Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty

In this study, a fuzzy two-stage quadratic programming (FTSQP) method is developed for planning waste-management systems under uncertainty. It incorporates approaches of fuzzy quadratic programming and two-stage stochastic programming within a general optimization framework, to better reflect uncertainties expressed as probability-density and fuzzy-membership functions. The FTSQP can be used for analyzing various policy scenarios that are associated with different levels of economic penalties when the promised policy targets are violated. Moreover, using fuzzy quadratic terms rather than linear ones, the proposed method can improve upon the existing fuzzy linear programs through (a) more effectively optimizing the general satisfaction of the objective and constraints, (b) minimizing the variation of satisfaction degrees among the constraints and leading to more robust solutions, and (c) reflecting the trade-off between the system cost and the constraint-violation risk. The developed method is applied to a case study of municipal solid waste management. The results indicate that reasonable solutions have been generated. They will allow in-depth analyses of trade-offs between environmental and economic objectives as well as those between system cost and decision-maker's satisfaction degree.     

Inexact two-phase fuzzy programming and its application to municipal solid waste management

In this study, an inexact two-phase fuzzy programming approach was proposed for municipal solid waste management. Through introducing multiple control variables, objective function and constraints of the management model were relaxed under different levels, and compromised decision schemes with a high satisfactory level can be expected. Compared to the previous studies, it showed sound capability in identifying key factors and/or input conditions that may significantly affect system outputs, and thus facilitating the decision maker adjusting current system status to benefit the future management. A MSW management problem was provided to demonstrate the performance of the approach. Special parameters having significant or no impact on system performance were specified, which were then respectively changed to constitute two scenarios. The scenario analysis proved the accuracy of the model in identifying key factors. It was also found that the average satisfactory level of optimal solutions from the two-phase model was [0.287, 0.829], which was higher than that obtained from the conventional approach (i.e. [0.130, 0.804]), indicating the advantage of the proposed approach in searching for optimal solutions with high satisfactory level.     

A weight space-based approach to fuzzy multiple-objective linear programming

In this paper, the effects of uncertainty on multiple-objective linear programming models are studied using the concepts of fuzzy set theory. The proposed interactive decision support system is based on the interactive exploration of the weight space. The comparative analysis of indifference regions on the various weight spaces (which vary according to intervals of values of the satisfaction degree of objective functions and constraints) enables to study the stability and evolution of the basis that correspond to the calculated efficient solutions with changes of some model parameters.     

A multistage fuzzy-stochastic programming model for supporting sustainable water-resources allocation and management

In this study, a multistage fuzzy-stochastic programming (MFSP) model is developed for tackling uncertainties presented as fuzzy sets and probability distributions. A vertex analysis approach is proposed for solving multiple fuzzy sets in the MFSP model. Solutions under a set of α-cut levels can be generated by solving a series of deterministic submodels. The developed method is applied to the planning of a case study for water-resources management. Dynamics and uncertainties of water availability (and thus water allocation and shortage) could be taken into account through generation of a set of representative scenarios within a multistage context. Moreover, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The modeling results can help to generate a range of alternatives under various system conditions, and thus help decision makers to identify desired water-resources management policies under uncertainty.     

Fuzzy parametric programming model for multi-objective integrated solid waste management under uncertainty

Solid waste management is increasingly becoming a challenging task for the municipal authorities due to increasing waste quantities, changing waste composition, decreasing land availability for waste disposal sites and increasing awareness about the environmental risk associated with the waste management facilities. The present study focuses on the optimum selection of the treatment and disposal facilities, their capacity planning and waste allocation under uncertainty associated with the long-term planning for solid waste management. The fuzzy parametric programming model is based on a multi-objective, multi-period system for integrated planning for solid waste management. The model dynamically locates the facilities and allocates the waste considering fuzzy waste quantity and capacity of waste management facility. The model addresses uncertainty in waste quantity as well as uncertainties in the operating capacities of waste management facilities simultaneously. It was observed that uncertainty in waste quantity is likely to affect the planning for waste treatment/disposal facilities more as compared with the uncertainty in the capacities of the waste management facilities. The relationship between increase in waste quantity and increase in the total cost/risk involved in waste management is found to be nonlinear. Therefore, it is possible that a marginal change in waste quantity could increase the total cost/risk substantially. The information obtained from the analysis of modeling results can be effectively used for understanding the effect of changing the priorities and objectives of planning decisions on facility selections and waste diversions.     

A two-stage programming approach for water resources management under randomness and fuzziness

In this study, a fuzzy stochastic two-stage programming (FSTP) approach is developed for water resources management under uncertainty. The concept of fuzzy random variable expressed as parameters’ uncertainties with both stochastic and fuzzy characteristics was used in the method. FSTP has advantages in uncertainty reflection and policy analysis. FSTP integrates the fuzzy robust programming, chance-constrained programming and two-stage stochastic programming (TSP) within a general optimization framework. FSTP can incorporate pre-regulated water resources management policies directly into its optimization process. Thus, various policy scenarios with different economic penalties (when the promised amounts are not delivered) can be analyzed. FSTP is applied to a water resources management system with three users. The results indicate that reasonable solutions were generated, thus a number of decision alternatives can be generated under different levels of stream flows, α-cut levels and different levels of constraint-violation probability. The developed FSTP was also compared with TSP to exhibit its advantages in dealing with multiple forms of uncertainties.     

An optimization model design for energy systems planning and management under considering air pollution control in Tangshan City,China

In this study, an interval-parameter fuzzy programming mixed integer programming method (IFMIP) is designed for supporting the planning of energy systems management (ESM) and air pollution mitigation control under multiple uncertainties. The IFMIP-ESM model is based on an integration of interval-parameter programming (IPP), fuzzy programming (FP), and mixed-integer programming (MIP), which can reflect multiple uncertainties presented as both interval values and fuzzy distributions numbers. Moreover, it can successfully identify dynamics of capacity expansion schemes, reflect dual dynamics in terms of interval membership function, and analyze various emission-mitigation scenarios through incorporating energy and environmental policies. The designed model is applied to a case of energy systems management in Tangshan City, China, and the results indicate that reasonable solutions obtained from the model would be helpful for decision makers to effectively (a) adjust the allocation patterns of energy resources and transform the patterns of energy consumption and economic development, (b) facilitate the implement of air pollution control action plan, and (c) analysis dynamic interactions among system cost, energy-supply security, and environmental requirement.     

Development of an optimization model for water resources systemsplanning

A number of inexact fuzzy programming methods have been developed for the planning of water-resources-management systems under uncertainty. However, most of them do not allow the parameters in the objective and constraints of a programming problem to be functional intervals (i.e., the lower and upper bounds of the intervals are functions of impact factors). In this study, an interval fuzzy bi-infinite De Novo programming (IFBDP) method is developed in response to the above concern. A case study is also conducted; the solutions are then compared with those obtained from inexact De Novo programming (IDNP) and interval-fuzzy De Novo programming (IFDNP) that takes no account of bi-infinite programming. It is indicated that the IFBDP method can generate more reliable solutions with a lower risk of system failure due to the possible constraints violation and provide a more flexible management planning since the budgets availability can be adjusted with the variations in water price. These solutions are more flexible than those identified through IFDNP since the tolerance intervals are introduced to measure the level of constraints satisfaction. Moreover, it can be used for analyzing various scenarios that are associated with different levels of economic consequences under uncertainty.     

An intuitionistic fuzzy goal programming approach for finding pareto-optimal solutions to multi-objective programming problems

Multi-objective optimization in the intuitionistic fuzzy environment is the process of finding a Pareto-optimal solution that simultaneously maximizes the degree of satisfaction and minimizes the degree of dissatisfaction of an intuitionistic fuzzy decision. In this paper, a new method for solving multi-objective programming problems is developed that unlike other methods in the literature, provides compromise solutions satisfying both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. This method combines the advantages of the intuitionistic fuzzy sets concept, goal programming, and interactive procedures, and supports the decision maker in the process of solving programming problems with crisp, fuzzy, or intuitionistic fuzzy objectives and constraints. A characteristic of the proposed method is that it provides a well-structured approach for determining satisfaction and the dissatisfaction degrees that efficiently uses the concepts of violation for both objective functions and constraints. Another feature of the proposed method comes from its continuous interaction with the decision maker. In this situation, through adjusting the problem's parameters, the decision maker would have the ability of revisiting the membership and non-membership functions. Therefore, despite the lack of information at the beginning of the solving process, a compromise solution that satisfies the decision maker's preferences can be obtained. A further feature of the proposed method is the introduction of a new two-step goal programming approach for determining the compromise solutions to multi-objective problems. This approach ensures that the compromise solution obtained during each iterative step satisfies both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The application of the proposed model is also discussed in this paper.     

Site selection in waste management by the VIKOR method using linguistic assessment

Site selection is an important issue in municipal solid waste (MSW) management. Selection of the appropriate solid waste site is an extensive evaluation process that requires consideration of multiple alternative solutions and evaluation criteria. In reality, it is easier for decision makers to express their judgments on the alternatives by using linguistic terms, and there usually exists uncertain and incomplete assessment information. Moreover, decision makers may have different risk attitudes in the siting process because of their different backgrounds and personalities. Therefore, an attitudinal-based interval 2-tuple linguistic VIKOR (ITL-VIKOR) method is proposed in this paper to select the best disposal site for MSW. The feasibility and practicability of the proposed method are further demonstrated through an example of refuse-derived fuel (RDF) combustion plant location. Results show that the new approach is more suitable and effective to handle the MSW site selection problems by considering the decision maker's attitudinal character and incorporating the uncertain and incomplete assessment information.     

Identification of filter management strategy in fluid power systems under uncertainty: an interval-fuzzy parameter integer nonlinear programming method

An interval-fuzzy integer nonlinear programming (IFINP) method is developed for the identification of filter allocation and replacement strategies in a fluid power system (FPS) under uncertainty. It can handle uncertainties expressed as interval-fuzzy values that exist in the left- and right-hand sides of constraints as well as in the objective function. The developed method is applied to a case of planning filter allocation and replacement strategies under uncertainty for a FPS with a single circuit. A piecewise linearisation approach is used to convert the nonlinear problem of FPS into a linear one. The generated fuzzy solutions will be used to analyse and interpret the multiple decision alternatives under various system conditions, and thus help decision-makers to make a compromise among the system contamination level, system cost, satisfaction degrees and system-failure risks under different contaminant ingression/generation rates. The results demonstrate that the suction and return filters can effectively reduce the contamination level associated with a low system cost, but the FPS will take lots of failure risk when the contaminant ingression/generation rate is high; and the combination of suction and pressure filters can bring the lowest system cost with more security instead. Furthermore, comparisons for the optimised solutions are made among IFINP, interval-parameter integer nonlinear programming and deterministic linear programming also. Generally, the IFINP method can effectively reduce the total design and operation cost of the filtration system when contaminants ingression/generation rate is high, and it could be extended to the lubricating system.     

Multiproduct aggregate production planning with fuzzy demands and fuzzy capacities

Given the uncertain market demands and capacities in production environment, this paper discusses some practical approaches to modeling multiproduct aggregate production planning problems with fuzzy demands, fuzzy capacities, and financial constraints. By formulating the fuzzy demand, fuzzy equation, and fuzzy capacities, a fuzzy production-inventory balance equation for single period and a dynamic balance equation are formulated as fuzzy/soft equations and they represent the possibility levels of meeting the market demands. Using this formulation and interpretation, a fuzzy multiproduct aggregate production planning model is developed, and its solutions using parametric programming, best balance and interactive techniques are introduced to cater to different scenarios under various decision making preferences. Using the proposed models and techniques, first, the decision maker can select a preferred production plan with a common satisfaction level or different combinations of preferred possibility level and satisfaction levels, according to the market demands and available production capacities, and second, the obtained structure of the optimal solution can help decision maker in aggregate production planning. The decision maker can also make a preferred and reasonable production plan corresponding to one's most concerned criteria. Hence, decision makers not only can come up with a reasonable aggregate production plan with minimum efforts, but also have more choices of making a preferred aggregate plan based on his most concerned criteria. These models can effectively enhance the capability of an aggregate plan to give feasible family disaggregation plans under different scenarios with fuzzy demands and capacities. Simulation and the results of analysis on the proposed techniques are also given in detail in this paper.     

Identifying and eliminating dominated alternatives in multi-attribute decision making with intuitionistic fuzzy information

Multi-attribute decision making under uncertainty is a usual task in our daily life. In the decision making process, the decision information provided by the decision maker (or expert) over alternatives may take the form of intuitionistic fuzzy numbers, and the weight information on attributes is usually incomplete. To this issue, we first transform the original decision matrix, whose elements are intuitionistic fuzzy numbers expressed by pairs of satisfaction degrees and dissatisfaction degrees, into its expected decision matrix, whose elements are composed of satisfaction degrees and hesitation degrees. We introduce the concept of dominated alternative, and give a method to identify the dominated alternatives. Then we develop an interactive method for eliminating any dominated alternatives by updating the decision maker's preferences gradually so as to find out the optimal one eventually. A further extension of the interactive method to interval-valued intuitionistic fuzzy situations is given, and the solution process of this interactive method is shown in detail through an illustrative example.     

An integrated optimization approach and multi-criteria decision analysis for supporting the waste-management system of the City of Beijing,China

An inexact chance-constrained mixed-integer linear programming (ICMILP) model was provided for supporting long-term planning of solid waste management in the City of Beijing, China. The model was formulated by integrating interval-parameter, mixed-integer, and chance-constrained programming methods into a general framework, and effectively dealing with multiple uncertainties associated with model parameters and constraints. Three scenarios were examined for waste management in Beijing: scenario 1 is designed according to the current situation of waste management in the city, which has the lowest diversion rate among the three scenarios; scenario 2 is based on the balance between a long-term planning objective and the current situation with the medium diversion rate; and scenario 3 is based on a long-term planning objective which has the highest diversion rate among the three scenarios. Results from the model indicate that a solution with a lower significance level would lead to a higher system reliability and system cost; conversely, a desire for reducing system cost would result in an increased risk of violating the constraints. The solutions associate with these three scenarios show that scenario 1 has the lowest system cost, but also the lowest diversion rate. A landfill’s lifespan may be prolonged by 5 and by 7 years under scenarios 2 and 3, respectively. A fuzzy MCDA model was applied for analyzing the optimal solutions among the three alternatives. With consideration of landfill lifespan, system cost, diversion rate, and public satisfaction, the results from the fuzzy MCDA method illustrate that scenario 3, which has the highest diversion rate and system cost, is the most favorable scheme for supporting the waste-management system in Beijing, and scenario 1, which has the lowest diversion rate and net system cost, is the least favorable solution among the different scenarios.     

ESTIMATION OF SOLID WASTE BIOMETHANIZATION: DEVELOPMENT OF NOVEL METHODOLOGY AND ANFIS MODELS

This article presents the application of a technique of artificial intelligence (AI) that explores the possibility of using a model to estimate the biomethanization of municipal solid waste (MSW). The model uses data from an experiment in which MSW is anaerobically digested under three different moisture regimes by leachate recycling. A method utilizing a neurofuzzy inference system is used because AI systems have a high capacity for empiric learning.

Considering the importance of finding an effective selection of the most valuable variables for the model, this methodology includes the following techniques: Exhaustive Search (or brute-force search); Stepwise, a step-by-step regression method; and the use of Expert Knowledge. With the use of the fuzzy logic toolbox (MATLAB®), nine models were generated. However, when a case study is used to detail the method, the proposed methodology can also be used with any other system with a set of input and output data.     

A two-phase approach for multi-objective programming problems with fuzzy coefficients

In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM.     

Decider: A fuzzy multi-criteria group decision support system

Multi-criteria group decision making (MCGDM) aims to support preference-based decision over the available alternatives that are characterized by multiple criteria in a group. To increase the level of overall satisfaction for the final decision across the group and deal with uncertainty in decision process, a fuzzy MCGDM process (FMP) model is established in this study. This FMP model can also aggregate both subjective and objective information under multi-level hierarchies of criteria and evaluators. Based on the FMP model, a fuzzy MCGDM decision support system (called Decider) is developed, which can handle information expressed in linguistic terms, boolean values, as well as numeric values to assess and rank a set of alternatives within a group of decision makers. Real applications indicate that the presented FMP model and the Decider  software are able to effectively handle fuzziness in both subjective and objective information and support group decision-making under multi-level criteria with a higher level of satisfaction by decision makers.     

A novel credibility-based group decision making method for Enterprise Architecture scenario analysis using Data Envelopment Analysis

Analysis and selection of Enterprise Architecture (EA) scenarios is a difficult and complex decision making process directly effecting the long-term business strategies realization. This complexity is associated with contradictory objectives and significant uncertainties involved in analysis process. Although a large body of intuitive and analytical models for EA analysis has evolved over the last few years, none of them leads to an efficient and optimized ranking in fuzzy environments. Moreover, it is necessary to simultaneously employ some complementary methods to reflect the ambiguity and vagueness as the main sources of uncertainty. This paper incorporates the concept of Data Envelopment Analysis (DEA) model into EA scenario analysis through a group analysis under uncertain conditions. To resolve the vagueness and ambiguity of the EA analysis, fuzzy credibility constrained programming and p-robustness technique are applied, respectively. Not only is the proposed DEA model linear, robust, and flexible in aggregating experts’ opinion in a group decision making process, but it also is successful in discrimination power improvement – a major shortcoming associated with classic DEA model. The proposed model provides useful solutions to support decision making process for large-scale Information Technology (IT) development planning.     

A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning

In this study a hybrid (including qualitative and quantitative objectives) fuzzy multi objective nonlinear programming (H-FMONLP) model with different goal priorities will be developed for aggregate production planning (APP) problem in a fuzzy environment. Using an interactive decision making process the proposed model tries to minimize total production costs, carrying and back ordering costs and costs of changes in workforce level (quantitative objectives) and maximize total customer satisfaction (qualitative objective) with regarding the inventory level, demand, labor level, machines capacity and warehouse space. A real-world industrial case study demonstrates applicability of proposed model to practical APP decision problems. GENOCOP III (Genetic Algorithm for Numerical Optimization of Constrained Problems) has been used to solve final crisp nonlinear programming problem.     

Interactive multiobjective fuzzy random programming through the level set-based probability model

This paper considers a multiobjective linear programming problem involving fuzzy random variable coefficients. A new fuzzy random programming model is proposed by extending the ideas of level set-based optimality and a stochastic programming model. The original problem involving fuzzy random variables is transformed into a deterministic equivalent problem through the proposed model. An interactive algorithm is provided to obtain a satisficing solution for a decision maker from among a set of newly defined Pareto optimal solutions. It is shown that an optimal solution of the problem to be solved iteratively in the interactive algorithm is analytically obtained by a combination of the bisection method and the simplex method.