Waste management under multiple complexities: inexact piecewise-linearization-based fuzzy flexible programming.

To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities.

An integrated multi-level watershed-reservoir modeling system for examining hydrological and biogeochemical processes in small prairie watersheds.

Eutrophication of small prairie reservoirs presents a major challenge in water quality management and has led to a need for predictive water quality modeling. Studies are lacking in effectively integrating watershed models and reservoir models to explore nutrient dynamics and eutrophication pattern. A water quality model specific to small prairie water bodies is also desired in order to highlight key biogeochemical processes with an acceptable degree of parameterization. This study presents a Multi-level Watershed-Reservoir Modeling System (MWRMS) to simulate hydrological and biogeochemical processes in small prairie watersheds. It integrated a watershed model, a hydrodynamic model and an eutrophication model into a flexible modeling framework. It can comprehensively describe hydrological and biogeochemical processes across different spatial scales and effectively deal with the special drainage structure of small prairie watersheds. As a key component of MWRMS, a three-dimensional Willows Reservoir Eutrophication Model (WREM) is developed to addresses essential biogeochemical processes in prairie reservoirs and to generate 3D distributions of various water quality constituents; with a modest degree of parameterization, WREM is able to meet the limit of data availability that often confronts the modeling practices in small watersheds. MWRMS was applied to the Assiniboia Watershed in southern Saskatchewan, Canada. Extensive efforts of field work and lab analysis were undertaken to support model calibration and validation. MWRMS demonstrated its ability to reproduce the observed watershed water yield, reservoir water levels and temperatures, and concentrations of several water constituents. Results showed that the aquatic systems in the Assiniboia Watershed were nitrogen-limited and sediment flux played a crucial role in reservoir nutrient budget and dynamics. MWRMS can provide a broad context of decision support for water resources management and water quality protection in the prairie region.

Quantitative effects of composting state variables on C/N ratio through GA-aided multivariate analysis.

It is widely known that variation of the C/N ratio is dependent on many state variables during composting processes. This study attempted to develop a genetic algorithm aided stepwise cluster analysis (GASCA) method to describe the nonlinear relationships between the selected state variables and the C/N ratio in food waste composting. The experimental data from six bench-scale composting reactors were used to demonstrate the applicability of GASCA. Within the GASCA framework, GA searched optimal sets of both specified state variables and SCA's internal parameters; SCA established statistical nonlinear relationships between state variables and the C/N ratio; to avoid unnecessary and time-consuming calculation, a proxy table was introduced to save around 70% computational efforts. The obtained GASCA cluster trees had smaller sizes and higher prediction accuracy than the conventional SCA trees. Based on the optimal GASCA tree, the effects of the GA-selected state variables on the C/N ratio were ranged in a descending order as: NH4+-N concentration>Moisture content>Ash Content>Mean Temperature>Mesophilic bacteria biomass. Such a rank implied that the variation of ammonium nitrogen concentration, the associated temperature and the moisture conditions, the total loss of both organic matters and available mineral constituents, and the mesophilic bacteria activity, were critical factors affecting the C/N ratio during the investigated food waste composting. This first application of GASCA to composting modelling indicated that more direct search algorithms could be coupled with SCA or other multivariate analysis methods to analyze complicated relationships during composting and many other environmental processes.

Radial-interval linear programming for environmental management under varied protection levels.

In this study, a radial-interval linear programming (RILP) approach was developed for supporting waste management under uncertainty. RILP improved interval-parameter linear programming and its extensions in terms of input reasonableness and output robustness. From the perspective of modeling inputs, RILP could tackle highly uncertain information at the bounds of interval parameters through introducing the concept of fluctuation radius. Regarding modeling outputs, RILP allows controlling the degree of conservatism associated with interval solutions and is capable of quantifying corresponding system risks and benefits. This could facilitate the reflection of interactive relationship between the feasibility of system and the uncertainty of parameters. A computationally tractable algorithm was provided to solve RILP. Then, a long-term waste management case was studied to demonstrate the applicability of the developed methodology. A series of interval solutions obtained under varied protection levels were compared, helping gain insights into the interactions among protection level, violation risk, and system cost. Potential waste allocation alternatives could be generated from these interval solutions, which would be screened in real-world practices according to various projected system conditions as well as decision-makers' willingness to pay and risk tolerance levels. Sensitivity analysis further revealed the significant impact of fluctuation radii of interval parameters on the system. The results indicated that RILP is applicable to a wide spectrum of environmental management problems that are subject to compound uncertainties.

Planning of municipal solid waste management under dual uncertainties.

Municipal solid waste management is a complex and multidisciplinary problem, involving a number of impact factors associated with various uncertainties. In this study, a hybrid interval-parameter possibilistic programming (IPP) approach was developed and applied for planning municipal solid waste management under dual uncertainties. The IPP improves upon the existing management approaches by allowing possibility distributions of the lower and upper bounds of some interval parameters in the objective function and interval information in the modelling coefficients to be effectively incorporated within its optimization. By introducing the concept of possibilistic interval numbers, the dual uncertainties can be communicated into the optimization process and the resulting solutions, such that the generated decision schemes can effectively reflect the highly complex system features under uncertainty. The results of the case study indicate that useful information can be obtained for providing feasible decision schemes for waste flow allocation. Different decision schemes can be generated by adjusting waste flow allocation patterns within the solution intervals. Lower decision variable values should be used to obtain lower system cost of waste treatment and disposal under advantageous conditions, and higher decision variable values should be used under demanding conditions (worst case conditions). A strong desire to acquire the lower system cost will lead to the decreased probability of meeting the treatment and disposal requirements (i.e. the increased risk of unforeseen conditions); willingness to accept the upper limit of the system cost will guarantee that waste treatment and disposal requirements are met.

Capacity planning for waste management systems: an interval fuzzy robust dynamic programming approach.

This study integrates the concepts of interval numbers and fuzzy sets into optimization analysis by dynamic programming as a means of accounting for system uncertainty. The developed interval fuzzy robust dynamic programming (IFRDP) model improves upon previous interval dynamic programming methods. It allows highly uncertain information to be effectively communicated into the optimization process through introducing the concept of fuzzy boundary interval and providing an interval-parameter fuzzy robust programming method for an embedded linear programming problem. Consequently, robustness of the optimization process and solution can be enhanced. The modeling approach is applied to a hypothetical problem for the planning of waste-flow allocation and treatment/disposal facility expansion within a municipal solid waste (MSW) management system. Interval solutions for capacity expansion of waste management facilities and relevant waste-flow allocation are generated and interpreted to provide useful decision alternatives. The results indicate that robust and useful solutions can be obtained, and the proposed IFRDP approach is applicable to practical problems that are associated with highly complex and uncertain information.

Robust stochastic fuzzy possibilistic programming for environmental decision making under uncertainty.

Nonpoint source (NPS) water pollution is one of serious environmental issues, especially within an agricultural system. This study aims to propose a robust chance-constrained fuzzy possibilistic programming (RCFPP) model for water quality management within an agricultural system, where solutions for farming area, manure/fertilizer application amount, and livestock husbandry size under different scenarios are obtained and interpreted. Through improving upon the existing fuzzy possibilistic programming, fuzzy robust programming and chance-constrained programming approaches, the RCFPP can effectively reflect the complex system features under uncertainty, where implications of water quality/quantity restrictions for achieving regional economic development objectives are studied. By delimiting the uncertain decision space through dimensional enlargement of the original fuzzy constraints, the RCFPP enhances the robustness of the optimization processes and resulting solutions. The results of the case study indicate that useful information can be obtained through the proposed RCFPP model for providing feasible decision schemes for different agricultural activities under different scenarios (combinations of different p-necessity and p(i) levels). A p-necessity level represents the certainty or necessity degree of the imprecise objective function, while a p(i) level means the probabilities at which the constraints will be violated. A desire to acquire high agricultural income would decrease the certainty degree of the event that maximization of the objective be satisfied, and potentially violate water management standards; willingness to accept low agricultural income will run into the risk of potential system failure. The decision variables under combined p-necessity and p(i) levels were useful for the decision makers to justify and/or adjust the decision schemes for the agricultural activities through incorporation of their implicit knowledge. The results also suggest that this developed approach is applicable to many practical problems where fuzzy and probabilistic distribution information simultaneously exist.

A stepwise-cluster microbial biomass inference model in food waste composting.

A stepwise-cluster microbial biomass inference (SMI) model was developed through introducing stepwise-cluster analysis (SCA) into composting process modeling to tackle the nonlinear relationships among state variables and microbial activities. The essence of SCA is to form a classification tree based on a series of cutting or mergence processes according to given statistical criteria. Eight runs of designed experiments in bench-scale reactors in a laboratory were constructed to demonstrate the feasibility of the proposed method. The results indicated that SMI could help establish a statistical relationship between state variables and composting microbial characteristics, where discrete and nonlinear complexities exist. Significance levels of cutting/merging were provided such that the accuracies of the developed forecasting trees were controllable. Through an attempted definition of input effects on the output in SMI, the effects of the state variables on thermophilic bacteria were ranged in a descending order as: Time (day)>moisture content (%)>ash content (%, dry)>Lower Temperature ( degrees C)>pH>NH(4)(+)-N (mg/Kg, dry)>Total N (%, dry)>Total C (%, dry); the effects on mesophilic bacteria were ordered as: Time>Upper Temperature ( degrees C)>Total N>moisture content>NH(4)(+)-N>Total C>pH. This study made the first attempt in applying SCA to mapping the nonlinear and discrete relationships in composting processes.

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.

Effects of sodium acetate as a pH control amendment on the composting of food waste.

A low level of microbial activity due to the production of organic acids is a recognized problem during the initial phase of food waste composting. Increasing such activity levels by adjusting the pH values during the initial composting phase was the primary concern to be investigated. In this study, sodium acetate (NaAc) was introduced as an amendment to an in-vessel composting system. NaAc was added when the pH of the compost mixture reached a low level (pH<5), and its effects on microbial activity, ammonia loss, and organic acid production were then evaluated. The addition of NaAc would lead to an increased pH level within the range from 5.2 to 5.5. This had a positive effect on the degradation of organic materials and the effect was statistically significant compared to the result of control treatment without NaAc addition (p<0.05). Microbial activity in the composting reactor treated with NaAc was also higher than that of the control one after the indigenous microorganisms adapted to the new conditions. However, the microbial populations of these two reactors were not significantly different. Although, ammonia loss was enhanced with the addition of NaAc, with 10.8 and 8.6g in NaAc amendment reactor and control one, respectively, the degree of enhancement was relatively small compared to the total amount of nitrogen in the raw materials (84g). The study results indicated that the NaAc was an effective amendment for inhibiting the production of propionic and butyric acids, and hence counteracting the adverse effects of organic acids to the composting process.

An Interval Mixed-Integer Semi-Infinite Programming Method for Municipal Solid Waste Management.

This study proposed an interval mixed-integer semi-infinite programming (IMISIP) method for solid waste management under uncertainty. The uncertainty can be expressed as various constants, intervals, and functional intervals. The method is mainly based on the previous efforts on interval mixed-integer linear programming (IMILP) and semi-infinite programming. The method is applied to a solid-waste management system to illustrate its effectiveness in handling complex inexact programming problems. Two scenarios are considered: one is a case with only expansions of waste-to-energy (WTE) facilities being considered, and the other is associated with potential expansions for both the WTE and the existing landfilling facilities. The results obtained can assist in identifying optimal waste management policies under uncertainties associated with interval and functional-interval parameters. Compared with conventional IMILP methods, the solutions obtained from IMISIP could be "globally" optimal because the dynamic fluctuations of the system inputs could be reflected effectively.

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.

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.

PeLM: modeling of pesticide-losses through runoff and sediment transport.

A GIS-aided pesticide loss model (PeLM) was developed to simulate pesticide losses through surface runoff and sediment transport in watershed systems. The PeLM could tackle the movement of eroded soil along with surface runoff as well as the pesticide losses in adsorbed and dissolved phases. The contributions of different soil types in the sediment were also examined. The model was applied to the Kintore Creek Watershed of southern Ontario, Canada. The simulation results were verified through observed data, indicating a correlation level of 0.89-0.98. The results also showed that clay particles usually held the largest share of contributions to pesticide losses through soil erosion. This study is significant in the efforts for modeling nonpoint source pollution in watershed systems. It provides useful information and support for the related decisions of watershed management.

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.

Using multiple criteria decision analysis for supporting decisions of solid waste management.

Design of solid-waste management systems requires consideration of multiple alternative solutions and evaluation criteria because the systems can have complex and conflicting impacts on different stakeholders. Multiple criteria decision analysis (MCDA) has been found to be a fruitful approach to solve this design problem. In this paper, the MCDA approach is applied to solve the landfill selection problem in Regina of Saskatchewan Canada. The systematic approach of MCDA helps decision makers select the most preferable decision and provides the basis of a decision support system. The techniques that are used in this study include: 1) Simple Weighted Addition method, 2) Weighted Product method, 3) TOPSIS, 4) cooperative game theory, and 5) ELECTRE. The results generated with these methods are compared and ranked so that the most preferable solution is identified.