Fuzzy Multi-objective Optimization Model Research Articles

Fuzzy Multi-Objective Optimization Model of Basketball Lineup

Fuzzy Multi-Objective Optimization Model of Basketball Lineup

An integrated methodology for the selection of sustainable suppliers and order allocation problem with quantity discounts, lost sales and varying supplier availabilities

In this study, selection of sustainable suppliers (SSS) and order allocation (OA) problem is generalized by considering multi-product, multi-supplier and multi-period scenarios with quantity discounts, lost sales and varying supplier availabilities. The study is designed in four phases. In the first phase, suppliers are ranked by using integrated the Fuzzy Analytic Hierarchy Process (F-AHP) and fuzzy Preference Ranking Organization Method for Enrichment Evaluation (F-PROMETHEE) considering social and environmental factors as well as economic factors. The output of the first phase is used in the second phase of the method. In the second phase, a fuzzy multi-objective optimization (FMOO) model is proposed to find quantities to be purchased from suppliers. In the third phase, both the Augmented ε-constraint (AUGMECON) method and LP-metrics are used to obtain the Pareto front of the problem. Finally, in the fourth phase, a solution is selected by the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) from the non-dominated solutions. The effectiveness of the proposed method is shown on real data from a firm selling medical devices.

A new weighted fuzzy programming model for supplier selection and order allocation in the food industry

Purpose The purpose of this paper is to develop a combined intuitionistic fuzzy analytic hierarchy process (IFAHP) and fuzzy multi-objective optimization approach to select suppliers and allocate the orders to them in the bottled water production context. Design/methodology/approach First, the primary weights of criteria associated with the supplier selection problem are calculated using the IFAHP technique. Then a fuzzy multi-objective optimization model is developed to allocate the appropriate amount of orders to each supplier. Findings The proposed methodology has been successfully implemented in the case of an Iranian food company in its bottled water factory. Results demonstrate our model is capable of practically handling the uncertainty in DMs’ preference that leads to effective and efficient supplier selection and order allocation decisions. Originality/value The authors develop a novel hybrid decision-making tool to tackle the uncertainty in decision-makers’ opinions with a demonstrated applicability and some promising outcomes in efficiently allocating the order quantity to suppliers in the area of bottled water production.

Deterministic Analysis and Research on Reasonable Purchase Price Range Based on Multi - Objective Fuzzy Optimization Model

Reasonable purchase price has multiple objectives, it is necessary to take into account the increase in food and industry income, but also take into account the development of the entire grain industry, and even to consider improving production efficiency. This paper chooses the minimum purchase price of wheat, the market purchase price, the output and the grain income and the production efficiency as variables, and takes the lower limit of the grain and farmers’ income, the upper limit of the market price and the minimum purchase price, the supply and demand relationship, the inventory restriction, the financial support ability And the scope of international food price as constraints, establishing multi-objective fuzzy optimization model to explore the government’s optimal minimum purchase price decision-making mechanism. Through analysis, it was found that the minimum purchase price developed by the state did not increase the area of grain cultivation, but it effectively inhibited the reduction of grain planting area. Finally, we use this model to predict the minimum purchase price for food for 2017, with a reasonable range of: (115.52, 121.54).

Joint order allocation and transportation planning under uncertainty within a socially responsible supply chain

PurposeThis paper aims to propose an integrated supplier selection, order allocation, transportation planning model, along with investment planning for corporate social responsibility (CSR), over a given multi-period horizon under uncertainty. Furthermore, a customer’s behavior to pay more money for items with CSR attributes is considered in the total market demand.Design/methodology/approachThe objective functions, i.e. social value of purchasing, total profit (TP), total delivery lead-time, total air pollution, total water pollution and total energy consumption with regard to a number of constraints are jointly considered in a multi-product system. It is worth noting that operational- and sustainable-related parameters are usually vague and imprecise in this area. Therefore, this paper develops a new fuzzy multi-objective optimization model to capture this inherent fuzziness in critical data.FindingsThrough the numerical examples in the textile industry, the application of the model and usefulness of solution procedures are carried out. The numerical results obtained from the proposed approach indicate the efficiency of the solution algorithm in different instances. Moreover, the authors observe that social investment of the buyer, to stimulate market demand, can affect the TP and also involve the total contribution of suppliers in social responsibility.Originality/valueThis research work concentrates on providing a procurement and inventory model through the lens of sustainability to enable textile supply chain managers and related industries to apply the approach to their inventory control and supply management. Totally, the proposed methodology could be applied by many fabric buyers of textile industry tackling purchasing issues and attempting to perfect understanding of social supply chains.

Developing an optimal renewable electricity generation mix for China using a fuzzy multi-objective approach

To achieve China’s 2030 goals for renewable energy development, this paper proposes a constrained fuzzy multi-objective optimization (FMO) model to obtain the optimal generation mix of four kinds of renewable power: hydropower, wind power, photovoltaic (PV) power, and biomass power. The optimization results show that a) the optimal mix of accumulated installed capacity of renewable energy in China from 2017 to 2022 is hydropower > wind > PV > biomass, while that from 2023 to 2030 is PV > hydropower > wind > biomass; b) the accumulated installed capacity of PV has the fastest growth between 2017 and 2030, and PV power will replace hydropower as the largest renewable power source in 2023. However, hydropower remains the largest renewable power through 2030 in terms of on-grid power generation; c) these four kinds of renewable power generation can eliminate 34.9–37.5 billion tonnes of CO2 emissions by replacing coal-fired power generation, with hydropower contributing the most to the reduction; and d) Investment cost per kilowatt or the rate of power curtailment is not sensitive factor for optimal cumulative installed capacity. The results mean that China should promote PV power generation in a rapid but systematic manner while continuing to develop hydropower.

A hybrid MCDM-FMOO approach for sustainable supplier selection and order allocation

The growing interest in sustainability increases the challenges for decision makers in selecting the sustainable suppliers in which consider economic, environmental and social aspects. Particularly, decision makers are being increasingly motivated to improve their supply chain activities in coping efficiently with the objectives of sustainable development. Where the era of sustainability threatens the current supply chain partners to either cope with the new regulations of sustainability or leave the field for new players. Notwithstanding, most of the recent studies considered economic and green criteria in handling sustainable supplier selection and order allocation (SSS/OA) problems overlooking the social criteria which represents the third pillar of sustainability. This work aims at putting forward a hybrid Multi Criteria Decision-Making (MCDM)-Fuzzy Multi-Objective Optimization (FMOO) approach for a sustainable supplier selection and order allocation problem by considering economic, environmental and social criteria. Thus, an integrated Fuzzy AHP-Fuzzy TOPSIS is proposed to assess and rank suppliers according to three sets of criteria (i.e. conventional, green and social). A Multi-Objective Optimization Model (MOOM) is developed for choosing suppliers and allocating the optimal order quantities. To cope with the multiple uncertainties in the input data, the MOOM is reformulated into a Fuzzy Multi-Objective Optimization Model. The ε-constraint and LP-metrics approaches are used to reveal two sets of Pareto solutions based on the developed FMOOmodel. Finally, TOPSIS is applied to select the final Pareto solution that is closest to the ideal solution and furthest from the nadir solution. The effectiveness and the applicability of the developed hybrid MCDM-FMOO approach is demonstrated through a case study.

A fuzzy multi-objective optimization model for recoverable manufacturing systems in uncertain environments

ABSTRACTThis study develops a fuzzy multi-objective linear programming (FMOLP) model with an interactive two-phase possibilistic linear programming (ITPPLP) approach for solving remanufacturing production system problems with multiple goals in a fuzzy environment. Because the related parameters are imprecise/fuzzy in nature, a triangular possibility distribution can be used. The proposed model aims to simultaneously minimize total production costs and total lead time, while integrating multiple suppliers, multiple components, multiple time periods, and multiple machines to realize a remanufacturing production system. An air-conditioning compressor case was used to test the proposed models. The analytical results presented in this work will allow decision-making managers to better understand the systematic analysis, potential for cost-effectiveness and lead time of recoverable remanufacturing planning.

Research on optimization and performance of Na2HPO4·12H2O mixture system combining fuzzy optimization model based on analytic hierarchy process

ABSTRACTIn order to determine optimal salt hydrates matching and adding fraction of Na2HPO4 · 12H2O, crystal characteristics, latent heat of phase change, supercooling degree, and phase change temperature were studied. According to experimental data, optimal salt hydrates matching and adding fraction of Na2HPO4 · 12H2O are determined by adopting multi-objective fuzzy optimization model based on analytic hierarchy process. Aimed at 3% Na2SiO3 · 9H2O-Na2HPO4 · 12H2O optimized by the method, thermal cycling performance test is implemented. Test results show the following: the Na2SiO3 · 9H2O-Na2HPO4 · 12H2O system has lower supercooling degree than Na2HPO4 · 12H2O. It forms stable crystal after multiple thermal cycles, the phase separation is eliminated completely, and supercooling degree is 3.6°C. Latent heat of phase change maintains at 164 J/g after 100 thermal cycles. It is a modified intermediate product of salt hydrates with development potential.

An integrated fuzzy MOORA method and FMEA technique for sustainable supplier selection considering quantity discounts and supplier's risk

Abstract Supplier selection is a complex process and plays a signification role in promoting the sustainable supply chain. In this study, a fuzzy multi-objective optimization model based on the ratio analysis (fuzzy MOORA) is applied to evaluate the supplier's overall performance. In reality, suppliers face risks like natural calamity or political variability. Hence, failure mode and effects analysis (FMEA) is implemented to evaluate the risks of a supplier. Moreover, a novel multi-objective mathematical model is developed to consider supplier's sustainability and order allocation simultaneously. The efficiency and applicability of the proposed approach is shown by a case study of the evaporative cooler in the home appliance industry. The current approach can be implemented in many manufacturing industries such as electrical, automotive and chemical. The results show that by employing the proposed model not only potent to increase total profit but also decrease the amount of risks which imposes on the sustainability.

Analysis of the Potential Impacts on China’s Industrial Structure in Energy Consumption

Industrial structure is one of the main factors that determine energy consumption. Based on China’s energy consumption in 2015 and the goals in 13th Five-Year Plan for Economic and Social Development of the People’s Republic of China (The 13th Five-Year Plan), this paper established an input–output fuzzy multi-objective optimization model to estimate the potential impacts of China’s industrial structure on energy consumption in 2015. Results showed that adjustments to industrial structure could save energy by 19% (1129.17 million ton standard coal equivalent (Mtce)). Second, China’s equipment manufacturing industry has a large potential to save energy. Third, the development of several high energy intensive and high carbon intensive sectors needs to be strictly controlled, including Sector 25 (electricity, heat production, and supply industry), Sector 11 (manufacture of paper and stationery, printing), and Sector 14 (non-metallic mineral products industry). Fourth, the territory industry in China has a great potential for energy saving, while its internal structure still needs to be upgraded. Finally, we provide policy suggestions that may be adopted to reduce energy consumption by adjusting China’s industrial structure.

A fuzzy hybrid integrated framework for portfolio optimization in private banking

Decision-making processes in private banking must comply with standards for risk management and transparency enforced by banking regulations. Therefore, investors must be supported throughout a risk-informed decision process. This paper contributes to the literature by presenting a hybrid integrated framework that considers personal features of the investor and additional characteristics imposed by regulations, for which linguistic evaluations are used with regard to risk exposure. The proposed approach for personal investment portfolios considers legal aspects and investor’s preferences as an input to the novel fuzzy multiple-attribute decision making approach for sorting problems proposed in this paper, called FTOPSIS-Class. Then, the next step of the proposed framework uses the sorting results for a fuzzy multi-objective optimization model that considers the risk and return associated with the investor’s profile over three objectives. The contributions of this paper are illustrated and validated by using a numerical application in line with a new trend for modern portfolio theory which enables a real world investor’s characteristics to be considered throughout the decision-making process.

A sustainable manufacturing system design: A fuzzy multi-objective optimization model.

In the past decade, there has been a growing concern about the environmental protection in public society as governments almost all over the world have initiated certain rules and regulations to promote energy saving and minimize the production of carbon dioxide (CO2) emissions in many manufacturing industries. The development of sustainable manufacturing systems is considered as one of the effective solutions to minimize the environmental impact. Lean approach is also considered as a proper method for achieving sustainability as it can reduce manufacturing wastes and increase the system efficiency and productivity. However, the lean approach does not include environmental waste of such as energy consumption and CO2 emissions when designing a lean manufacturing system. This paper addresses these issues by evaluating a sustainable manufacturing system design considering a measurement of energy consumption and CO2 emissions using different sources of energy (oil as direct energy source to generate thermal energy and oil or solar as indirect energy source to generate electricity). To this aim, a multi-objective mathematical model is developed incorporating the economic and ecological constraints aimed for minimization of the total cost, energy consumption, and CO2 emissions for a manufacturing system design. For the real worldscenario, the uncertainty in a number of input parameters was handled through the development of a fuzzy multi-objective model. The study also addresses decision-making in the number of machines, the number of air-conditioning units, and the number of bulbs involved in each process of a manufacturing system in conjunction with a quantity of material flow forprocessed products. A real case study was used for examining the validation and applicability of the developed sustainable manufacturing system model using the fuzzy multi-objective approach.

A systematic decision making approach for product conceptual design based on fuzzy morphological matrix

Conceptual design plays an important role in development of new products and redesign of existing products. Morphological matrix is a popular tool for conceptual design. Although the morphological-matrix based conceptual design approaches are effective for generation of conceptual schemes, quantitative evaluation to each of the function solution principle is seldom considered, thus leading to the difficulty to identify the optimal conceptual design by combining these function solution principles. In addition, the uncertainties due to the subjective evaluations from engineers and customers in early design stage are not considered in these morphological-matrix based conceptual design approaches. To solve these problems, a systematic decision making approach is developed in this research for product conceptual design based on fuzzy morphological matrix to quantitatively evaluate function solution principles using knowledge and preferences of engineers and customers with subjective uncertainties. In this research, the morphological matrix is quantified by associating the properties of function solution principles with the information of customer preferences and product failures. Customer preferences for different function solution principles are obtained from multiple customers using fuzzy pairwise comparison (FPC). The fuzzy customer preference degree of each solution principle is then calculated by fuzzy logarithmic least square method (FLLSM). In addition, the product failure data are used to improve product reliability through fuzzy failure mode effects analysis (FMEA). Unlike the traditional FMEA, the causality relationships among failure modes of solution principles are analyzed to use failure information more effectively through constructing a directed failure causality relationship diagram (DFCRD). A fuzzy multi-objective optimization model is also developed to solve the conceptual design problem. The effectiveness of this new approach is demonstrated using a real-world application for conceptual design of a horizontal directional drilling machine (HDDM).

Fuzzy multi-objective modeling of effectiveness and user experience in online advertising

The focus placed on maximizing user engagement in online advertising negatively affects the user experience because of advertising clutter and increasing intrusiveness. An intelligent decision support system providing balance between user experience and profits from online advertising based on the fuzzy multi-objective optimization model is presented in this paper. The generalized mathematical model uses uncertain parameters for content descriptors that are difficult to be precisely defined and measured, such as the level of intrusiveness and the change in performance over time. The search for final decision solutions and the verification of the proposed model are based on experimental results from both perceptual studies, which are evaluating visibility and intrusiveness of marketing content as well as online campaigns providing interaction data for estimation of effectiveness. Surprisingly, the online response to the most noticeable advertisements with highly perceived visibility and intrusiveness was relatively low. During the field study performed in order to compute the model parameters, the best results were achieved for advertising content with moderate visual influence on web users. Simulations with the proposed model revealed that a growing level of persuasion can increase results only to a certain extent. Above a saturation point, a strategy based on extensive visual effects, such as high-frequency flashing, resulted in a very high increase of intrusiveness and a slightly better performance in terms of acquired interactions. Proposed balanced content design with the use of intelligent decision support system creates directions towards sustainable advertising and a friendlier online environment.

A fuzzy multi-objective optimization model for sustainable reverse logistics network design

Decreasing the environmental impact, increasing the degree of social responsibility, and considering the economic motivations of organizations are three significant features in designing a reverse logistics network under sustainability respects. Developing a model, which can simultaneously consider these environmental, social, and economic aspects and their indicators, is an important problem for both researchers and practitioners. In this paper, we try to address this comprehensive approach by using indicators for measurement of aforementioned aspects and by applying fuzzy mathematical programming to design a multi-echelon multi-period multi-objective model for a sustainable reverse logistics network. To reflect all aspects of sustainability, we try to minimize the present value of costs, as well as environmental impacts, and optimize the social responsibility as objective functions of the model. In order to deal with uncertain parameters, fuzzy mathematical programming is used, and to obtain solutions on Pareto front, a customized multi-objective particle swarm optimization (MOPSO) algorithm is applied. The validity of the proposed solution procedure has been analyzed in small and large size test problems based on four comparison metrics and computational time using analysis of variance. Finally, in order to indicate the applicability of the suggested model and the practicality of the proposed solution procedure, the model has been implemented in a medical syringe recycling system. The results reveal that the suggested MOPSO algorithm overtakes epsilon-constraint method from the aspects of quality of the solutions as well as computational time. Proper use of the proposed process could help managers efficiently manage the flow of recycled products with regard to environmental and social considerations, and the process offers a sustainable competitive advantage to corporations.

Stochastic Optimal Operation of Microgrid Based on Chaotic Binary Particle Swarm Optimization

Based on fuzzy mathematics theory, this paper proposes a fuzzy multi-objective optimization model with related constraints to minimize the total economic cost and network loss of microgrid. Uncontrollable microsources are considered as negative load, and stochastic net load scenarios are generated for taking the uncertainty of their output power and load into account. Cooperating with storage devices of the optimal capacity controllable microsources are treated as variables in the optimization process with the consideration of their start and stop strategy. Chaos optimization algorithm is introduced into binary particle swarm optimization (BPSO) to propose chaotic BPSO (CBPSO). Search capability of BPSO is improved via the chaotic search approach of chaos optimization algorithm. Tests of four benchmark functions show that the proposed CBPSO has better convergence performance than BPSO. Simulation results validate the correctness of the proposed model and the effectiveness of CBPSO.

Fuzzy multi-objective optimization for movement performance of deep-notch elliptical flexure hinges.

Compared with commonly used flexure hinges, deep-notch elliptical flexure hinges are more suitable for flexible mechanisms with high precise transmission requirements. The rotation stiffness model of deep-notch elliptical flexure hinges was built first, and the compliance matrix was analyzed and solved by using Newton-Cotes quadrature formula to simplify the calculation of compliance coefficients; on the other hand, the fuzzy multi-objective optimization model with distribution was constructed, and a detailed example was given out to validate the effectiveness of the fuzzy optimization. The experiment results show that the desired angular displacement α(z) around the z axis is increased by 30.13%; while the undesired α(y) that around the y axis is decreased by 15.74% in experiment. The line displacements of Δ(y) and Δ(z) along the Y and Z axes are decreased by 18.15% and 47.69%, respectively. All the optimization data show that after the fuzzy optimization, the rotation capacity of z axis has been raised, and the motion capacity of the undesired directions has been restrained, so that the movement precision and the performance of the deep-notch elliptical flexure hinge can be improved, which is more suitable for the optical waveguide packaging positioning platform with high precision transmission.

Multiobjective fuzzy optimization for sustainable groundwater management using particle swarm optimization and analytic element method

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright (c) 2015 John Wiley & Sons, Ltd.

A Multi-objective Matching Approach for One-Shot Multi-attribute Exchanges Under a Fuzzy Environment

Although many researchers have realized that the trade determination problem in one-shot multi-attribute exchanges is an important decision problem, few studies can be really applied to deal with this issue under a fuzzy environment. This paper proposes a multi-objective matching approach for one-shot multi-attribute exchanges with fuzzy information. First, we use fuzzy set theory to represent the traders’ orders with fuzzy information and then give a framework for the proposed multi-objective matching approach. Second, we present a novel calculation method of the matching degree based on the improved fuzzy information axiom. According to the matching degree, we build a fuzzy multi-objective optimization model (FMOM) for the trade determination problem, where two criteria, i.e., profits and satisfactions, are considered simultaneously. Afterward, in order to solve the FMOM, the fuzzy chance constrained programming technique based on credibility measures and the fuzzy goal programming method are introduced to convert it into a crisp single objective one. Finally, we conduct the numerical study and analysis on a practical example to illustrate the application and effectiveness of the proposed multi-objective matching approach.