Grey fuzzy integer programming: An application to regional waste management planning under uncertainty (original) (raw)
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Waste Management & Research, 1997
In this paper, a grey integer-programming (GIP) formulation for the capacity planning of an integrated waste management system under uncertainty is applied to a North American case study. The GIP model is formulated by introducing concepts of grey systems and grey decisions into a mixed integer linear programming (MILP) framework. The approach has an advantage in that uncertain information (presented as interval numbers) can be effectively communicated into the optimization processes and resulting solutions, such that feasible decision alternatives can be generated through interpretation and analysis of the grey solutions according to projected applicable system conditions. Moreover, the GIP solution algorithm does not lead to more complicated intermediate models, and thus has lower computational requirements than other integer-programming methods that deal with uncertainties.
Fuzzy Sets and Systems, 1997
Various deterministic mathematical programming models were developed to evaluate single objective or multiple objectives planning alternatives for municipal solid waste management. The common objective of minimizing the present value of overall management cost/benefit was extended to deal explicitly with environmental considerations, such as air pollution, traffic flow limitation, and leachate and noise impacts. But uncertainty plays an important role in the search for sustainable solid waste management strategies. This paper proposes a new approach a fuzzy interval multiobjective mixed integer programming (FIMOMIP) model for the evaluation of management strategies for solid waste management in a metropolitan region. In particular, it demonstrates how uncertain messages can be quantified by specific membership functions and combined through the use of interval numbers in a multiobjective analytical framework. @ 1997 Elsevier Science B.V.
Environmental Management, 2006
Solid waste management (SWM) is at the forefront of environmental concerns in the Lower Rio Grande Valley (LRGV), South Texas. The complexity in SWM drives area decision makers to look for innovative and forward-looking solutions to address various waste management options. In decision analysis, it is not uncommon for decision makers to go by an option that may minimize the maximum regret when some determinant factors are vague, ambiguous, or unclear. This article presents an innovative optimization model using the grey mini-max regret (GMMR) integer programming algorithm to outline an optimal regional coordination of solid waste routing and possible landfill/incinerator construction under an uncertain environment. The LRGV is an ideal location to apply the GMMR model for SWM planning because of its constant urban expansion, dwindling landfill space, and insufficient data availability signifying the planning uncertainty combined with vagueness in decision-making. The results give local decision makers hedged sets of options that consider various forms of systematic and eventbased uncertainty. By extending the dimension of decisionmaking, this may lead to identifying a variety of beneficial solutions with efficient waste routing and facility siting for the time frame of 2005 through 2010 in LRGV. The results show the ability of the GMMR model to open insightful scenario planning that can handle situational and data-driven uncertainty in a way that was previously unavailable. Research findings also indicate that the large capital investment of incineration facilities makes such an option less competitive among municipal options for landfills. It is evident that the investment from a municipal standpoint is out of the question, but possible public-private partnerships may alleviate this obstacle.
Waste Management, 2020
Long-term planning of municipal solid waste management systems is a complex decision making problem which includes a large number of decision layers. Since all different waste treatment and disposal processes will show different responses to each municipal solid waste component, it is necessary to separately evaluate all waste components for all processes. This obligation creates an obstacle in the programming of mass balances for long-term planning of municipal solid waste management systems. The development of an ideal mixed integer linear programming model that can simultaneously respond to all essential decision layers including waste collection, process selection, waste allocation, transportation, location selection, and capacity assessment has not been made possible yet due to this important modeling obstacle. According to the current knowledge of the literature, all mixed integer linear programming studies aiming to address this obstacle so far have had to restrict many different possibilities in their mass balances. In this study, a novel mixed integer linear programming model was formulated. ALOMWASTE, the new model structure developed in this study, was built to take into consideration different process, capacity, and location possibilities that may occur in complex waste management processes at the same time. The results obtained from a case study showed the feasibility of new mixed integer linear programming model obtained in this study for the simultaneous solution of all essential decision layers in an unrestricted mass balance. The model is also able to provide significant convenience for the multi-objective optimization of financial-environmental-social costs and the solution of some uncertainty problems of decision-making tools such as life cycle assessment.
Computational Intelligence and Neuroscience
The purpose of this study is to achieve a novel and efficient method for treating the interval coefficient linear programming (ICLP) problems. The problem is used for modeling an uncertain environment that represents most real-life problems. Moreover, the optimal solution of the model represents a decision under uncertainty that has a risk of selecting the correct optimal solution that satisfies the optimality and the feasibility conditions. Therefore, a proposed algorithm is suggested for treating the ICLP problems depending on novel measures such as the optimality ratio, feasibility ratio, and the normalized risk factor. Depending upon these measures and the concept of possible scenarios, a novel and effective analysis of the problem is done. Unlike other algorithms, the proposed algorithm involves an important role for the decision-maker (DM) in defining a satisfied optimal solution by using a utility function and other required parameters. Numerical examples are used for compari...
Fuzzy Waste Load Allocation Model: Application to a Case Study
Journal of Intelligent Systems, 2008
A fuzzy optimization model, developed earlier to address uncertainty due to imprecision in management goals in river water quality management problems, is applied to a case study in this paper by addressing uncertainty due to randomness implicitly through Monte Carlo simulations. Municipal and industrial effluents, characterized by their Biochemical Oxygen Demand (BOD) loads are considered as point sources of pollution and the Dissolved Oxygen (DO) level at specified checkpoints in the river stretch is taken as the single water quality indicator. Conflicting goals related to water quality and fraction removal levels are expressed as fuzzy sets with appropriate membership functions in the model. The fuzzy optimization model is solved for a number of simulated sets of inputs to obtain optimal solutions, thus generating a large set of optimal objective function values and associated decisions. This information is used to obtain waste-load allocation decisions for a specified level of reliability.
FSILP: Fuzzy-stochastic-interval linear programming for supporting municipal solid waste management
Journal of Environmental Management, 2011
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 fuzzystochastic 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.
Engineering Applications of Artificial Intelligence, 2003
This paper reports on an integration of multi-criteria decision analysis (MCDA) and inexact mixed integer linear programming (IMILP) methods to support selection of an optimal landfill site and a waste-flow-allocation pattern such that the total system cost can be minimized. Selection of a landfill site involves both qualitative and quantitative criteria and heuristics. In order to select the best landfill location, it is often necessary to compromise among possibly conflicting tangible and intangible factors. Different multi-objective programming models have been proposed to solve the problem. A weakness with the different multi-objective programming models used to solve the problem is that they are basically mathematical and ignore qualitative and often subjective considerations such as the risk of groundwater pollution as well as other environmental and socioeconomic factors which are important in landfill selection. The selection problem also involves a change in allocation pattern of waste-flows required by construction of a new landfill. A waste flow refers to the routine of transferring waste from one location in a city to another. In selection of landfill locations, decision makers need to consider both the potential sites that should be used as well as the allocation pattern of the waste-flow at different periods of time. This paper reports on our findings in applying an integrated IMILP/MCDA approach for solving the solid waste management problem in a prairie city. The five MCDA methods of simple weighted addition, weighted product, cooperative game theory, TOPSIS, and complementary ELECTRE are adopted to evaluate the landfill site alternatives considered in the solid waste management problem, and results from the evaluation process are presented.
Journal of the American Water Resources Association, 2006
This paper uses the grey fuzzy multiobjective programming to aid in decision making for the allocation of waste load in a river system under versatile uncertainties and risks. It differs from previous studies by considering a multicriteria objective function with combined grey and fuzzy messages under a cost benefit analysis framework. Such analysis technically integrates the prior information of water
Canadian Journal of Civil Engineering, 1996
A grey hop, skip, and jump (GHSJ) approach is developed and applied to the area of municipal solid waste management planning. The method improves upon existing modelling to generate alternative approaches by allowing uncertain information to be effectively communicated into the optimization process and resulting solutions. Feasible decision alternatives can be generated through interpretation of the GHSJ solutions, which are capable of reflecting potential system condition variations caused by the existence of input uncertainties. Results from a hypothetical case study indicate that useful solutions for the expansion planning of waste management facilities can be generated. The decision alternatives obtained from the GHSJ solutions may be interpreted and analyzed to internalize environmental-economic tradeoffs, which may be of interest to solid waste decision makers faced with difficult and controversial choices.