7,770 research outputs found

    Multistage scenario-based interval-stochastic programming for planning water resources allocation

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    In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit

    Shades of Grey: A Critical Review of Grey-Number Optimization

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    A grey number is an uncertain number with fixed lower and upper bounds but unknown distribution. Grey numbers find use in optimization to systematically and proactively incorporate uncertainties expressed as intervals plus communicate resulting stable, feasible ranges for the objective function and decision variables. This article critically reviews their use in linear and stochastic programs with recourse. It summarizes grey model formulation and solution algorithms. It advances multiple counter-examples that yield risk-prone grey solutions that perform worse than a worst-case analysis and do not span the stable feasible range of the decision space. The article suggests reasons for the poor performance and identifies conditions for which it typically occurs. It also identifies a fundamental shortcoming of grey stochastic programming with recourse and suggests new solution algorithms that give more risk-adverse solutions. The review also helps clarify the important advantages, disadvantages, and distinctions between risk-prone and risk-adverse grey-programming and best/worst case analysis

    Nonlinear Interval Parameter Programming Combined with Cooperative Games: a Tool for Addressing Uncertainty in Water Allocation Using Water Diplomacy Framework

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    This paper shows the utility of a new interval cooperative game theory as an effective water diplomacy tool to resolve competing and conflicting needs of water users from different sectors including agriculture, domestic, industry and environment. Interval parameter programming is applied in combination with cooperative game theoretic concepts such as Shapley values and the Nucleolus to provide mutually beneficial solutions for water allocation problems under uncertainty. The allocation problem consists of two steps: water resources are initially allocated to water users based on the Nash bargaining model and the achieved nonlinear interval parameter model is solved by transforming it into a problem with a deterministic weighted objective function. Water amounts and net benefits are reallocated to achieve efficient water usage through net benefit transfers. The net benefit reallocation is done by the application of different cooperative game theoretical methods. Then, the optimization problem is solved by linear interval programming and by converting it into a problem with two deterministic objective functions. The suggested model is then applied to the Zarrinehrud sub-basin, within Urmia Lake basin in Northwestern Iran. Findings suggest that a reframing of the problem using cooperative strategies within the context of water diplomacy framework - creating flexibility in water allocation using mutual gains approach - provides better outcomes for all competing users of water

    Energy and environmental systems planning under uncertainty-An inexact fuzzy-stochastic programming approach

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    In this study, an inexact fuzzy-stochastic energy model (IFS-EM) is developed for planning energy and environmental systems (EES) management under multiple uncertainties. In the IFS-EM, methods of interval parameter fuzzy linear programming (IFLP) and multistage stochastic programming with recourse (MSP) are introduced into a mixed-integer linear programming (MILP) framework, such that the developed model can tackle uncertainties described in terms of interval values, fuzzy sets and probability distributions. Moreover, it can reflect dynamic decisions for facility-capacity expansion and energy supply over a multistage context. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability, where three cases are considered based on different energy and environmental management policies. The results indicate that reasonable solutions have been generated. They are helpful for supporting: (a) adjustment or justification of allocation patterns of regional energy resources and services, (b) formulation of local policies regarding energy consumption, economic development and environmental protection, and (c) in-depth analysis of tradeoffs among system cost, satisfaction degree and environmental requirement under multiple uncertainties. (C) 2010 Elsevier Ltd. All rights reserved

    Water Resources Decision Making Under Uncertainty

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    Uncertainty is in part about variability in relation to the physical characteristics of water resources systems. But uncertainty is also about ambiguity (Simonovic, 2009). Both variability and ambiguity are associated with a lack of clarity because of the behaviour of all system components, a lack of data, a lack of detail, a lack of structure to consider water resources management problems, working and framing assumptions being used to consider the problems, known and unknown sources of bias, and ignorance about how much effort it is worth expending to clarify the management situation. Climate change, addressed in this research project (CFCAS, 2008), is another important source of uncertainty that contributes to the variability in the input variables for water resources management. This report presents a set of examples that illustrate (a) probabilistic and (b) fuzzy set approaches for solving various water resources management problems. The main goal of this report is to demonstrate how information provided to water resources decision makers can be improved by using the tools that incorporate risk and uncertainty. The uncertainty associated with water resources decision making problems is quantified using probabilistic and fuzzy set approaches. A set of selected examples are presented to illustrate the application of probabilistic and fuzzy simulation, optimization, and multi-objective analysis to water resources design, planning and operations. Selected examples include dike design, sewer pipe design, optimal operations of a single purpose reservoir, and planning of a multi-purpose reservoir system. Demonstrated probabilistic and fuzzy tools can be easily adapted to many other water resources decision making problems.https://ir.lib.uwo.ca/wrrr/1035/thumbnail.jp

    A two-stage inexact-stochastic programming model for planning carbon dioxide emission trading under uncertainty

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    In this study, a two-stage inexact-stochastic programming (TISP) method is developed for planning carbon dioxide (CO2) emission trading under uncertainty. The developed TISP incorporates techniques of interval-parameter programming (IPP) and two-stage stochastic programming (TSP) within a general optimization framework. The TISP can not only tackle uncertainties expressed as probabilistic distributions and discrete intervals, but also provide an effective linkage between the pre-regulated greenhouse gas (GHG) management policies and the associated economic implications. The developed method is applied to a case study of energy systems and CO2 emission trading planning under uncertainty. The results indicate that reasonable solutions have been generated. They can be used for generating decision alternatives and thus help decision makers identify desired GHG abatement policies under various economic and system-reliability constraints. (C) 2009 Elsevier Ltd. All rights reserved

    Interactive Two-Stage Stochastic fuzzy Rough Programming for Water Resources Management

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    This paper deals with a fuzzy programming approach for treating an interactive two-stage stochastic rough-interval water resource management. The approach has been developed by incorporating an interactive fuzzy resolution method within a rough two-stage stochastic programming framework. The approach can not only tackle dual rough intervals presented as an inexact boundary intervals that exist in the objective function and the left- and right-hand sides of the constraints that are associated with different levels of economic penalties when the promised policy targets are violated. 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 to conduct in depth analysis 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. A management example in terms of rough-intervals water resources allocation has been treated for the sake of applicability of the proposed approach

    Interval-Parameter Robust Minimax-regret Programming and Its Application to Energy and Environmental Systems Planning

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    In this study, an interval-parameter robust minimax-regret programming method is developed and applied to the planning of energy and environmental systems. Methods of robust programming, interval-parameter programming, and minimax-regret analysis are incorporated within a general optimization framework to enhance the robustness of the optimization effort. The interval-parameter robust minimax-regret programming can deal with uncertainties expressed as discrete intervals, fuzzy sets, and random variables. It can also be used for analyzing multiple scenarios associated with different system costs and risk levels. In its solution process, the fuzzy decision space is delimited into a more robust one through dimensional enlargement of the original fuzzy constraints; moreover, an interval-element cost matrix can be transformed into an interval-element regret matrix, such that the decision makers can identify desired alternatives based on the inexact minimax regret criterion. The developed method has been applied to a case study of energy and environmental systems planning under uncertainty. The results indicate that reasonable solutions have been generated

    Inexact fuzzy-stochastic constraint-softened programming - A case study for waste management

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    In this study, an inexact fuzzy-stochastic constraint-softened programming method is developed for municipal solid waste (MSW) management under uncertainty, The developed method can deal with multiple uncertainties presented in terms of fuzzy sets, interval values and random variables. Moreover, a number of violation levels for the system constraints are allowed. This is realized through introduction of violation variables to soften system constraints, such that the model's decision space can be expanded under demanding conditions. This can help generate a range of decision alternatives under various conditions, allowing in-depth analyses of tradeoffs among economic objective, satisfaction degree, and constraint-violation risk. The developed method is applied to a case study of planning a MSW management system. The uncertain and dynamic information can be incorporated within a multi-layer scenario tree; revised decisions are permitted in each time period based on the realized values of uncertain events. Solutions associated with different satisfaction degree levels have been generated, corresponding to different constraint-violation risks. They are useful for supporting decisions of waste flow allocation and system-capacity expansion within a multistage context. (C) 2008 Elsevier Ltd. All rights reserved
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