A two-stage inexact joint-probabilistic programming method for air quality management under uncertainty

A two-stage inexact joint-probabilistic programming (TIJP) method is developed for planning a regional air quality management system with multiple pollutants and multiple sources. The TIJP method incorporates the techniques of two-stage stochastic programming, joint-probabilistic constraint programming and interval mathematical programming, where uncertainties expressed as probability distributions and interval values can be addressed. Moreover, it can not only examine the risk of violating joint-probability constraints, but also account for economic penalties as corrective measures against any infeasibility. The developed TIJP method is applied to a case study of a regional air pollution control problem, where the air quality index (AQI) is introduced for evaluation of the integrated air quality management system associated with multiple pollutants. The joint-probability exists in the environmental constraints for AQI, such that individual probabilistic constraints for each pollutant can be efficiently incorporated within the TIJP model. The results indicate that useful solutions for air quality management practices have been generated; they can help decision makers to identify desired pollution abatement strategies with minimized system cost and maximized environmental efficiency.     

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk.     

Inexact multistage stochastic integer programming for water resources management under uncertainty

In this study, an inexact multistage stochastic integer programming (IMSIP) method is developed for water resources management under uncertainty. This method incorporates techniques of inexact optimization and multistage stochastic programming within an integer programming framework. It can deal with uncertainties expressed as both probabilities and discrete intervals, and reflect the dynamics in terms of decisions for water allocation through transactions at discrete points of a complete scenario set over a multistage context. Moreover, the IMSIP can facilitate analyses of the multiple policy scenarios that are associated with economic penalties when the promised targets are violated as well as the economies-of-scale in the costs for surplus water diversion. A case study is provided for demonstrating the applicability of the developed methodology. The results indicate that reasonable solutions have been generated for both binary and continuous variables. For all scenarios under consideration, corrective actions can be undertaken dynamically under various pre-regulated policies and can thus help minimize the penalties and costs. The IMSIP can help water resources managers to identify desired system designs against water shortage and for flood control with maximized economic benefit and minimized system-failure risk.     

Waste management with recourse: An inexact dynamic programming model containing fuzzy boundary intervals in objectives and constraints

The existing inexact optimization methods based on interval-parameter linear programming can hardly address problems where coefficients in objective functions are subject to dual uncertainties. In this study, a superiority–inferiority-based inexact fuzzy two-stage mixed-integer linear programming (SI-IFTMILP) model was developed for supporting municipal solid waste management under uncertainty. The developed SI-IFTMILP approach is capable of tackling dual uncertainties presented as fuzzy boundary intervals (FuBIs) in not only constraints, but also objective functions. Uncertainties expressed as a combination of intervals and random variables could also be explicitly reflected. An algorithm with high computational efficiency was provided to solve SI-IFTMILP. SI-IFTMILP was then applied to a long-term waste management case to demonstrate its applicability. Useful interval solutions were obtained. SI-IFTMILP could help generate dynamic facility-expansion and waste-allocation plans, as well as provide corrective actions when anticipated waste management plans are violated. It could also greatly reduce system-violation risk and enhance system robustness through examining two sets of penalties resulting from variations in fuzziness and randomness. Moreover, four possible alternative models were formulated to solve the same problem; solutions from them were then compared with those from SI-IFTMILP. The results indicate that SI-IFTMILP could provide more reliable solutions than the alternatives.     

A stochastic fuzzy chance-constrained programming model for energy–environment system planning and management in the City of Beijing

A stochastic and fuzzy chance-constrained programming (SFCCP) model was developed in this study for supporting energy–environment management in the city of Beijing, China. SFCCP was capable of tackling the variables in constraints as fuzzy random variables, which were integration of randomness and vagueness. SFCCP was applied to an energy–environment management system in the city of Beijing. The study results indicated that SFCCP was useful in helping decision makers gain in-depth insights into proposed management system and establish environment-friendly energy allocation alternatives. The application of SFCCP is expected to provide a good demonstration to energy–environment management problems under complex uncertainties.     

Violation analysis for solid waste management systems: an interval fuzzy programming approach

This paper introduces a violation analysis approach for the planning of regional solid waste management systems under uncertainty, based on an interval-parameter fuzzy integer programming (IPFIP) model. In this approach, several given levels of tolerable violation for system constraints are permitted. This is realized through a relaxation of the critical constraints using violation variables, such that the model's decision space can be expanded. Thus, solutions from the violation analysis will not necessarily satisfy all of the model's original constraints. Application of the developed methodology to the planning of a waste management system indicates that reasonable solutions can be generated through this approach. Considerable information regarding decisions of facility expansion and waste flow allocation within the waste management system were generated. The modeling results help to generate a number of decision alternatives under various system conditions, allowing for more in-depth analyses of tradeoffs between environmental and economic objectives as well as those between system optimality and reliability.     

An inexact dynamic optimization model for municipal solid waste management in association with greenhouse gas emission control

Municipal solid waste (MSW) should be properly disposed in order to help protect environmental quality and human health, as well as to preserve natural resources. During MSW disposal processes, a large amount of greenhouse gas (GHG) is emitted, leading to a significant impact on climate change. In this study, an inexact dynamic optimization model (IDOM) is developed for MSW-management systems under uncertainty. It grounds upon conventional mixed-integer linear programming (MILP) approaches, and integrates GHG components into the modeling framework. Compared with the existing models, IDOM can not only deal with the complex tradeoff between system cost minimization and GHG-emission mitigation, but also provide optimal allocation strategies under various emission-control standards. A case study is then provided for demonstrating applicability of the developed model. The results indicate that desired waste-flow patterns with a minimized system cost and GHG-emission amount can be obtained. Of more importance, the IDOM solution is associated with over 5.5 million tonnes of TEC reduction, which is of significant economic implication for real implementations. Therefore, the proposed model could be regarded as a useful tool for realizing comprehensive MSW management with regard to mitigating climate-change impacts.     

A dual-interval fixed-mix stochastic programming method for water resources management under uncertainty

In this study, a dual-interval fixed-mix stochastic programming (DFSP) method is developed for planning water resources management systems under uncertainty. DFSP incorporates interval-parameter programming (IPP) and fuzzy vertex analysis (FVA) within a fixed-mix stochastic programming (FSP) framework to address uncertain parameters described as probability distributions and dual intervals. It can also be used for analyzing various policy scenarios that are associated with different levels of economic consequences since penalties are exercised with recourse actions against any infeasibility. A real case for water resources management planning of Zhangweinan River Basin in China is then conducted for demonstrating the applicability of the developed DFSP method. Solutions in association with α-cut levels are generated by solving a set of deterministic submodels, which are useful for generating a range of decision alternatives under compound uncertainties. The results can help to identify desired water-allocation schemes for local sustainable development that the prerequisite water demand can be guaranteed when the available water resource is scarce.     

IFRP: a hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty

In this study, an interval-parameter fuzzy-robust programming (IFRP) model is developed and applied to the planning of solid waste management systems under uncertainty. As an extension of the existing fuzzy-robust programming and interval-parameter linear programming methods, the IFRP can explicitly address system uncertainties with complex presentations. Parameters in the IFRP model can be represented as interval numbers and/or fuzzy membership functions, such that the uncertainties can be directly communicated into the optimization process and resulting solution. Furthermore, highly uncertain information for the lower and upper bounds of interval parameters that exist due to the complexity of the real world can be effectively handled through introducing the concept of fuzzy boundary interval. Consequently, robustness of the optimization process and solution can be enhanced. Results of the case study indicate that useful solutions for planning municipal solid waste management practices can be generated. They reflect a compromise between optimality and stability of the study system. Willingness to pay higher costs will guarantee the system stability; however, a desire to reduce the costs will run the risk of potential instability of the system. The results also suggest that the proposed hybrid methodology is applicable to practical problems that are associated with highly complex and uncertain information.     

Risk explicit interval linear programming model for long-term planning of vehicle recycling in the EU legislative context under uncertainty

With the number of vehicles expected to increase to 1.85 billion by 2030 and the scrap generated from end-of-life vehicles (ELVs) expected to be 3.71 billion tonnes, there is a strong motivation to properly process the flow of these materials. The EU Directive on end-of-life vehicles (EU ELV Directive) aims to increase recovery and recycling rates of ELVs in order to reduce waste and improve environmental performances. Long-term optimization planning of vehicle recycling is increasingly important. However, there is a lack of research of uncertainties in the vehicle recycling system, none of the previous studies analyzed the linkage and trade-offs between decision risk and system performances, and no previous research was reported on interval-based programming for vehicle recycling planning problem. In order to meet the imposed eco-efficiency quotas, maximize system profit and minimize decision risk, and at the same time fill the identified research gaps, a risk explicit interval linear programming model for optimal long-term planning in the EU vehicle recycling factories was developed. It can create optimal plans for procuring vehicle hulks, sorting of generated material fractions, allocation of sorted waste flows and allocation of sorted metals for desired value of the system aspiration level. A numerical study demonstrated the potentials and applicability of the proposed model. Vehicle recycling factories aim at reaching the highest possible level of quantity and quality of sorted metal flows. The future eco-efficiency quotas will not endanger their business. The success of the final phase of implementation of the EU ELV Directive is not jeopardized, because even the future eco-efficiency quotas were reached in all created test problems. Quantity of land-filled wastes will be radically reduced after January 1, 2015. The model results and trade-offs would be valuable for supporting the EU vehicle recycling factories in creating optimal long-term production strategies and reducing the risk for uncertain situations.     

A multi-objective location-allocation optimization for sustainable management of municipal solid waste

The location problem of treatment and service facilities in municipal solid waste (MSW) management system is of significant importance due to the socioeconomic and environmental concerns. The consideration of waste treatment costs, environmental impact, greenhouse gas (GHG) emissions, social fairness as well as other relevant aspects should be simultaneously taken into account when a MSW management system is planned. Development of sophisticated decision support tools for planning MSW management system in an economic-efficient and environmental friendly manner is therefore important. In this paper, a general multi-objective location-allocation model for optimally managing the interactions among those conflicting factors in MSW management system is proposed. The model is comprised of a three-stage conceptual framework and a mixed integer mathematical programming. The inclusion of environmental impact and GHG emission objectives push the output of the model tightening toward more environmentally friendly and sustainable solutions in MSW management. The application of this model is demonstrated through an illustrative example, and the computational efficiency of the programming is also tested through a set of incremental parameters. Latter in this paper, a comparison with previous case studies of MSW system design is presented in order to show the applicability and adaptability of the generic model in practical decision-making process, and the perspectives of future study are also discussed.     

Land Resources Allocation Strategies in an Urban Area Involving Uncertainty: A Case Study of Suzhou,in the Yangtze River Delta of China

A large number of mathematical models have been developed to support land resource allocation decisions and land management needs; however, few of them can address various uncertainties that exist in relation to many factors presented in such decisions (e.g., land resource availabilities, land demands, land-use patterns, and social demands, as well as ecological requirements). In this study, a multi-objective interval-stochastic land resource allocation model (MOISLAM) was developed for tackling uncertainty that presents as discrete intervals and/or probability distributions. The developed model improves upon the existing multi-objective programming and inexact optimization approaches. The MOISLAM not only considers economic factors, but also involves food security and eco-environmental constraints; it can, therefore, effectively reflect various interrelations among different aspects in a land resource management system. Moreover, the model can also help examine the reliability of satisfying (or the risk of violating) system constraints under uncertainty. In this study, the MOISLAM was applied to a real case of long-term urban land resource allocation planning in Suzhou, in the Yangtze River Delta of China. Interval solutions associated with different risk levels of constraint violation were obtained. The results are considered useful for generating a range of decision alternatives under various system conditions, and thus helping decision makers to identify a desirable land resource allocation strategy under uncertainty.     

A hybrid inexact optimization approach for solid waste management in the city of Foshan,China

An interval-parameter two-stage chance-constraint mixed integer linear programming (ITCMILP) model is provided for supporting long-term planning of solid waste management in the City of Foshan, China. The ITCMILP is formulated by integrating interval-parameter, two-stage, mixed integer, and chance-constraint programming methods into a general framework, and can thus deal with multiple uncertainties associated with model parameters, constraints and objectives. Three scenarios are examined, covering combinations of various system conditions and waste management policies. Scenario 1 is designed for comparison purposes. Scenarios 2 and 3 correspond to situations when the existing landfill's life is to be extended. The results demonstrate that the centralized composting and incinerating facilities are desired for treating the organic waste flows. The tradeoff among system cost, violation risk, and the related policy implications are also analyzed. The results obtained could help decision makers gain in-depth insights into the impact of uncertainties on long-term solid waste management in the City of Foshan.     

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max–min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga–Bhadra river system in India.     

An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina

In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probability density functions but also discrete intervals can be reflected. The model can help tackle the dynamic, interactive and uncertain characteristics of the solid waste management system in the City, and can address issues concerning plans for cost-effective waste diversion and landfill prolongation. Three scenarios are considered based on different waste management policies. The results indicate that reasonable solutions have been generated. They are valuable for supporting the adjustment or justification of the existing waste flow allocation patterns, the long-term capacity planning of the City's waste management system, and the formulation of local policies and regulations regarding waste generation and management.     

An Interval-Parameter Waste-Load-Allocation Model for River Water Quality Management Under Uncertainty

A simulation-based interval quadratic waste load allocation (IQWLA) model was developed for supporting river water quality management. A multi-segment simulation model was developed to generate water-quality transformation matrices and vectors under steady-state river flow conditions. The established matrices and vectors were then used to establish the water-quality constraints that were included in a water quality management model. Uncertainties associated with water quality parameters, cost functions, and environmental guidelines were described as intervals. The cost functions of wastewater treatment units were expressed in quadratic forms. A water-quality planning problem in the Changsha section of Xiangjiang River in China was used as a study case to demonstrate applicability of the proposed method. The study results demonstrated that IQWLA model could effectively communicate the interval-format uncertainties into optimization process, and generate inexact solutions that contain a spectrum of potential wastewater treatment options. Decision alternatives can be generated by adjusting different combinations of the decision variables within their solution intervals. The results are valuable for supporting local decision makers in generating cost-effective water quality management strategies.     

Interactive two-stage stochastic fuzzy programming for water resources management

In this study, an interactive two-stage stochastic fuzzy programming (ITSFP) approach has been developed through incorporating an interactive fuzzy resolution (IFR) method within an inexact two-stage stochastic programming (ITSP) framework. ITSFP can not only tackle dual uncertainties presented as fuzzy boundary intervals that exist in the objective function and the left- and right-hand sides of constraints, but also permit in-depth analyses of various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. A management problem in terms of water resources allocation has been studied to illustrate applicability of the proposed approach. The results indicate that a set of solutions under different feasibility degrees has been generated for planning the water resources allocation. They can help the decision makers (DMs) to conduct in-depth analyses of tradeoffs between economic efficiency and constraint-violation risk, as well as enable them to identify, in an interactive way, a desired compromise between satisfaction degree of the goal and feasibility of the constraints (i.e., risk of constraint violation).     

Optimizing the treatment and disposal of municipal solid wastes using mathematical programming—A case study in a Greek region

Goal of the work is to present a simplified methodology to optimize an integrated solid waste management system. The methodology performs two optimizations, namely: (i) minimization of the total cost of the MSW system and (ii) minimization of the equivalent carbon dioxide emissions (CO_2e) generated by the whole system. The methodology is modeled via non-linear mathematical equations, uses 32 decision variables and does not require complex LCA databases. The proposed model optimally allocates eight MSW components (paper, cardboard, plastics, metals, glass, food wastes, yard wastes and other wastes) to four MSW management technologies (incineration, composting, anaerobic digestion, and landfilling) after source separation of recyclables has taken place. The Region of East-Macedonia and Thrace in Greece was selected as a case study. Results showed that there is a trade off between cost and CO_2e emissions. Incineration and composting were favored as the principal treatment technologies, while landfilling was always the least desirable management technology under both objective functions. The recycling participation rate significantly affected all optimum scenarios.     

Techno-economic analysis and environmental impact assessment of energy recovery from Municipal Solid Waste (MSW) in Brazil

Due to the lack of appropriate policies in the last decades, 60% of Brazilian cities still dump their waste in non-regulated landfills (the remaining ones dump their trash in regulated landfills), which represent a serious environmental and social problem. The key objective of this study is to compare, from a techno-economic and environmental point of view, different alternatives to the energy recovery from the Municipal Solid Waste (MSW) generated in Brazilian cities. The environmental analysis was carried out using current data collected in Betim, a 450,000 inhabitants city that currently produces 200 tonnes of MSW/day. Four scenarios were designed, whose environmental behaviour were studied applying the Life Cycle Assessment (LCA) methodology, in accordance with the ISO 14040 and ISO 14044 standards. The results show the landfill systems as the worst waste management option and that a significant environmental savings is achieved when a wasted energy recovery is done. The best option, which presented the best performance based on considered indicators, is the direct combustion of waste as fuel for electricity generation. The study also includes a techno-economical evaluation of the options, using a developed computer simulation tool. The economic indicators of an MSW energy recovery project were calculated. The selected methodology allows to calculate the energy content of the MSW and the CH₄ generated by the landfill, the costs and incomes associated with the energy recovery, the sales of electricity and carbon credits from the Clean Development Mechanism (CDM). The studies were based on urban centres of 100,000, 500,000 and 1,000,000 inhabitants, using the MSW characteristics of the metropolitan region of Belo Horizonte. Two alternatives to recovering waste energy were analyzed: a landfill that used landfill biogas to generate electricity through generator modules and a Waste-to-Energy (WtE) facility also with electricity generation. The results show that power generation projects using landfill biogas in Brazil strongly depend on the existence of a market for emissions reduction credits. The WtE plant projects, due to its high installation, Operation and Maintenance (O&M) costs, are highly dependent on MSW treatment fees. And they still rely on an increase of three times the city taxes to become attractive.     

A two-stage support-vector-regression optimization model for municipal solid waste management - a case study of Beijing, China

In this study, a two-stage support-vector-regression optimization model (TSOM) is developed for the planning of municipal solid waste (MSW) management in the urban districts of Beijing, China. It represents a new effort to enhance the analysis accuracy in optimizing the MSW management system through coupling the support-vector-regression (SVR) model with an interval-parameter mixed integer linear programming (IMILP). The developed TSOM can not only predict the city's future waste generation amount, but also reflect dynamic, interactive, and uncertain characteristics of the MSW management system. Four kernel functions such as linear kernel, polynomial kernel, radial basis function, and multi-layer perception kernel are chosen based on three quantitative simulation performance criteria [i.e. prediction accuracy (PA), fitting accuracy (FA) and over all accuracy (OA)]. The SVR with polynomial kernel has accurate prediction performance for MSW generation rate, with all of the three quantitative simulation performance criteria being over 96%. Two cases are considered based on different waste management policies. The results are valuable for supporting the adjustment of the existing waste-allocation patterns to raise the city's waste diversion rate, as well as the capacity planning of waste management system to satisfy the city's increasing waste treatment/disposal demands.