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.     

IFTCIP: An Integrated Optimization Model for Environmental Management under Uncertainty

In this study, an interval-fuzzy two-stage chance-constrained integer programming (IFTCIP) method is developed for supporting environmental management under uncertainty. The IFTCIP improves upon the existing interval, fuzzy, and two-stage programming approaches by allowing uncertainties expressed as probability distributions, fuzzy sets, and discrete intervals to be directly incorporated within a general mixed integer linear programming framework. It has advantages in uncertainty reflection, policy investigation, risk assessment, and capacity-expansion analysis in comparison to the other optimization methods. Moreover, it can help examine the risk of violating system constraints and the associated consequences. The developed method is applied to the planning for facility expansion and waste-flow allocation within a municipal solid waste management system. Violations of capacity constraints are allowed under a range of significance levels, which reflects tradeoffs between the system cost and the constraint-violation risk. The results indicate that reasonable solutions for both binary and continuous variables have been generated under different risk levels. They are useful for generating desired decision alternatives with minimized system cost and constraint-violation risk under various environmental, economic, and system-reliability conditions. Generally, willingness to take a higher risk of constraint violation will guarantee a lower system cost; a strong desire to acquire a lower risk will run into a higher system cost.     

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.

     

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.     

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.     

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.     

Multi-objective, decision-based assessment of a water quality monitoring network in a river system

Water quality monitoring network design has historically tended to use experience, intuition and subjective judgement in locating monitoring stations. Better design procedures to optimize monitoring systems need to simultaneously identify significant planning objectives and consider a number of social, economic and environmental constraints. The consideration of multiple objectives may require further decision analysis to determine the preference weights associated with the objectives to aid in the decision-making process. This may require the application of an optimization study to extract such information from decision makers or experts and to evaluate the overall effectiveness of locating strategies. This paper assesses the optimal expansion and relocation strategies of a water quality monitoring network using a two-stage analysis. The first stage focuses on the information retrieval of preference weights with respect to the designated planning objectives. With the aid of a pre-emptive goal programming model, data analysis is applied to obtain the essential information from the questionnaire outputs. The second stage then utilizes a weighted multi-objective optimization approach to search for the optimal locating strategies of the monitoring stations in the river basin. Practical implementation is illustrated by a case study in the Kao-Ping River Basin, south Taiwan.     

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?”     

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.     

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.     

A fuzzy multi-stakeholder multi-criteria methodology for water allocation and reuse in metropolitan areas

In this paper, a fuzzy decision making methodology is proposed to find a socially optimal scenario for allocating effluent of wastewater treatment plants and urban and suburban runoffs to agricultural regions and recharging aquifers. The presented methodology named modified fuzzy social choice (MFSC) considers multi-stakeholder multi-criteria problems under uncertainties inherent in a decision making process utilizing a fuzzy ranking method and the fuzzy social choice (FSC) theory. A set of water and wastewater allocation scenarios are proposed for water quantity and quality management of the study area, while six main stakeholders with conflicting utilities and different negotiation powers are involved. The proposed methodology is applied to Tehran metropolitan area, the capital city of Iran with the population of about 8 million people, to examine its applicability and effectiveness. The results shows that using fuzzy multi-stakeholder multi-criteria decision making method considering equal and different negotiation powers can lead to different outcomes. Based on the results, the MFSC method, which considers a number of decision makers having different negotiation powers, degrees of importance of decision making criteria, and some important uncertainties, performs more promising in real water resources management problems.     

基于信息资源规划的流域水环境数据中心设计与实践

由于跨界和跨部门等原因导致的流域水环境数据信息标准不一,无法有效共享、综合利用等问题,是目前水环境信息使用过程中的主要问题之一.基于信息资源规划理论,充分调研水环境监测管理、政府规划与决策、科学技术研究和社会公众使用等对水环境监测信息的需求,以太湖流域为例,分析与水环境相关各种数据资源,研究流域水环境信息的数据体系及数据库体系,设计并建立流域水环境数据中心,初步完成太湖流域水环境数据的管理、分析及共享服务平台设计,为流域水环境监测信息综合管理做出了示范.     

Optimization and Decision Heuristics for Chesapeake Bay Nutrient Reduction Strategies

Regional policies to achieve water quality goals assign a unique pollution control technology to every pollution source in a watershed, thereby defining a watershed strategy. For watersheds with even a modest number of pollution sources and control alternatives, the decision problem has combinatorial complexity. The perception of complexity—manifested in innumerable feasible watershed strategies—commonly induces the use of simplifying decision heuristics and ad hoc decision rules that reduce decision complexity by limiting the choice set to a “manageable” number of alternatives. In problems with large complex choice sets, these decision heuristics simplify decision making by excluding the vast majority of feasible alternatives a priori. In contrast, watershed-scale optimization enables decision makers to consider all feasible alternatives implicitly, exploiting rather than restricting the complexity of the feasible choice set. This contrast is illustrated using mixed-integer linear programming to identify interstate watershed strategies that achieve Chesapeake Bay nutrient reduction goals for the Potomac River Basin. The use of optimization in collaborative decision making helped refine and capture decision makers’ underlying values and preferences in policy-relevant constraints reflecting equity and political feasibility. Optimization formulations incorporating these constraints identified more effective and desirable management alternatives that would not otherwise have been considered using familiar decision heuristics and traditional comparisons among a limited number of ad hoc scenarios. Incorporating optimization in collaborative decision making generated superior watershed strategies and eased the cognitive limitations on decision making by substituting the computational burden of solving mixed-integer linear programs for decision makers’ cognitive burden of enumerating alternatives and scenarios for environmental systems with combinatorial complexity.     

Probability of misclassifying biological elements in surface waters

Measurement uncertainties are inherent to assessment of biological indices of water bodies. The effect of these uncertainties on the probability of misclassification of ecological status is the subject of this paper. Four Monte-Carlo (M-C) models were applied to simulate the occurrence of random errors in the measurements of metrics corresponding to four biological elements of surface waters: macrophytes, phytoplankton, phytobenthos, and benthic macroinvertebrates. Long series of error-prone measurement values of these metrics, generated by M-C models, were used to identify cases in which values of any of the four biological indices lay outside of the “true” water body class, i.e., outside the class assigned from the actual physical measurements. Fraction of such cases in the M-C generated series was used to estimate the probability of misclassification. The method is particularly useful for estimating the probability of misclassification of the ecological status of surface water bodies in the case of short sequences of measurements of biological indices. The results of the Monte-Carlo simulations show a relatively high sensitivity of this probability to measurement errors of the river macrophyte index (MIR) and high robustness to measurement errors of the benthic macroinvertebrate index (MMI). The proposed method of using Monte-Carlo models to estimate the probability of misclassification has significant potential for assessing the uncertainty of water body status reported to the EC by the EU member countries according to WFD. The method can be readily applied also in risk assessment of water management decisions before adopting the status dependent corrective actions.     

Decision support model for assessing aquifer pollution hazard and prioritizing groundwater resources management in the wet Pampa plain, Argentina

This paper gives an account of the implementation of a decision support system for assessing aquifer pollution hazard and prioritizing subwatersheds for groundwater resources management in the southeastern Pampa plain of Argentina. The use of this system is demonstrated with an example from Dulce Stream Basin (1,000 km² encompassing 27 subwatersheds), which has high level of agricultural activities and extensive available data regarding aquifer geology. In the logic model, aquifer pollution hazard is assessed as a function of two primary topics: groundwater and soil conditions. This logic model shows the state of each evaluated landscape with respect to aquifer pollution hazard based mainly on the parameters of the DRASTIC and GOD models. The decision model allows prioritizing subwatersheds for groundwater resources management according to three main criteria including farming activities, agrochemical application, and irrigation use. Stakeholder participation, through interviews, in combination with expert judgment was used to select and weight each criterion. The resulting subwatershed priority map, by combining the logic and decision models, allowed identifying five subwatersheds in the upper and middle basin as the main aquifer protection areas. The results reasonably fit the natural conditions of the basin, identifying those subwatersheds with shallow water depth, loam–loam silt texture soil media and pasture land cover in the middle basin, and others with intensive agricultural activity, coinciding with the natural recharge area to the aquifer system. Major difficulties and some recommendations of applying this methodology in real-world situations are discussed.     

Energy Security: A Robust Optimization Approach to Design a Robust European Energy Supply via TIAM-WORLD

Energy supply routes to a given region are subject to random events, resulting in partial or total closure of a route (corridor). For instance, a pipeline may be subject to technical problems that reduce its capacity. Or, oil supply by tanker may be reduced for political reasons or because of equipment mishaps at the point of origin or again, by a conscious decision by the supplier in order to obtain economic benefits. The purpose of this article is to formulate a simplified version of the above issue that mainly addresses long-term uncertainties. The formulation is done via a version of the TIAM-WORLD Integrated Model, modified to implement the approach of robust optimization. In our case, the approach can be interpreted as a revival of chance-constrained programming under the name of distributionally robust, or ambiguous, chance-constrained programming. We apply the approach to improve the security of supply to the European Energy system. The resulting formulation provides several interesting features regarding the security of EU energy supply and has also the advantage to be numerically tractable.     

Urban water resource management for sustainable environment planning using artificial intelligence techniques

In the current era, water is a significant resource for socio-economic growth and the protection of healthy environments. Properly controlled water resources are considered a vital part of development, which reduces poverty and equity. Conventional Water system Management maximizes the existing water flows available to satisfy all competing demands, including on-site water and groundwater. Therefore, Climatic change would intensify the specific challenges in water resource management by contributing to uncertainty. Sustainable water resources management is an essential process for ensuring the earth's life and the future. Nonlinear effects, stochastic dynamics, and hydraulic constraints are challenging in ecological planning for sustainable water development. In this paper, Adaptive Intelligent Dynamic Water Resource Planning (AIDWRP) has been proposed to sustain the urban areas' water environment. Here, an adaptive intelligent approach is a subset of the Artificial Intelligence (AI) technique in which environmental planning for sustainable water development has been modeled effectively. Artificial intelligence modeling improves water efficiency by transforming information into a leaner process, improving decision-making based on data-driven by combining numeric AI tools and human intellectual skills. In AIDWRP, Markov Decision Process (MDP) discusses the dynamic water resource management issue with annual use and released locational constraints that develop sensitivity-driven methods to optimize several efficient environmental planning and management policies. Consequently, there is a specific relief from the engagement of supply and demand for water resources, and substantial improvements in local economic efficiency have been simulated with numerical outcomes.     

Time Series Analysis to Monitor and Assess Water Resources: A Moving Average Approach

An understanding of the behavior of the groundwater body and its long-term trends are essential for making any management decision in a given watershed. Geostatistical methods can effectively be used to derive the long-term trends of the groundwater body. Here an attempt has been made to find out the long-term trends of the water table fluctuations of a river basin through a time series approach. The method was found to be useful for demarcating the zones of discharge and of recharge of an aquifer. The recharge of the aquifer is attributed to the return flow from applied irrigation. In the study area, farmers mainly depend on borewells for water and water is pumped from the deep aquifer indiscriminately. The recharge of the shallow aquifer implies excessive pumping of the deep aquifer. Necessary steps have to be taken immediately at appropriate levels to control the irrational pumping of deep aquifer groundwater, which is needed as a future water source. The study emphasizes the use of geostatistics for the better management of water resources and sustainable development of the area.