I-VFRP: An interval-valued fuzzy robust programming approach for municipal waste-management planning under uncertainty

In this study, an interval-valued fuzzy robust programming (I-VFRP) model has been developed and applied to municipal solid-waste management under uncertainty. The I-VFRP model can explicitly address system uncertainties with multiple presentations, and can directly communicate the waste manager's confidence gradients into the optimization process, facilitating the reflection of weak or strong confidence when subjectively estimating parameter values. Parameters in the I-VFRP model can be represented as either intervals or interval-valued fuzzy sets. Thus, variations of the waste manager's confidence gradients over defining parameters can be effectively handled through interval-valued membership functions, leading to enhanced robustness of the optimization efforts. The results of a theoretical case study indicate that useful solutions for planning municipal solid-waste-management practices can be generated. The waste manager's confidence gradients over various subjective judgments can be directly incorporated into the modeling formulation and solution process. The results also suggest that the proposed methodology can be applied to practical problems that are associated with complex and uncertain information.     

A fuzzy linear programming approach for municipal solid-waste management under uncertainty

In this study, a fuzzy linear programming (FLP) method is developed for dealing with uncertainties expressed as fuzzy sets that exist in the constraints’ left-hand and right-hand sides and the objective function. A direct transforming algorithm is advanced for solving the FLP model that improves upon the existing method through provision of a quantitative expression for uncertain relationships among a large number of fuzzy sets. The proposed solution method can greatly reduce computational requirements, which is particularly meaningful for the application of FLP to large-scale practical problems with many fuzzy sets. The developed FLP method is applied to a case of long-term waste-management planning. The results indicate that reasonable solutions have been obtained. They can be used for generating decision alternatives and to help managers identify desired policies for waste management under uncertainty. Compared with the conventional interval-parameter linear programming approach, FLP can provide more information for solutions, containing not only the lower and upper bounds but also the most possible value for decision variables and objective function.     

A hybrid interval-parameter fuzzy robust programming method and its application to filter management strategy in fluid power systems

An interval-parameter fuzzy robust programming (IFRP) method is developed for the assessment of filter allocation and replacement strategies in a fluid power system (FPS) under uncertainty. The developed IFRP can effectively handle the uncertainties expressed as fuzzy sets, interval values, and their combinations, which exist in contaminant ingression/generation of the system and contaminant-holding capacity of filter without making assumptions on their probabilistic distributions. 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, leading to enhanced robustness for the optimization process. Results indicate that the developed IFRP can not only help decision-maker to identify optimal filter allocation and replacement strategies to control the contamination level of FPS with a minimized system-cost and system-failure risk under multiple uncertainties, but also mitigate uncertainties through abating interval widths of the replacement periods and service life under different contamination ingression/generation rates.     

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.     

Part-period balancing with uncertainty: a fuzzy sets theory approach

The part-period balancing lot-sizing algorithm is modified to use fuzzy data for the single-stage lot-sizing problem. Triangular fuzzy numbers are used to represent uncertainty in the master production schedule. This paper shows that uncertain demand can be easily incorporated into the part-period balancing lot-sizing algorithm and that a fuzzy master production schedule can be used to determine production lot sizes. A detailed example is presented to illustrate the technique.     

A fuzzy chance-constrained programming model with type 1 and type 2 fuzzy sets for solid waste management under uncertainty

Effective management of municipal solid waste (MSW) is critical for urban planning and development. This study aims to develop an integrated type 1 and type 2 fuzzy sets chance-constrained programming (ITFCCP) model for tackling regional MSW management problem under a fuzzy environment, where waste generation amounts are supposed to be type 2 fuzzy variables and treated capacities of facilities are assumed to be type 1 fuzzy variables. The evaluation and expression of uncertainty overcome the drawbacks in describing fuzzy possibility distributions as oversimplified forms. The fuzzy constraints are converted to their crisp equivalents through chance-constrained programming under the same or different confidence levels. Regional waste management of the City of Dalian, China, was used as a case study for demonstration. The solutions under various confidence levels reflect the trade-off between system economy and reliability. It is concluded that the ITFCCP model is capable of helping decision makers to generate reasonable waste-allocation alternatives under uncertainties.     

基于遗传算法解决河流环境需水量优化调度的模糊多目标规划方法的研究

为实现城市受污染河流的环境需水量的合理调配,以各蓄水构筑物的调水量为决策变量,研究了在保证河流生态环境需求的基础上,实现整个流域的污染负荷的环境容量最大化、水量最大节约和调水成本最小化的方法,建立了环境需水调度的模糊多目标规划模型.模型中采用整合的非线性梯度隶属度函数作为目标函数,以遗传算法作为求解此模型的工具,并将该模型用于大庆市黎明河流域的环境水量调配,取得较好的效果.     

Forest harvesting planning under uncertainty: a cardinality-constrained approach

Harvesting planning (HP) is a key tactical decision in lumber supply chains. Harvesting areas in the forests are divided into different blocks with different types and quantities of raw materials (logs). Predicting the availability of raw materials in each block along with log demand is impossible in this industry. Hence, incorporating uncertainty into the HP problem is essential in order to obtain robust plans that do not drastically fluctuate in the presence of future perturbations in the forest and log market. In this paper, we propose a robust harvesting planning model formulated based on cardinality-constrained method. The latter provides some insights into the adjustment of the level of robustness of the harvesting plan over the planning horizon and protection against uncertainty. An extensive set of experiments based on Monte-Carlo simulation is also conducted in order to better validate the proposed robust optimisation approach.     

A multi-objective optimization model for hub network design under uncertainty: An inexact rough-interval fuzzy approach

This article proposes a multi-objective mixed-integer model to optimize the location of hubs within a hub network design problem under uncertainty. The considered objectives include minimizing the maximum accumulated travel time, minimizing the total costs including transportation, fuel consumption and greenhouse emissions costs, and finally maximizing the minimum service reliability. In the proposed model, it is assumed that for connecting two nodes, there are several types of arc in which their capacity, transportation mode, travel time, and transportation and construction costs are different. Moreover, in this model, determining the capacity of the hubs is part of the decision-making procedure and balancing requirements are imposed on the network. To solve the model, a hybrid solution approach is utilized based on inexact programming, interval-valued fuzzy programming and rough interval programming. Furthermore, a hybrid multi-objective metaheuristic algorithm, namely multi-objective invasive weed optimization (MOIWO), is developed for the given problem. Finally, various computational experiments are carried out to assess the proposed model and solution approaches.     

Duality in fuzzy linear programming: a survey

The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed and comprehensively and practically applied in an abundance of cases. Consequently, their joint application is highly appealing for both scholars and practitioners. However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent. For example, there are no consistent concepts of weak duality and strong duality. The contributions of this survey are (1) to provide the first comprehensive overview of literature results on duality in FLP, (2) to analyze these results in terms of research gaps in FLP duality theory, and (3) to show avenues for further research. We systematically analyze duality in fuzzy linear programming along potential fuzzifications of linear programs (fuzzy classes) and along fuzzy order operators. Our results show that research on FLP duality is fragmented along both dimensions; more specifically, duality approaches and related results vary in terms of homogeneity, completeness, consistency with crisp duality, and complexity. Fuzzy linear programming is still far away from a unifying theory as we know it from crisp linear programming. We suggest further research directions, including the suggestion of comprehensive duality theories for specific fuzzy classes while dispensing with restrictive mathematical assumptions, the development of consistent duality theories for specific fuzzy order operators, and the proposition of a unifying fuzzy duality theory.     

Maintenance supplier selection considering life cycle costs and risks: a fuzzy goal programming approach

In this study, we address a new variant of supplier selection problem named maintenance supplier selection problem faced by a manufacturer. The production system consists of different multi-component equipments whose maintenance activities require several components (parts) each of which could be provided by multiple suppliers. A multi-objective mathematical model is developed to decide about the supply base of each part as well as the purchasing quantity of each part from each selected supplier. The model accounts for the total life cycle costs of purchased parts and various risks threatening the candidate suppliers. A fuzzy/soft lexicographic goal programming approach with soft priorities between objectives is proposed to enable the decision-maker to make preferred trade-offs between objectives by which the effects of various risks in each phase of life cycle of procured parts are investigated. The capability and effectiveness of the proposed model is validated through a case study. Some sensitivity analyses are also carried out for investigating the impact of cost, risk and objectives’ priorities on the final preferred compromise solution. Finally, some managerial insights and concluding remarks are provided.     

Operation allocation and materials-handling system selection in a flexible manufacturing system: A sequential modelling approach

Materials-handling systems are an integrating component of manufacturing operations and as such must be considered within a common framework in manufacturing systems design. This work proposes a first approach to the simultaneous consideration of the operation allocation and the materials-handling system selection problems in a flexible manufacturing system. The objective of the operation allocation model is to select a group of machines where the operations of the part types will be performed and then to assign those operations to the selected machines. The operation allocation model interfaces with the materials-handling system selection model by providing input data in the form of the manufacturing operations to be performed at each machining centre. The selection of the materials-handling system is centred on the matching of the parts visiting a machining centre to perform a manufacturing operation and the abilities of the handling equipment to perform the required materials handling functions of those part types. The objective is to select an optimal group of materials-handling equipment to be assigned to a cell.     

Nonlinear vibration analysis of a rotor system with parallel and angular misalignments under uncertainty via a Legendre collocation approach

International Journal of Mechanics and Materials in Design - In this paper, the propagation of bounded uncertainties in the dynamic response of a misaligned rotor is investigated using a Legendre...     

Modeling uncertainty in risk assessment: An integrated approach with fuzzy set theory and Monte Carlo simulation

Modeling uncertainty during risk assessment is a vital component for effective decision making. Unfortunately, most of the risk assessment studies suffer from uncertainty analysis. The development of tools and techniques for capturing uncertainty in risk assessment is ongoing and there has been a substantial growth in this respect in health risk assessment. In this study, the cross-disciplinary approaches for uncertainty analyses are identified and a modified approach suitable for industrial safety risk assessment is proposed using fuzzy set theory and Monte Carlo simulation. The proposed method is applied to a benzene extraction unit (BEU) of a chemical plant. The case study results show that the proposed method provides better measure of uncertainty than the existing methods as unlike traditional risk analysis method this approach takes into account both variability and uncertainty of information into risk calculation, and instead of a single risk value this approach provides interval value of risk values for a given percentile of risk. The implications of these results in terms of risk control and regulatory compliances are also discussed.     

Long-term optimal allocation of hydro generation for a price-maker company in a competitive market: latest developments and a stochastic dual dynamic programming approach

Since the liberalisation of the power industry, there has been a large amount of literature on the determination of optimal bidding decisions for price-maker energy producers. The vast majority of the work developed so far has focused on short-term horizons and may be viewed as successful approaches for systems whose operation is generally deterministic. In the case of price-maker hydro plants with significant storage capacity, however, the solution of the strategic bidding problem is more subtle. The reason is that hydro reservoirs allow the bidder to postpone energy production if future prices are expected to be higher than the current price. This demands the management of an energy-constrained resource and determines a timecoupling characteristic to the problem, implying that the bidding strategy should ideally take into account the following stages and consider the stochasticity of inflows. These aspects characterise the strategic bidding for price-maker hydro agents as a multi-stage stochastic programming problem, with significant computational challenges. The objective of this work is to present a new methodology for the strategic bidding problem of a price-maker hydropower-based company, taking into account several hydro plants, time-coupling and stochastic inflow scenarios. The proposed approach considers a deterministic residual demand curve and is based on stochastic dual dynamic programming (SDDP), which has been successfully applied to the least-cost hydrothermal scheduling problem. Since the technique requires the problem to be concave, a piecewise linear approximation of the expected future benefit function is proposed. The application of the methodology is exemplified with a real case study based on the hydrothermal system of El Salvador.     

An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty

We present a robust optimization framework that is applicable to general nonlinear programs (NLP) with uncertain parameters. We focus on design problems with partial differential equations (PDE), which involve high computational cost. Our framework addresses the uncertainty with a deterministic worst-case approach. Since the resulting min–max problem is computationally intractable, we propose an approximate robust formulation that employs quadratic models of the involved functions that can be handled efficiently with standard NLP solvers. We outline numerical methods to build the quadratic models, compute their derivatives, and deal with high-dimensional uncertainties. We apply the presented approach to the parametrized shape optimization of systems that are governed by different kinds of PDE and present numerical results.     

A fuzzy knowledge based method for maintenance planning in a power system

The inspection planning in electric power industry is used to assess the safety and reliability of system components and to increase the ability of failure situation identification before it actually occurs. It reflects the implications of the available information on the operational and maintenance history of the system. The output is a ranked list of components, with the most critical ones at the top, which indicates the selection of the components to be inspected.In this paper, we demonstrate the use of a fuzzy relational database model for manipulating the data required for the criticality component ranking in thermal power systems inspection planning, incorporating criteria concerning aspects of safety and reliability, economy, variable operational conditions and environmental impacts. Often, qualitative thresholds and linguistic terms are used for the component criticality analysis. Fuzzy linguistic terms for criteria definitions along with fuzzy inference mechanisms allow the exploitation of the operators' expertise.The proposed database model ensures the representation and handling of the aforementioned fuzzy information and additionally offers to the user the functionality for specifying the precision degree by which the conditions involved in a query are satisfied.In order to illustrate the behavior of the model, a case study is given using real inspection data.     

一种新的扬声器功率测试系统设计及其不确定度分析

目的:为保证扬声器质量,研制了一种新的扬声器功率测试系统,并评估测试系统测量的准确性。方法:该系统以单片机作为中央处理器,采用直接数字频率合成技术提供输入信号,采用基于AD8436真有效值转换芯片的信号检测电路,测量信号经过A/D处理后发送至单片机,通过以太网通讯发给上位机进行扬声器功率的实时监测与分析,并对系统不确定度进行评定。结果:该测试系统的输出信号准确度优于0.01%,失真度小于0.5%,可以同时实现20路扬声器测试。结论:该系统在进行扬声器功率测试时,系统简单,准确度高,成本低,检测效率高,具有较高的实际应用价值。     

Topology optimization of tensegrity structures under compliance constraint: a mixed integer linear programming approach

A tensegrity structure is a prestressed pin-jointed structure consisting of discontinuous struts and continuous cables. For exploring new configurations of tensegrity structures, this paper addresses a topology optimization problem of tensegrity structures under the compliance constraint and the stress constraints. It is assumed that a cable loosens and loses the elongation stiffness when its tensile prestress vanishes due to the applied external load. It is shown that the topology optimization problem can be formulated as a mixed integer linear programming (MILP) problem. The proposed method does not require any connectivity information of cables and struts to be known in advance. Numerical experiments illustrate that various configurations of tensegrity structures can be found as the optimal solutions.