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.     

Two-stage planning for sustainable water-quality management under uncertainty

In water-quality management problems, uncertainties may exist in a number of impact factors and pollution-related processes (e.g., the volume and strength of industrial wastewater and their variations can be presented as random events through identifying a statistical distribution for each source); moreover, nonlinear relationships may exist among many system components (e.g., cost parameters may be functions of wastewater-discharge levels). In this study, an inexact two-stage stochastic quadratic programming (ITQP) method is developed for water-quality management under uncertainty. It is a hybrid of inexact quadratic programming (IQP) and two-stage stochastic programming (TSP) methods. The developed ITQP can handle not only uncertainties expressed as probability distributions and interval values but also nonlinearities in the objective function. It can be used for analyzing various scenarios that are associated with different levels of economic penalties or opportunity losses caused by improper policies. The ITQP is applied to a case of water-quality management to deal with uncertainties presented in terms of probabilities and intervals and to reflect dynamic interactions between pollutant loading and water quality. Interactive and derivative algorithms are employed for solving the ITQP model. The solutions are presented as combinations of deterministic, interval and distributional information, and can thus facilitate communications for different forms of uncertainties. They are helpful for managers in not only making decisions regarding wastewater discharge but also gaining insight into the tradeoff between the system benefit and the environmental requirement.     

Inexact rough-interval two-stage stochastic programming for conjunctive water allocation problems

An inexact rough-interval two-stage stochastic programming (IRTSP) method is developed for conjunctive water allocation problems. Rough intervals (RIs), as a particular case of rough sets, are introduced into the modeling framework to tackle dual-layer information provided by decision makers. Through embeding upper and lower approximation intervals, rough intervals are capable of reflecting complex parameters with the most reliable and possible variation ranges being identified. An interactive solution method is also derived. A conjunctive water-allocation system is then structured for characterizing the proposed model. Solutions indicate a detailed optimal allocation scheme with a rough-interval form; a total of [[1048.83, 2078.29]:[1482.26, 2020.60]] would be obtained under the pre-regulated inputs. Comparisons of the proposed model to a conventional and an interval two-stage stochastic programming model are also conducted. The results indicate that the optimal objective function values of TSP and ITSP always fall into the range of , while they are sometimes out of the range of ; the optimal solutions of decision variables also present this feature. This implies the reliability of IRTSP in handling conjunctive water allocation problems.     

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).     

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.     

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.     

Toward quantifying the effectiveness of water trading under uncertainty

This paper presents a methodology for quantifying the effectiveness of water-trading under uncertainty, by developing an optimization model based on the interval-parameter two-stage stochastic program (TSP) technique. In the study, the effectiveness of a water-trading program is measured by the water volume that can be released through trading from a statistical point of view. The methodology can also deal with recourse water allocation problems generated by randomness in water availability and, at the same time, tackle uncertainties expressed as intervals in the trading system. The developed methodology was tested with a hypothetical water-trading program in an agricultural system in the Swift Current Creek watershed, Canada. Study results indicate that the methodology can effectively measure the effectiveness of a trading program through estimating the water volume being released through trading in a long-term view. A sensitivity analysis was also conducted to analyze the effects of different trading costs on the trading program. It shows that the trading efforts would become ineffective when the trading costs are too high. The case study also demonstrates that the trading program is more effective in a dry season when total water availability is in shortage.     

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.     

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.     

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 multiobjective programming framework for integrating timber and wildlife management

This article describes a multiobjective programming (MOP) framework for integrating timber and wildlife management. The framework allows for the simultaneous consideration of timber and wildlife objectives. Management strategies are defined in terms of management regimes consisting of a time-identified and site-specific schedule of activities. A MOP model is described and demonstrated using an integrated planning example involving a forest managed for timber production and a variety of wildlife species.     

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.     

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.     

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.     

Evaluating the effectiveness of air quality management within the class I area of great smoky mountains national park

The Clean Air Act Amendments of 1977 designated national parks and wilderness areas larger than 1894 ha to be class I areas for air quality management, setting more restrictive criteria than the National Ambient Air Quality Standards. Class I areas are afforded the greatest degree of air quality protection under the Clear Air Act of 1970. In recent years, several studies have documented air pollution effects in the Great Smoky Mountains National Park (GSMNP), the second-largest class I area in the eastern United States. Air pollution problems of greatest concern in the GSMNP are effects of acid deposition, visibility impairment, and tropospheric ozone. Several recent events have increased concerns about air quality management in the class I area of the GSMNP. A forum, sponsored by the Southern Appalachian Man and the Biosphere Cooperative (SAMAB), was held in March 1992, which involved representative. parties-at-interest and began to address strategies for better management of air resources in the Southern Appalachians. This paper summarizes those discussions and recommendations and reports actions occurring as a result of the forum. Another objective of this paper is to present a conceptual framework for more effective management of the class I area of the GSMNP.     

A human ecological assessment of air quality management: A convergence in economic and ecological thinking?

Traditional air pollution management practices are examined using the human ecological framework adopted by Boyden and others (1981) in their study of Hong Kong—the biohistorical or biosocial approach. The subsequent analysis of current air quality management practices assesses their effectiveness in protecting the overall health of both humans and the natural environment. The uncertainties inherent in air pollution management practices which emerge highlight the need to reduce emissions rather than rely on scientific knowledge to define clean air. The assessment also clearly defines roles for research in various areas such as atmospheric models, health effects, and environmental damage. The final recommendations emphasize the need for the introduction of such incentives to reduce emissions as economic instruments and warn against using health information to define clean air. Health and environmental damage information can, however, be used in risk assessment strategies together with atmospheric dispersion models.     

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.     

Cost allocation of river water quality management based on the Separable Cost Remaining Benefit (SCRB) method

This paper presents a cost allocation method that applies the cooperative game theory and the Separable Costs Remaining Benefit method to a project that involves two local governments in water quality management in South Korea. The total project cost was estimated by using a parametric estimation method for reduction loads in accordance with the Total Pollution Load Management system. As a result, the cost allocation ratios between the City of Gwangju and Jeonnam Province are suggested to be 69.85% and 30.15% of the total project cost. The final cost allocation confirms the benefits to both governments and illustrates the cooperative game theory.     

Stochastic Watershed Water Quality Simulation for TMDL Development – A Case Study in the Newport Bay Watershed1

Abstract: Systematic consideration of uncertainty in data, model structure, and other factors is generally unaddressed in most Total Maximum Daily Load (TMDL) calculations. Our previous studies developed the Management Objectives Constrained Analysis of Uncertainty (MOCAU) approach as an uncertainty analysis technique specifically for watershed water quality models, based on a synthetic case. In this study, we applied MOCAU to analyze diazinon loading in the Newport Bay watershed (Southern California). The study objectives included (1) demonstrating the value of performing stochastic simulation and uncertainty analysis for TMDL development, using MOCAU as the technique and (2) evaluating the existing diazinon TMDL and generating insights for the development of scientifically sound TMDLs, considering uncertainty. The Watershed Analysis Risk Management Framework model was used as an example of a complex watershed model. The study revealed the importance and feasibility of conducting stochastic watershed water quality simulation for TMDL development. The critical role of management objectives in a systematic uncertainty assessment was well demonstrated. The results of this study are intuitive to TMDL calculation, model structure improvement and sampling strategy design.