level and in technical terms.

Conclusions

This research showed that a GIS-based water management system needs to be backed by some basic data management tools that form the necessary support upon which a GIS can be deployed. The main lesson gained is that technology transfer has to pay much attention to the differences in existing situations and backgrounds in general, and therefore must be able to show much flexibility. The fact that the original objectives could be adapted to meet the real needs of the local end-users is considered as a major aspect in achieving a successful adaptation and development of water resources management tools. Time needed to setup things in real life was probably the most underestimated aspect in this technology transfer process.

Recommendations and perspectives

The whole material produced (conceptual data model, database and GIS tools) was disseminated among all river basin authorities in Romania on the behalf of the national water administration (ANAR). The fact that further developments, for example, to address water quantity issues more precisely, as envisaged by ANAR, can be seen as an indication that this project succeeded in providing an appropriate input to improve water quality in Romania on the long term.

     

Uncertainty Analysis of Ozone Formation and Response to Emission Controls Using Higher-Order Sensitivities

Abstract

Understanding ozone response to its precursor emissions is crucial for effective air quality management practices. This nonlinear response is usually simulated using chemical transport models, and the modeling results are affected by uncertainties in emissions inputs. In this study, a high ozone episode in the southeastern United States is simulated using the Community Multiscale Air Quality (CMAQ) model. Uncertainties in ozone formation and response to emissions controls due to uncertainties in emission rates are quantified using the Monte Carlo method. Instead of propagating emissions uncertainties through the original CMAQ, a reduced form of CMAQ is formulated using directly calculated first- and second-order sensitivities that capture the nonlinear ozone concentration-emission responses. This modification greatly reduces the associated computational cost. Quantified uncertainties in modeled ozone concentrations and responses to various emissions controls are much less than the uncertainties in emissions inputs. Average uncertainties in modeled ozone concentrations for the Atlanta area are less than 10% (as measured by the inferred coefficient of variance [ICOV]) even when emissions uncertainties are assumed to vary between a factor of 1.5 and 2. Uncertainties in the ozone responses generally decrease with increased emission controls. Average uncertainties (ICOV) in emission-normalized ozone responses range from 4 to 22%, with the smaller being associated with controlling of the relatively certain point nitrogen oxide (NO_x) emissions and the larger resulting from controlling of the less certain mobile NO_x emissions. These small uncertainties provide confidence in the model applications, such as in performance evaluation, attainment demonstration, and control strategy development.     

A robust simulation–optimization modeling system for effluent trading—a case study of nonpoint source pollution control

In this study, a robust simulation–optimization modeling system (RSOMS) is developed for supporting agricultural nonpoint source (NPS) effluent trading planning. The RSOMS can enhance effluent trading through incorporation of a distributed simulation model and an optimization model within its framework. The modeling system not only can handle uncertainties expressed as probability density functions and interval values but also deal with the variability of the second-stage costs that are above the expected level as well as capture the notion of risk under high-variability situations. A case study is conducted for mitigating agricultural NPS pollution with an effluent trading program in Xiangxi watershed. Compared with non-trading policy, trading scheme can successfully mitigate agricultural NPS pollution with an increased system benefit. Through trading scheme, [213.7, 288.8]?×?10³ kg of TN and [11.8, 30.2]?×?10³ kg of TP emissions from cropped area can be cut down during the planning horizon. The results can help identify desired effluent trading schemes for water quality management with the tradeoff between the system benefit and reliability being balanced and risk aversion being considered.     

An Optimal Model and Its Application for the Management of Municipal Solid Waste from Regional Small Cities in China

Abstract

Based on the basic characteristics of municipal solid waste (MSW) from regional small cities in China, some optimal management principles have been put forward: regional optimization, long-term optimization, and integrated treatment/disposal optimization. According to these principles, an optimal MSW management model for regional small cities is developed and provides a useful method to manage MSW from regional small cities. A case study application of the optimal model is described and shows that the optimal management scenarios in the controlling region can be gained, adequately validating and accounting for the advantages of the optimal model.