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.     

Two-Stage Fuzzy-Stochastic Robust Programming: A Hybrid Model for Regional Air Quality Management

Abstract

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.     

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.     

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

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.     

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.     

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.     

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.     

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.

     

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.     

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.     

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.

     

Air Quality Modeling and Decisions for Ozone Reduction Strategies

Abstract

Despite the widespread application of photochemical air quality models (AQMs) in U.S. state implementation planning (SIP) for attainment of the ambient ozone standard, documentation for the reliability of projections has remained highly subjective. An “idealized” evaluation framework is proposed that provides a means for assessing reliability. Applied to 18 cases of regulatory modeling in the early 1990s in North America, a comparative review of these applications is reported. The intercomparisons suggest that more than two thirds of these AQM applications suffered from having inadequate air quality and meteorological databases. Emissions representations often were unreliable; uncertainties were too high. More than two thirds of the performance evaluation efforts were judged to be substandard compared with idealized goals. Meteorological conditions chosen according regulatory guidelines were limited to one or two cases and tended to be similar, thus limiting the extent to which public policy makers could be confident that the emission controls adopted would yield attainment for a broad range of adverse atmospheric conditions. More than half of the studies reviewed did not give sufficient attention to addressing the potential for compensating errors. Corroborative analyses were conducted in only one of the 18 studies reviewed. Insufficient attention was given to the estimation of model and/or input database errors, uncertainties, or variability in all of the cases examined. However, recent SIP and policy‐related regional modeling provides evidence of substantial improvements in the underlying science and available modeling systems used for regulatory decision making. Nevertheless, the availability of suitable databases to support increasingly sophisticated modeling continues to be a concern for many locations. Thus, AQM results may still be subject to significant uncertainties. The evaluative process used here provides a framework for modelers and public policy makers to assess the adequacy of contemporary and future modeling work.     

Modeling Pareto efficient PM10 control policies in Northern Italy to reduce health effects

High PM10 concentrations can cause human health problems, both related to short-term and long-term exposure to particles. In this work the impact of efficient PM10 control problems in Northern Italy is assessed by means of a two-stage methodology. In the first stage a multi-objective optimization approach is applied. The multi-objective problem defines two control objectives (the emission reduction costs and the air quality index) to be minimized varying the decision variables (precursor emission reductions). The solution of the multi-objective problem is the Pareto efficient PM10 control policies. In the second stage, the ExternE methodology is applied to estimate health impacts and external costs for the efficient emission reduction scenarios computed in the first stage. The methodology has been applied over Lombardia region, one of the most polluted areas in Europe.     

Air quality modeling and decisions for ozone reduction strategies

Despite the widespread application of photochemical air quality models (AQMs) in U.S. state implementation planning (SIP) for attainment of the ambient ozone standard, documentation for the reliability of projections has remained highly subjective. An "idealized" evaluation framework is proposed that provides a means for assessing reliability. Applied to 18 cases of regulatory modeling in the early 1990s in North America, a comparative review of these applications is reported. The intercomparisons suggest that more than two thirds of these AQM applications suffered from having inadequate air quality and meteorological databases. Emissions representations often were unreliable; uncertainties were too high. More than two thirds of the performance evaluation efforts were judged to be substandard compared with idealized goals. Meteorological conditions chosen according regulatory guidelines were limited to one or two cases and tended to be similar, thus limiting the extent to which public policy makers could be confident that the emission controls adopted would yield attainment for a broad range of adverse atmospheric conditions. More than half of the studies reviewed did not give sufficient attention to addressing the potential for compensating errors. Corroborative analyses were conducted in only one of the 18 studies reviewed. Insufficient attention was given to the estimation of model and/or input database errors, uncertainties, or variability in all of the cases examined. However, recent SIP and policy-related regional modeling provides evidence of substantial improvements in the underlying science and available modeling systems used for regulatory decision making. Nevertheless, the availability of suitable databases to support increasingly sophisticated modeling continues to be a concern for many locations. Thus, AQM results may still be subject to significant uncertainties. The evaluative process used here provides a framework for modelers and public policy makers to assess the adequacy of contemporary and future modeling work.     

Managing soil remediation problems

Soil remediation has only a short history but the problem addressed is a significant one. Cost estimates for the clean-up of contaminated sites in the European Union and the United States are in the order of magnitude of 1,400 billion ECU. Such an enormous operation deserves the best management it can get. Reliable cost estimations per contaminated site are an important prerequisite. This paper addresses the problems related to site-wise estimations. When solving soil remediation problems, we have to deal with a large number of scientific disciplines. Too often solutions are presented from the viewpoint of only one discipline. In order to benefit from the combined disciplinary knowledge and experience, we think that it is necessary to describe the interrelations between these disciplines. This can be realized by developing an adequate model of the desired process which enables to consider and evaluate the essential factors as interdependent components of the total system. The resulting model provides a binding paradigm to the contributing disciplines which will result in improved efficiency and effectivity of the decision and the cost estimation process. In the near future, we will release the “Biosparging and Bioventing Expert Support System”, an expert support system for problem owners, consultants and authorities dealing with the design and operation of a biosparging and/or a bioventing system.     

Multi-stage optimal design for groundwater remediation: A hybrid bi-level programming approach

This paper presents the development of a hybrid bi-level programming approach for supporting multi-stage groundwater remediation design. To investigate remediation performances, a subsurface model was employed to simulate contaminant transport. A mixed-integer nonlinear optimization model was formulated in order to evaluate different remediation strategies. Multivariate relationships based on a filtered stepwise clustering analysis were developed to facilitate the incorporation of a simulation model within a nonlinear optimization framework. By using the developed statistical relationships, predictions needed for calculating the objective function value can be quickly obtained during the search process. The main advantage of the developed approach is that the remediation strategy can be adjusted from stage to stage, which makes the optimization more realistic. The proposed approach was examined through its application to a real-world aquifer remediation case in western Canada. The optimization results based on this application can help the decision makers to comprehensively evaluate remediation performance.     

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.     

A multiobjective optimization model and an orthogonal design–based hybrid heuristic algorithm for regional urban mining management problems

In this paper, a multiobjective mixed-integer piecewise nonlinear programming model (MOMIPNLP) is built to formulate the management problem of urban mining system, where the decision variables are associated with buy-back pricing, choices of sites, transportation planning, and adjustment of production capacity. Different from the existing approaches, the social negative effect, generated from structural optimization of the recycling system, is minimized in our model, as well as the total recycling profit and utility from environmental improvement are jointly maximized. For solving the problem, the MOMIPNLP model is first transformed into an ordinary mixed-integer nonlinear programming model by variable substitution such that the piecewise feature of the model is removed. Then, based on technique of orthogonal design, a hybrid heuristic algorithm is developed to find an approximate Pareto-optimal solution, where genetic algorithm is used to optimize the structure of search neighborhood, and both local branching algorithm and relaxation-induced neighborhood search algorithm are employed to cut the searching branches and reduce the number of variables in each branch. Numerical experiments indicate that this algorithm spends less CPU (central processing unit) time in solving large-scale regional urban mining management problems, especially in comparison with the similar ones available in literature. By case study and sensitivity analysis, a number of practical managerial implications are revealed from the model.

Implications: Since the metal stocks in society are reliable overground mineral sources, urban mining has been paid great attention as emerging strategic resources in an era of resource shortage. By mathematical modeling and development of efficient algorithms, this paper provides decision makers with useful suggestions on the optimal design of recycling system in urban mining. For example, this paper can answer how to encourage enterprises to join the recycling activities by government’s support and subsidies, whether the existing recycling system can meet the developmental requirements or not, and what is a reasonable adjustment of production capacity.     

At the Crossroads

ABSTRACT

Modeling transit bus emissions and fuel economy requires a large amount of experimental data over wide ranges of operational conditions. Chassis dynamometer tests are typically performed using representative driving cycles defined based on vehicle instantaneous speed as sequences of “microtrips”, which are intervals between consecutive vehicle stops. Overall significant parameters of the driving cycle, such as average speed, stops per mile, kinetic intensity, and others, are used as independent variables in the modeling process. Performing tests at all the necessary combinations of parameters is expensive and time consuming. In this paper, a methodology is proposed for building driving cycles at prescribed independent variable values using experimental data through the concatenation of “microtrips” isolated from a limited number of standard chassis dynamometer test cycles. The selection of the adequate “microtrips” is achieved through a customized evolutionary algorithm. The genetic representation uses microtrip definitions as genes. Specific mutation, crossover, and karyotype alteration operators have been defined. The Roulette-Wheel selection technique with elitist strategy drives the optimization process, which consists of minimizing the errors to desired overall cycle parameters. This utility is part of the Integrated Bus Information System developed at West Virginia University.

IMPLICATIONS It is expected that the paper will provide a useful tool for modeling and analysis of vehicle fuel economy and emissions and for the design, optimization, and analysis of driving cycles for testing and vehicle fleet management.