Interval-parameter Fuzzy-stochastic Semi-infinite Mixed-integer Linear Programming for Waste Management under Uncertainty

An interval-parameter fuzzy-stochastic semi-infinite mixed-integer linear programming (IFSSIP) method is developed for waste management under uncertainties. The IFSSIP method integrates the fuzzy programming, chance-constrained programming, integer programming and interval semi-infinite programming within a general optimization framework. The model is applied to a waste management system with three disposal facilities, three municipalities, and three periods. Compared with the previous methods, IFSSIP have two major advantages. One is that it can help generate solutions for the stable ranges of the decision variables and objective function value under fuzzy satisfaction degree and different levels of probability of violating constraints, which are informative and flexible for solution users to interpret/justify. The other is that IFSSIP can not only handle uncertainties through constructing fuzzy and random parameter, but also reflect dynamic features of the system conditions through interval function of time over the planning horizon. By comparing IFSSIP with interval-parameter mixed-integer linear semi-infinite programming and parametric programming, the IFSSIP method is more reasonable than others.     

An Inexact Fuzzy-robust Two-stage Programming Model for Managing Sulfur Dioxide Abatement Under Uncertainty

In this study, an inexact fuzzy-robust two-stage programming (IFRTSP) method is developed for tackling multiple forms of uncertainties that can be expressed as discrete intervals, probabilistic distributions and/or fuzzy membership functions. The model can reflect economic penalties of corrective measures against any infeasibilities arising due to a particular realization of system uncertainties. Moreover, the fuzzy decision space can be delimited into a more robust one with the uncertainties being specified through dimensional enlargement of the original fuzzy constraints. A management problem in terms of regional air pollution control has been studied to illustrate the applicability of the proposed approach. Results indicate that useful solutions for planning the air quality management practices have been generated. They can help decision makers identify desired pollution-abatement strategy with minimized system cost and maximized environmental efficiency.     

A Superiority-Inferiority-Based Inexact Fuzzy Stochastic Programming Approach for Solid Waste Management Under Uncertainty

A superiority–inferiority-based inexact fuzzy stochastic programming (SI-IFSP) model was developed for planning municipal solid waste management systems under uncertainty. The SI-IFSP approach represents a new attempt to tackle multiple uncertainties in objective function coefficients which are beyond the capabilities of existing inexact programming methods. Through introducing the concept of fuzzy random boundary interval, SI-IFSP is capable of reflecting multiple uncertainties (i.e., interval values, fuzzy sets, probability distributions, and their combinations) in both the objective function and constraints, leading to enhanced system robustness. The developed SI-IFSP method was applied to a case study of long-term municipal solid waste management. Useful solutions were generated. A number of decision alternatives could be generated based on projected applicable conditions, reflecting the compromise between system optimality and reliability as well as the tradeoffs between economic and environmental objectives. Moreover, the consequences of system violations could be quantified through introducing a set of economic penalties, reflecting the relationships between system costs and constraint violation risks. The results suggest that the proposed SI-IFSP method can explicitly address complexities in municipal solid waste management systems and is applicable to practical waste management problems.     

Inexact Fuzzy-Stochastic Programming for Water Resources Management Under Multiple Uncertainties

In this study, an interval-parameter fuzzy-stochastic two-stage programming (IFSTP) approach is developed for irrigation planning within an agriculture system under multiple uncertainties. A concept of the distribution with fuzzy-interval probability (DFIP) is defined to address multiple uncertainties expressed as integration of intervals, fuzzy sets, and probability distributions. IFSTP integrates the interval programming, two-stage stochastic programming, and fuzzy-stochastic programming within a general optimization framework. IFSTP incorporates the pre-regulated water resources management policies directly into its optimization process to analyze various policy scenarios; each scenario has different economic penalty when the promised amounts are not delivered. IFSTP is applied to an irrigation planning in a water resources management system. Solutions from IFSTP provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable solutions are generated for objective function values and decision variables; thus, a number of decision alternatives can be generated under different levels of stream flows.     

An Interval-Parameter Fuzzy-Stochastic Programming Approach for Municipal Solid Waste Management and Planning

In this study, an integrated fuzzy-stochastic linear programming model is developed and applied to municipal solid waste management. Methods of chance-constrained programming and fuzzy linear programming are incorporated within a general interval-parameter mixed-integer linear programming framework. It improves upon the existing optimization methods with advantages in uncertainty reflection, data availability, and computational requirement. The model can be used for answering questions related to types, times and sites of solid waste management practices, with the objective of minimizing system costs over the planning horizon. The model can effectively reflect dynamic, interactive, and uncertain characteristics of municipal waste management systems. In its solution process, the model is transformed into two deterministic submodels, corresponding to upper and lower bounds of the desired objective function values under a given significance level, based on an interactive algorithm. Results of the method's application to a hypothetical case indicate that reasonable outputs have been obtained. It demonstrates the practical applicability of the proposed methodology.     

Interval-Parameter Conditional Value-at-Risk Two-Stage Stochastic Programming Model for Management of End-of-Life Vehicles

The management of end-of-life vehicles conserves natural resources, provides economic benefits, and reduces water, air, and soil pollution. Sound management of end-of-life vehicles is vitally important worldwide thus requiring sophisticated decision-making tools for optimizing its efficiency and reducing system risk. This paper proposes an interval-parameter conditional value-at-risk two-stage stochastic programming model for management of end-of-life vehicles. A case study is conducted in order to demonstrate the usefulness of the developed model. The model is able to provide the trade-offs between the expected profit and system risk. It can effectively control risk at extremely disadvantageous availability levels of end-of-life vehicles. The formulated model can produce optimal solutions under predetermined decision-making risk preferences and confidence levels. It can simultaneously determine the optimal long-term allocation targets of end-of-life vehicles and reusable parts as well as capital investment, production planning, and logistics management decisions within a multi-period planning horizon. The proposed model can efficiently handle uncertainties expressed as interval values and probability distributions. It is able to provide valuable insights into the effects of uncertainties. Compared to the available models, the resulting solutions are far more robust.

     

Optimal water and waste-load allocations in rivers using a fuzzy transformation technique: a case study

In this paper, a new methodology is developed for integrated allocation of water and waste-loads in river basins utilizing a fuzzy transformation method (FTM). The fuzzy transformation method is used to incorporate the existing uncertainties in model inputs. In the proposed methodology, the FTM, as a simulation model, is utilized in an optimization framework for constructing a fuzzy water and waste-loads allocation model. In addition, economic as well as environmental impacts of water allocation to different water users are considered. For equitable water and waste load allocation, all possible coalition of water users are considered and total benefit of each coalition, which is a fuzzy number, is reallocated to water users who are participating in the coalition. The fuzzy cost savings are reallocated using a fuzzy nucleolus cooperative game and the FTM. As a case study, the Dez River system in south-west of Iran is modeled and analyzed using the methodology developed here. The results show the effectiveness of the methodology in optimal water and waste-loads allocations under uncertainty.     

Connectivity in priority area selection for conservation

The spatial relations of sites within networks of priority areas for conservation is critical to the long-term maintenance of key genetic, population and ecosystem processes. However, these relations have received relatively little attention in the development of mathematical methods for objectively identifying such networks. Here we present a novel heuristic for incorporating connectivity explicitly as part of the model constraints, provide an integer linear programming formulation for the same problem, describe an integer cutting procedure which defines a sequence of non-decreasing lower bounds on the optimal solution and report the results of some computational experiments using these algorithms.     

A Robust Optimization Model for an Invasive Species Management Problem

Invasive species pose a significant threat to global biodiversity. Managing invasive species often involves modeling the species’ spread pattern, estimating control costs and damage costs due to the invasion, designing control efforts, and accounting for uncertainties in model parameters. Dealing with uncertainty is arguably the most important part of the process, since biological, environmental, and economic factors can cause parameter values to vary greatly. Managers need decision tools that are robust to such limited or variable information. Here, we present a robust spatial optimization model to select treatment sites in a way that maximally reduces the size of an invasive population, given a constraint on financial resources. We develop an integer programming model that includes population dynamics and management costs over space and time. The model incorporates uncertainty in the available budget and the invasive spread rate as sets of discrete scenarios to determine a robust, cost-effective management plan in a novel way.     

中国环境风险评价体系的完善:来自美国的经验和启示

分析总结了美国在比较风险评价研究、环境风险评价指南、环境风险评价过程中的不确定性分析和风险交流等方面的经验,并结合我国环境风险评价现状和存在问题,提出,开展比较风险评价研究,完善环境风险评价指南体系,减小环境风险评价的不确定性和建立有效可行的环境风险交流体系的建议,从而完善我国环境风险评价体系,提高环境风险评价结果的真实性和可靠性。     

Optimal Expansion Strategy for a Sewer System under Uncertainty

Because of fast urban sprawl, land use competition, and the gap in available funds and needed funds, municipal decision makers and planners are looking for more cost-effective and sustainable ways to improve their sewer infrastructure systems. The dominant approaches have turned to planning the sanitary sewer systems within a regional context, while the decentralized and on-site/cluster wastewater systems have not overcome the application barriers. But regionalization policy confers uncertainties and risks upon cities while planning for future events. Following the philosophy of smart growth, this paper presents several optimal expansion schemes for a fast-growing city in the US/Mexico borderlands—the city of Pharr in Texas under uncertainty. The waste stream generated in Pharr is divided into three distinct sewer sheds within the city limit, including south region, central region, and north region. The options available include routing the wastewater to a neighboring municipality (i.e., McAllen) for treatment and reuse, expanding the existing wastewater treatment plant (WWTP) in the south sewer shed, and constructing a new WWTP in the north sewer shed. Traditional deterministic least-cost optimization applied in the first stage can provide a cost-effective and technology-based decision without respect to associated uncertainties system wide. As the model is primarily driven by the fees charged for wastewater transfer, sensitivity analysis was emphasized by the inclusion of varying flat-rate fees for adjustable transfer schemes before contracting process that may support the assessment of fiscal benefits to all parties involved. Yet uncertainties might arise from wastewater generation, wastewater reuse, and cost increase in constructing and operating the new wastewater treatment plant simultaneously. When dealing with multiple sources of uncertainty, the grey mixed integer programming (GIP) model, formulated in the second stage, can further allow all sources of uncertainties to propagate throughout the optimization context, simultaneously leading to determine a wealth of optimal decisions within a reasonable range. Both models ran for three 5-year periods beginning in 2005 and ending in 2020. The dynamic outputs of this analysis reflect the systematic concerns about integrative uncertainties within this decision analysis, which enable decision makers and stakeholders to make all-inclusive decisions for sanitary sewer system expansion in an economically growing region.     

DMSP-IEES: A Stochastic Programming Model Based on Dual-Interval and Multi-Stage Scenarios Modeling Approaches for Energy Systems Management and GHG Emissions Control

Energy-related activities contribute a major portion of anthropogenic greenhouse gas (GHG) emissions into the atmosphere. In this study, a dual-interval multi-stage stochastic programming model for the planning of integrated energy-environment systems (DMSP-IEES) model is developed for integrated energy-environment systems management, in which issues of GHG-emission mitigation can be reflected throughout the process of energy systems planning. By integrating methodologies of interval linear programming (when numbers are described as interval values without distribution information), dual-interval programming (when lower and upper bounds of interval values are not available as deterministic values but as discrete intervals), and multi-stage stochastic programming, the DMSP-IEES model is capable of dealing with uncertainties expressed as discrete intervals, dual intervals, and probability distributions within a multi-stage context. Decision alternatives can also be generated through analysis of the single- and dual-interval solutions according to projected applicable conditions. A case study is provided for demonstrating the applicability of the developed methodology. The results indicate that the developed model can tackle the dual uncertainties and the dynamic complexities in the energy-environment management systems through a multi-layer scenario tree. In addition, it can reflect the interactions among multiple system components and the associated trade-offs.     

A game theoretic approach for interbasin water resources allocation considering the water quality issues

In this paper, a new game theoretic methodology is developed for interbasin water transfer management with regard to economic, equity, and environmental criteria. The main objective is to supply the competing users in a fair way, while the efficiency and environmental sustainability criteria are satisfied and the utilities of water users are incorporated. Firstly, an optimization model is developed to proportionally allocate water to the competing users in water donor and receiving basins based on their water demands. Secondly, for different coalitions of water users, the water shares of the coalitions are determined using an optimization model with economic objectives regarding the physical and environmental constraints of the system. In order to satisfy water-quality requirements, the impacts of decreasing the instream flow in donor basin are estimated using a water-quality simulation model, and the required treatment levels for effluents discharged into the river, downstream of the water transfer point are determined. Finally, to achieve equity and to provide sufficient incentives for water users to participate in the cooperation, some cooperative game theoretic approaches are utilized for reallocation of net benefits to water users. This model is applied to a large-scale interbasin water allocation problem including two different basins struggling with water scarcity in Iran. The results show that this model can be utilized as an effective tool for optimal interbasin water allocation management involving stakeholders with conflicting objectives subject to physical and environmental constraints.     

Long-Term Planning of Waste Management System in the City of Regina – an Integrated Inexact Optimization Approach

In this study, an integrated solid waste management system based on inexact fuzzy-stochastic mixed integer linear programming (IFSMILP) has been applied to the long-term planning of waste management activities in the City of Regina. The model can effectively reflect dynamic, interactive, and uncertain characteristics of the solid waste management system in the city. The results have provided useful answers for the following questions: “What waste reduction goals are desired if the existing landfill's life is prolonged for 15 years?”, “What should be the waste flow allocation pattern in the city?”, “What should be done if the waste generation rate increases rapidly, while the relevant handling capacity is limited?”, and “What level of reliability will we have given the suggested waste management plan?”     

An approach to deal with uncertainty in energy and environmental planning: the MARKAL case

This paper presents a new concept to include uncertainty management in energy and environmental planning models developed in algebraic modeling languages. SETSTOCH is a tool for linking algebraic modeling languages with specialized stochastic programming solvers. Its main role is to retrieve from the modeling language a dynamically ordered core model (baseline scenario) that is sent automatically to the stochastic solver. The case presented herein concerns such a study realized with the IEAMARKAL model used by many research teams around the world.     

An Overview of EPA's Regional Vulnerability Assessment (ReVA) Program

Regional Vulnerability Assessment (ReVA) is an approach to place-based ecological risk assessment that is currently under development by EPA's Office of Research and Development. The pilot assessment will be done for the mid-Atlantic region and builds on data collected for the Environmental Monitoring and Assessment Program. ReVA is being developed to identify those ecosystems most vulnerable to being lost or degraded in the next 5 to 50 years and to elucidate which stressors cause the greatest risk to ecosystem goods and services. The goal here is not exact predictions, but an early warning system to identify and prioritize the undesirable environmental changes we should expect over the next few decades. As such, ReVA represents a new risk paradigm for EPA that will require innovative approaches to combine existing knowledge, focus new research, and synthesize many types of information into a meaningful assessment designed to inform environmental decision-makers about future environmental risk.     

Evaluation of a real-time monitoring system for river quality — a trade-off between risk attitudes,costs, and uncertainty

Uncertainty is definitely one of the key topics in environmental assessment and management. Typically, attempts to reduce uncertainty are subject to expenses. But how to compare and trade-off expenses and the reduced uncertainty? They only seldom allow the use of a single unit. Instead, the whole analysis and decision procedure is very subjective. This paper presents one approach to handle such problems, namely the combined use of Bayesian influence diagrams, and probabilistic risk attitude analysis. The approach was used in the evaluation of three alternatives for a real time river water quality forecasting system. A trade-off analysis of risk attitudes, costs and uncertainty indicated the levels of socioeconomic utility required for investments in the respective systems, and accordingly illuminated the impact of the uncertainties involved on inference and decision-making with various risk attitudes and discount rates.     

An Linear Programming Model for Batch Optimization in the Ecological Zinc Production

This paper presents a mathematical model for solving the blending composition problem used in the zinc smelting process. The model proposes an objective function maximizing profit in terms of the total income from the sale of zinc on the market and the cost of producing zinc. In addition to the constraints contained in the basic mathematical model, the constraints, which are in accordance with the specific production process of zinc and environmental requirements, are developed. This paper proposes a model that can align three contradictory demands (technological, economic, and environmental) present in zinc production. The results, obtained by numerical experiments, confirm the assumption that it is possible to assemble such an optimal batch that will “reconcile” all contradictory demands. This model can be applied to other similar processes of production with minor changes.     

Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty

Economic development, variation in weather patterns and natural disasters focus attention on the management of water resources. This paper reviews the literature on the development of mathematical programming models for water resource management under uncertainty between 2010 and 2017. A systematic search of the academic literature identified 448 journal articles on water resource management for examination. Bibliometric analysis is employed to investigate the methods that researchers are currently using to address this problem and to identify recent trends in research in the area. The research reveals that stochastic dynamic programming and multistage stochastic programming are the methods most commonly applied. Water resource allocation, climate change, water quality and agricultural irrigation are amongst the most frequently discussed topics in the literature. A more detailed examination of the literature on each of these topics is included. The findings suggest that there is a need for mathematical programming models of large-scale water systems that deal with uncertainty and multiobjectives in an effective and computationally efficient way.