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.     

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.     

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.     

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 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 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.     

Combining Stochastic Optimization and Monte Carlo Simulation to Deal with Uncertainties in Climate Policy Assessment

In this paper, we explore the impact of several sources of uncertainties on the assessment of energy and climate policies when one uses in a harmonized way stochastic programming in a large-scale bottom-up (BU) model and Monte Carlo simulation in a large-scale top-down (TD) model. The BU model we use is the TIMES Integrated Assessment Model, which is run in a stochastic programming version to provide a hedging emission policy to cope with the uncertainty characterizing climate sensitivity. The TD model we use is the computable general equilibrium model GEMINI-E3. Through Monte Carlo simulations of randomly generated uncertain parameter values, one provides a stochastic micro- and macro-economic analysis. Through statistical analysis of the simulation results, we analyse the impact of the uncertainties on the policy assessment.     

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.     

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.     

Optimal Policy Mechanism Design for Cross-Sector and Multi-Stage Pollution Control with a Bilevel Model: Application to SO<Subscript>2</Subscript> Emission in China

In this paper, we construct a multi-stage coordinated programming model under tax system to control SO₂ emission. The model is based on an explicitly formulated SO₂ abatement cost function created under Chinese condition. Analysis of the effectiveness and impact on the economy of the model is carried out with consideration of game theory. By solving the model, theoretical results show that the volume-based multi-stage SO₂ tax system has two properties: effectiveness and equal-rate. Based on these theoretical results, empirical study is also performed using Chinese historical data. Compared with yearly single-stage programming model, the tax rate generated by the coordinated multi-stage programming model is time-invariant and rather moderate in scale. The total abatement cost among planning years in our model is 21.03 % less than the actual number and 6.68 % less than that in the single-stage situation. The tax payment suggested by our model is 10.62 % less than by the single-stage model. In general, a coordinated multi-stage programming model helps reduce the overall costs of environmental protection while achieving the same emission control target with less burden added to the economy.     

Developing Alternative Forest Management Planning Strategies Incorporating Timber, Water and Carbon Values: An Examination of their Interactions

Currently, the integration of carbon and water values of forest ecosystems into forest management planning models has become increasingly important in sustainable forest management. This study focuses on developing a multiple-use forest management planning model to examine the interactions of timber and water production as well as net carbon sequestration in a forest ecosystem. Each forest value is functionally linked to stand structure and quantified economically. A number of forest management planning strategies varying in the amount of water, carbon, and timber targets and flows as constraints are developed and implemented in a linear programming (LP) environment. The outputs of each strategy are evaluated with a number of performance indicators such as standing timber volume, ending forest inventory, area harvested, and net present value (NPV) of water, timber, and carbon over time. Results showed that the cycling time of forest stands for renewal has important implications for timber, water, and carbon values. The management strategies indicated that net carbon sequestration can be attained at a significant cost in terms of foregone timber harvest and financial returns. The standing timber volumes and ending forest inventories were among the most important factors determining whether the forest constitutes a net carbon sink or source. Finally, the interactions among the forest values were generally found to be complementary, yet sometimes contradictory (i.e., negatively affecting each other), depending on the assumed relationship between forest values and stand structure.     

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.     

Deterministic and Stochastic Simulations for Solid Waste Collection Systems – A SWIM Approach

The SWIM model is the first systems model in Australia that deals with integrated waste management systems. The main modelling approach adopted is simulation, which is based on both deterministic and stochastic models for collection systems.These models are described in this paper, after a number of modelling approaches are reviewed. An example of the application of the SWIM model is given, and planned extensions to the SWIM model are briefly outlined.     

Combinatorial optimization of elk habitat effectiveness and timber harvest volume

Forest resource planning processes in the western United States have been placing an increasing emphasis on wildlife and fish habitat goals. With this in mind, we developed a method that incorporates a Habitat Effectiveness Index (HEI) for Roosevelt elk (Cervus elaphus roosevelti) into the objective function of a mathematical forest planning model. In addition, a commodity production goal is proposed (maximum timber production), and the habitat and commodity production goals are allowed to act as goals in a multi-objective goal programming planning problem. A heuristic programming technique (tabu search) is used to develop feasible solutions to the resulting non-linear, integer programming problem. Using a hypothetical example, we illustrate results of five scenarios, where the emphasis of the achievement of one or both goals is altered. The main contribution of this approach is the ability to measure and evaluate the trade-offs among achieving a certain level of a complex wildlife goal and achieving commodity production goals. These trade-offs are measured using a flexible model, allowing planners to formulate non-linear spatial goals as objectives of a problem, rather than forcing them to rely on posterior evaluations of the suitability of management plans to goals such as elk HEI.     

Multi-stand Forest Management under a Climatic Risk: Do Time and Risk Preferences Matter?

We propose a stochastic dynamic programming framework to model the management of a multi-stand forest under climate risk (strong wind occurrence). The preferences of the forest-owner are specified by a non-expected utility in order to separately analyze intertemporal substitution and risk aversion effects. A numerical method is developed to characterize the optimal forest management policies and the optimal consumption-saving strategy. The stochastic dynamic programming framework is applied to a non-industrial private forest-owner located in North-East of France. We show that the optimal decisions both depend upon risk and time preferences. The authors would like to thank participants at the international conference on Economics of Sustainable Forest Management in Toronto, at the PARIS 1 seminar on Environmental and Natural Resource Economics, at the 2004 Applied Microeconomics Conference in Lille and at the 13th annual conference of the European Association of Environmental and Resource Economists at Budapest.     

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?”     

Estimation of Water Demand in Iran Based on SARIMA Models

The generation of synthetic, residential water demands that can reproduce essential statistical features of historical residential water consumption is essential for planning, design, and operation of water resource systems. Most residential water consumption series are seasonal and nonstationary. We employ the seasonal autoregressive integrated moving average (SARIMA) model. We fit this model to monthly residential water consumption in Iran from May 2001 to March 2010. We find that a three-parameter log-logistic distribution fits the model residuals adequately. We forecast values for 1 year ahead using the fitted SARIMA model.     

A Mathematical Framework for Resilience: Dynamics,Uncertainties, Strategies,and Recovery Regimes

Resilience is a rehashed concept in natural hazard management—resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to “normal” after any perturbation. What formal flesh can we put on such a malleable notion? We propose to frame the concept of resilience in the mathematical garbs of control theory under uncertainty. Our setting covers dynamical systems both in discrete or continuous time, deterministic or subject to uncertainties. We will say that a system state is resilient if there exists an adaptive strategy such that the generated state and control paths, contingent on uncertainties, lay within an acceptable domain of random processes, called recovery regimes. We point out how such recovery regimes can be delineated thanks to so-called risk measures, making the connection with resilience indicators. Our definition of resilience extends others, be they “à la Holling” or rooted in viability theory. Indeed, our definition of resilience is a form of controllability for whole random processes (regimes), whereas others require that the state values must belong to an acceptable subset of the state set.     

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.