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.     

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).     

An integrated fuzzy-stochastic modeling approach for risk assessment of groundwater contamination

An integrated fuzzy-stochastic risk assessment (IFSRA) approach was developed in this study to systematically quantify both probabilistic and fuzzy uncertainties associated with site conditions, environmental guidelines, and health impact criteria. The contaminant concentrations in groundwater predicted from a numerical model were associated with probabilistic uncertainties due to the randomness in modeling input parameters, while the consequences of contaminant concentrations violating relevant environmental quality guidelines and health evaluation criteria were linked with fuzzy uncertainties. The contaminant of interest in this study was xylene. The environmental quality guideline was divided into three different strictness categories: "loose", "medium" and "strict". The environmental-guideline-based risk (ER) and health risk (HR) due to xylene ingestion were systematically examined to obtain the general risk levels through a fuzzy rule base. The ER and HR risk levels were divided into five categories of "low", "low-to-medium", "medium", "medium-to-high" and "high", respectively. The general risk levels included six categories ranging from "low" to "very high". The fuzzy membership functions of the related fuzzy events and the fuzzy rule base were established based on a questionnaire survey. Thus the IFSRA integrated fuzzy logic, expert involvement, and stochastic simulation within a general framework. The robustness of the modeling processes was enhanced through the effective reflection of the two types of uncertainties as compared with the conventional risk assessment approaches. The developed IFSRA was applied to a petroleum-contaminated groundwater system in western Canada. Three scenarios with different environmental quality guidelines were analyzed, and reasonable results were obtained. The risk assessment approach developed in this study offers a unique tool for systematically quantifying various uncertainties in contaminated site management, and it also provides more realistic support for remediation-related decisions.     

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.     

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.     

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.     

A Level‐of‐Service Concept for Planning Future Water Supply Projects under Probabilistic Demand and Supply Framework

One of the most challenging tasks of water supply utilities is planning the timing and quantity of new water supply sources as demand for water consumption grows. Many water supply utilities target on meeting 100% of their customers' needs based on scenario‐based deterministic demand projections numbers even though there are uncertainties in both supply and demand values. This may result in under or overly conservative approach in assessing future needs. In this article, a level‐of‐service concept is introduced to capture a utility's willingness to accept a given level of risk, plan for it, and invoke a management strategy during extreme events than build a facility to accommodate those in planning for new water supply sources. Accounting for uncertainties in both supply and demand help quantify reliability by achieving a prescribed level of service. The major benefit of such an approach for planning future water supply is that it allows policy makers to evaluate the use of adaptive water management strategies and develop supply in an incremental fashion as demand warrants it. For example, if a given level of service cannot be reliably met with the existing system at a future time t, an incremental water supply project would come online to bring the required reliability level up but no more.     

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 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.     

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.     

Optimization of regional economic and environmental systems under fuzzy and random uncertainties

Environmental problems associated with socio-economic development have been growing concerns faced by many regional and/or national authorities. However, effective planning may encounter difficulties since uncertainties existing in a number of impact factors and pollution-related processes are often not well acknowledged and reflected. This study advances an interval-fuzzy chance-constrained programming (IFCP) method for planning regional economic and environmental systems, where uncertainties presented as intervals, fuzzy sets and probability distributions can be tackled. The developed method is applied to a real-world case for economic and environmental planning in the New Binhai District in the Municipality of Tianjin, China. Two scenarios based on multiple environmental constraints are examined. The results can help identify desired alternatives for planning regional development strategies, where compromised schemes are provided under an integrated consideration of economic efficiency and environmental protection under multiple uncertainties.     

Risk-based optimal operation of hybrid power system using multiobjective optimization

ABSTRACT

This paper solves an optimal generation scheduling problem of hybrid power system considering the risk factor due to uncertain/intermittent nature of renewable energy resources (RERs) and electric vehicles (EVs). The hybrid power system considered in this work includes thermal generating units, RERs such as wind and solar photovoltaic (PV) units, battery energy storage systems (BESSs) and electric vehicles (EVs). Here, the two objective functions are formulated, i.e., minimization of operating cost and system risk, to develop an optimum scheduling strategy of hybrid power system. The objective of proposed approach is to minimize operating cost and system risk levels simultaneously. The operating cost minimization objective consists of costs due to thermal generators, wind farms, solar PV units, EVs, BESSs, and adjustment cost due to uncertainties in RERs and EVs. In this work, Conditional Value at Risk (CVaR) is considered as the risk index, and it is used to quantify the risk due to intermittent nature of RERs and EVs. The main contribution of this paper lies in its ability to determine the optimal generation schedules by optimizing operating cost and risk. These two objectives are solved by using a multiobjective-based nondominated sorting genetic algorithm-II (NSGA-II) algorithm, and it is used to develop a Pareto optimal front. A best-compromised solution is obtained by using fuzzy min-max approach. The proposed approach has been implemented on modified IEEE 30 bus and practical Indian 75 bus test systems. The obtained results show the best-compromised solution between operating cost and system risk level, and the suitability of CVaR for the management of risk associated with the uncertainties due to RERs and EVs.     

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 credibility constrained programming for environmental system management

This study proposed an inexact credibility constrained programming (ICCP) to deal with multi-formats of uncertainties in parameters and variables for an agricultural water planning system. The study system includes three subareas with different crop distributions. The redundant water in the wet season can be stored in the reservoir and utilized in the dry season. The ICCP method can reflect not only inexact uncertainties in the objective function, variables and parameters, but also fuzzy uncertainties in the right-hand side. Interval credibility levels which represent satisfaction degrees of the constraints can be analyzed. Scenario analysis is conducted to analyze possible events in wet and dry years. The resulting solutions can provide stable intervals for the objective function and decision variables with different levels of risk when violating the constraints.     

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.     

Distributed travel time savings of a multiscale transportation access management program

Access management in transportation planning can save travel time, reduce crashes, and increase route capacities. The planning literature suggests a need for performance metrics and a decision-aiding framework to guide access management programs across large corridor networks and diverse time horizons. This paper describes a quantitative framework to support access management programs, applying multicriteria analysis and cost-benefit analysis with parameter uncertainties. The metrics used to assess relative priorities at existing access points include the following: travel time delay index, traffic exposure, value of time, and costs of typical access management activities. Uncertain parameters that influence the estimates of the potential benefits and costs are identified and treated via a numerical interval analysis. The framework is demonstrated at several geographic scales and locations including 7,000 km of highway arterials of a 110,000 square-kilometer region and several sub-regions. The results assist decision makers to identify route segments that should be addressed sooner by eliciting additional information, reserving right-of-way, closing access points, planning new alignments, facilitating development proffers, etc. The approach is transferable to other topics involving resource allocation for preservation and improvement of multiscale infrastructure systems.     

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.     

Managing for Multiple Resources Under Climate Change: National Forests

This study explores potential adaptation approaches in planning and management that the United States Forest Service might adopt to help achieve its goals and objectives in the face of climate change. Availability of information, vulnerability of ecological and socio-economic systems, and uncertainties associated with climate change, as well as the interacting non-climatic changes, influence selection of the adaptation approach. Resource assessments are opportunities to develop strategic information that could be used to identify and link adaptation strategies across planning levels. Within a National Forest, planning must incorporate the opportunity to identify vulnerabilities to climate change as well as incorporate approaches that allow management adjustments as the effects of climate change become apparent. The nature of environmental variability, the inevitability of novelty and surprise, and the range of management objectives and situations across the National Forest System implies that no single approach will fit all situations. A toolbox of management options would include practices focused on forestalling climate change effects by building resistance and resilience into current ecosystems, and on managing for change by enabling plants, animals, and ecosystems to adapt to climate change. Better and more widespread implementation of already known practices that reduce the impact of existing stressors represents an important “no regrets” strategy. These management opportunities will require agency consideration of its adaptive capacity, and ways to overcome potential barriers to these adaptation options.     

Handling uncertainty through adaptiveness in planning approaches: comparing adaptive delta management and the water diplomacy framework

Planners and water managers seek to be adaptive to handle uncertainty through the use of planning approaches. In this paper, we study what type of adaptiveness is proposed and how this may be operationalized in planning approaches to adequately handle different uncertainties. We took a comparative case study approach to study two planning approaches: the water diplomacy framework (WDF) and adaptive delta management (ADM). We found that the approaches differ in their conceptualization of uncertainty and show that different types of adaptiveness are used in the approaches. While WDF builds on collaborative adaptive management as a set of ongoing adjustments and continuous learning to handle uncertainty, ADM deliberately attempts to anticipate future adaptations through a set of tools which allows for seizing opportunities and avoiding lock-in and lock-out mechanisms. We conclude that neither of the approaches is fully able to account for different uncertainties. Both approaches may benefit from specific insights in what uncertainty and adaptiveness entail for the development of water management plans.     

Case studies of scenario analysis for adaptive management of natural resource and infrastructure systems

Management of natural resources and infrastructure systems for sustainability is complicated by uncertainties in the human and natural environment. Moreover, decisions are further complicated by contradictory views, values, and concerns that are rarely made explicit. Scenario analysis can play a major role in addressing the challenges of sustainability management, especially the core question of how to scan the future in a structured, integrated, participatory, and policy-relevant manner. In a context of systems engineering, scenario analysis can provide an integrated and timely understanding of emergent conditions and help to avoid regret and belated action. The purpose of this paper is to present several case studies in natural resources and infrastructure systems management where scenario analysis has been used to aide decision making under uncertainty. The case studies include several resource and infrastructure systems: (1) water resources (2) land-use corridors (3) energy infrastructure, and (4) coastal climate change adaptation. The case studies emphasize a participatory approach, where scenario analysis becomes a means of incorporating diverse stakeholder concerns and experience. This approach to scenario analysis provides insight into both high-performing and robust initiatives/policies, and, perhaps more importantly, influential scenarios. Identifying the scenarios that are most influential to policy making helps to direct further investigative analysis, modeling, and data-collection efforts to support the learning process that is emphasized in adaptive management.