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 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.     

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.     

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.     

An inexact reverse logistics model for municipal solid waste management systems

This paper proposed an inexact reverse logistics model for municipal solid waste management systems (IRWM). Waste managers, suppliers, industries and distributors were involved in strategic planning and operational execution through reverse logistics management. All the parameters were assumed to be intervals to quantify the uncertainties in the optimization process and solutions in IRWM. To solve this model, a piecewise interval programming was developed to deal with Min-Min functions in both objectives and constraints. The application of the model was illustrated through a classical municipal solid waste management case. With different cost parameters for landfill and the WTE, two scenarios were analyzed. The IRWM could reflect the dynamic and uncertain characteristics of MSW management systems, and could facilitate the generation of desired management plans. The model could be further advanced through incorporating methods of stochastic or fuzzy parameters into its framework. Design of multi-waste, multi-echelon, multi-uncertainty reverse logistics model for waste management network would also be preferred.     

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.     

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.     

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.     

Optimal Land Use Management for Soil Erosion Control by Using an Interval-Parameter Fuzzy Two-Stage Stochastic Programming Approach

Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China’s Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 10⁹ $ was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.     

An interval-based regret-analysis method for identifying long-term municipal solid waste management policy under uncertainty

In this study, an interval-based regret-analysis (IBRA) model is developed for supporting long-term planning of municipal solid waste (MSW) management activities in the City of Changchun, the capital of Jilin Province, China. The developed IBRA model incorporates approaches of interval–parameter programming (IPP) and minimax–regret (MMR) analysis within an integer programming framework, such that uncertainties expressed as both interval values and random variables can be reflected. The IBRA can account for economic consequences under all possible scenarios associated with different system costs and risk levels without making assumptions on probabilistic distributions for random variables. A regret matrix with interval elements is generated based on a matrix of interval system costs, such that desired decision alternatives can be identified according to the interval minimax regret (IMMR) criterion. The results indicate that reasonable solutions have been generated. They can help decision makers identify the desired alternatives regarding long-term MSW management with a compromise between minimized system cost and minimized system-failure risk.     

Inexact fuzzy-stochastic mixed-integer programming approach for long-term planning of waste management – Part A: Methodology

In this study, an inexact fuzzy chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is proposed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing inexact two-stage programming and mixed-integer linear programming techniques by incorporating uncertainties expressed as multiple uncertainties of intervals and dual probability distributions within a general optimization framework. The developed method can provide an effective linkage between the predefined environmental policies and the associated economic implications. Four special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it provides a linkage to predefined policies that have to be respected when a modeling effort is undertaken; secondly, it is useful for tackling uncertainties presented as intervals, probabilities, fuzzy sets and their incorporation; thirdly, it facilitates dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period, multi-level, and multi-option context; fourthly, the penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised solid waste-generation rates are violated. In a companion paper, the developed method is applied to a real case for the long-term planning of waste management in the City of Regina, Canada.     

An interval type-2 fuzzy stochastic approach for regional-scale electric power system under parameter uncertainty

In this study, an interval type-2 fuzzy stochastic linear programming method (IT2FSLP) is developed to support regional-scale electric power system (REM) planning. The IT2FSLP-REM model is based on an integration of interval type-2 fuzzy sets boundary programming and stochastic linear programming techniques enable it to have robust abilities to the deal with uncertainties expressed as type-2 fuzzy intervals and probabilistic distributions within a general optimization framework. Moreover, it can reflect dynamic decisions for energy supply and energy conversion processes, as well as provide capacity expansion options with multiple periods. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability. Based on a two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs among economic cost, environmental requirements, and energy-supply security. Thus, the lower and upper solutions of IT2FSLP-REM would then help energy authorities adjust or justify allocation patterns of regional energy resources and services.     

Two-stage vertex analysis method for planning electric power systems with greenhouse gas abatement consideration

This study presents a two-stage vertex analysis (TSVA) method for the planning of electric power systems (EPS) under uncertainty. TSVA has advantages in comparison to other optimization techniques. Firstly, TSVA can incorporate greenhouse gas (GHG) abatement policies directly into its optimization process, and, secondly, it can readily integrate inherent system uncertainties expressed as fuzzy sets and probability distributions directly into its modeling formulation and solution procedure. The TSVA method is applied to a case study of planning EPS and it is demonstrated how the TSVA efficiently identify optimal electricity-generation schemes that could help to minimize system cost under different GHG-abatement considerations. Different combinative considerations on the uncertain inputs lead to varied system costs and GHG emissions. Results reveal that the total electricity supply will rise up along with the time period due to the increasing demand and, at the same time, more non-fossil fuels should be used to satisfy the increasing requirement for GHG mitigation. Moreover, uncertainties in connection with complexities in terms of information quality (e.g., capacity, efficiency, and demand) result in changed electricity-generation patterns, GHG-abatement amounts, as well as system costs. Minimax regret (MMR) analysis technique is employed to identify desired alternative that reflects compromises between system cost and system-failure risk.     

Factorial fuzzy programming for planning water resources management systems

In this paper, we propose a factorial fuzzy programming (FFP) approach for planning water resources management systems. The conventional fuzzy method cannot reflect the interactions among uncertain system parameters nor quantify their interactive effects. This may lead to important interrelationships among system parameters being neglected in systems analysis, and the derived decisions may not be robust enough to support the management under uncertainties. The objective of this study is to develop an FFP approach to deal with such interactive uncertainties. Factorial analysis (FA) was integrated with the fuzzy technique to quantify the effects of multiple fuzzy modeling parameters on the system performance and to reveal their implicit interrelationships. A flood-diversion planning case was studied to illustrate the applicability of the FFP approach. The individual and interactive effects of fuzzy parameters on the system objectives were evaluated. The influential effects were identified and the implicit interrelationships within influential interactions were revealed.     

Flexible interval mixed-integer bi-infinite programming for environmental systems management under uncertainty

A number of inexact programming methods have been developed for municipal solid waste management under uncertainty. However, most of them do not allow the parameters in the objective and constraints of a programming problem to be functional intervals (i.e., the lower and upper bounds of the intervals are functions of impact factors). In this study, a flexible interval mixed-integer bi-infinite programming (FIMIBIP) method is developed in response to the above concern. A case study is also conducted; the solutions are then compared with those obtained from interval mixed-integer bi-infinite programming (IMIBIP) and fuzzy interval mixed-integer programming (FIMIP) methods. It is indicated that the solutions through FIMIBIP can provide decision support for cost-effectively diverting municipal solid waste, and for sizing, timing and siting the facilities’ expansion during the entire planning horizon. These schemes are more flexible than those identified through IMIBIP since the tolerance intervals are introduced to measure the level of constraints satisfaction. The FIMIBIP schemes may also be robust since the solutions are “globally-optimal” under all scenarios caused by the fluctuation of gas/energy prices, while the conventional ones are merely “locally-optimal” under a certain scenario.     

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.     

Policy planning under uncertainty: efficient starting populations for simulation-optimization methods applied to municipal solid waste management

Evolutionary simulation-optimization (ESO) techniques can be adapted to model a wide variety of problem types in which system components are stochastic. Grey programming (GP) methods have been previously applied to numerous environmental planning problems containing uncertain information. In this paper, ESO is combined with GP for policy planning to create a hybrid solution approach named GESO. It can be shown that multiple policy alternatives meeting required system criteria, or modelling-to-generate-alternatives (MGA), can be quickly and efficiently created by applying GESO to this case data. The efficacy of GESO is illustrated using a municipal solid waste management case taken from the regional municipality of Hamilton-Wentworth in the Province of Ontario, Canada. The MGA capability of GESO is especially meaningful for large-scale real-world planning problems and the practicality of this procedure can easily be extended from MSW systems to many other planning applications containing significant sources of uncertainty.     

An inexact optimization approach for river water-quality management

A previously developed fuzzy waste load allocation model (FWLAM) for a river system is extended to address uncertainty involved in fixing the membership functions for the fuzzy goals of the pollution control agency (PCA) and the dischargers using the concept of grey systems. The model provides flexibility for the PCA and the dischargers to specify their goals independently, as the parameters for membership functions are considered as interval grey numbers instead of deterministic real numbers. An inexact or a grey fuzzy optimization model is developed in a multiobjective framework, to maximize the width of the interval valued fractional removal levels for providing latitude in decision-making and to minimize the width of the goal fulfillment level for reducing the system uncertainty. The concept of an acceptability index for order relation between two partially or fully overlapping intervals is used to get a deterministic equivalent of the grey fuzzy optimization model developed. The improvement of the optimal solutions over a previously developed grey fuzzy waste load allocation model (GFWLAM) is shown through an application to a hypothetical river system. The fuzzy multiobjective optimization and fuzzy goal programming techniques are used to solve the deterministic equivalent of the GFWLAM.     

A Recourse‐Based Interval Fuzzy Programming Model for Point‐Nonpoint Source Effluent Trading under Uncertainty

In this study, a recourse‐based interval fuzzy programming (RIFP) model is developed for tackling uncertainties expressed as fuzzy, interval, and/or probabilistic forms in an effluent trading program. It can incorporate preregulated water‐pollution control policies directly into its optimization process, such that an effective linkage between environmental regulations and economic implications (i.e., penalties) caused by improper policies due to uncertainty existence can be provided. The RIFP model is applied to point‐nonpoint source effluent trading of the Xiangxi River in China. The efficiency of trading efforts between water quality improvement and net system benefit under different degrees of satisfying discharge limits is analyzed. The results are able to help support (1) formulation of water‐pollution control strategies under various economic objectives and system‐reliability constraints, (2) selection of the desired effluent trading pattern for point and nonpoint sources, and (3) generation of tradeoffs among system benefit, satisfaction degree, and pollutant mitigation under multiple uncertainties. Compared with the traditional regulatory approaches, the results demonstrate that the water‐pollution control program can be performed more cost‐effectively through trading than nontrading.     

Sustainable pattern analysis of a publicly owned Material Recovery Facility in a fast-growing urban setting under uncertainty

Sustainable development goals are achievable through the installation of Material Recovery Facilities (MRFs) in certain solid waste management systems, especially those in rapidly expanding multi-district urban areas. MRFs are a cost-effective alternative when curbside recycling does not demonstrate long-term success. Previous capacity planning uses mixed integer programming optimization for the urban center of the city of San Antonio, Texas to establish that a publicly owned material recovery facility is preferable to a privatized facility. As a companion study, this analysis demonstrates that a MRF alleviates economic, political, and social pressures facing solid waste management under uncertainty. It explores the impact of uncertainty in decision alternatives in an urban environmental system. From this unique angle, waste generation, incidence of recyclables in the waste stream, routing distances, recycling participation, and other planning components are taken as intervals to expand upon previous deterministic integer-programming models. The information incorporated into the optimization objectives includes economic impacts for recycling income and cost components in waste management. The constraint set consists of mass balance, capacity limitation, recycling limitation, scale economy, conditionality, and relevant screening restrictions. Due to the fragmented data set, a grey integer programming modeling approach quantifies the consequences of inexact information as it propagates through the final solutions in the optimization process. The grey algorithm screens optimal shipping patterns and an ideal MRF location and capacity. Two case settings compare MRF selection policies where optimal solutions exemplify the value of grey programming in the context of integrated solid waste management.