Interactive Fuzzy Approach Research Articles

Bi-level multi-objective optimization for a hybrid carbon pricing initiative towards biomass co-firing with coal

Coal-fired power generation is one of the major contributors to global carbon emissions. Biomass co-firing with coal is a cost-effective approach for carbon abatement. This paper formulates a hybrid carbon pricing initiative that combines an emission trading system (ETS) and a carbon tax, with ETS being applied to large power plants and carbon tax being applied to small power plants. A bi-level multi-objective optimization model is established to assist the multiple stakeholders to develop optimal strategies, and quantify environmental and economic impacts. In the proposed model, decision sequence from the authority to the coal-fired power plants is considered, and trade-offs between social welfare and carbon intensity is determined. Bi-level interactive fuzzy approach is adopted to search for satisfactory solutions. A case study is conducted to demonstrate the model’s practicality and efficiency, and the results reveal that this model is adequate for finding Stackelberg equilibrium between the hierarchical decision-makers with conflicting objectives. Sensitivity analyses are conducted to provide the stakeholders with reasonable and practical strategies under various situations. It is found that higher preferences for economic benefits and satisfactory degrees would increase carbon tax price. Management recommendations are provided to support the hybrid initiative for biomass co-firing with coal.

Optimizing Multi-Channel Green Supply Chain Dynamics with Renewable Energy Integration and Emissions Reduction

In response to the global imperative of mitigating greenhouse gas emissions (GHGs) and the shifting landscape of business models toward multi-channel structures, this study delves into the intricacies of a green supply chain. Operating through both online and traditional channels with uncertain demands, the producer’s distribution strategy prompts an exploration of supply chain dynamics. Utilizing an integer programming model, this study calculates optimal prices, optimizes total profit, and minimizes transportation costs to curtail carbon dioxide emissions, depending on the transportation mode. Additionally, this study incorporates renewable energy sources into the production and transportation processes to further minimize carbon dioxide emissions. The integration of renewable energy not only supports environmental goals, but also contributes to the overall profitability of the supply chain by reducing energy costs. Employing a theoretical technique for linearization, the model, resolved through the Jimenez and TH methods, demonstrates efficacy in reconciling economic and environmental goals. The Jimenez method enables the transformation of fuzzy parameters into deterministic equivalents, allowing for a more reliable optimization during uncertainty, while the TH method provides an interactive fuzzy multi-objective approach, aligning the model’s dual objectives for both economic and environmental goals. Notably, when transportation costs to both markets are equal, the model prioritizes devices with a lower environmental impact, showcasing adaptability. Furthermore, the proposed solution empowers decision makers to influence pricing and enhance the entire supply chain’s profitability. In conclusion, this research offers nuanced insights, strategically aligning economic viability with environmental sustainability in the discourse on green supply chains.

Designing a Fuzzy Mathematical Model for a Two-Echelon Allocation-Routing Problem by Applying Route Conditions: A New Interactive Fuzzy Approach

In vehicle routing problems (VRP), the optimal allocation of transportation by considering factors such as route hardness, driver experience and vehicle worn-out has a significant effect on costs reduction and approaching real-world conditions. In this paper, a novel fuzzy mixed integer non-linear mathematical model to address the two-echelon allocation-routing problem under uncertainty is proposed by applying route and fleet conditions. The cost of allocating drivers to diverse vehicles is computed at the first echelon of the problem, considering factors such as vehicle type, vehicle wear-out, and driver experience. Additionally, different routes are defused with varying levels of hardness. The goal of the second echelon of the model is to improve reliability by defining the reliability of routes within each section. To solve the model, the Torabi and Hessini (TH), the Selimi and Ozkarahan (SO) methods, and a newly proposed approach (PIA) were utilized to transform the multi-objective model into a single-objective one. Numerical tests and performance indicators were used to validate the effectiveness of both the multi-objective mathematical model and the proposed solution method. The validation computation results indicate that the proposed solution approach outperforms both the TH and SO approaches.

A novel interactive intuitionistic fuzzy approach to find satisfactory Pareto-optimal solutions for general bilevel multi-followers programming

This paper focuses on the approach for solving the satisfactory Pareto-optimal solutions of the general form of bilevel multi-followers programming(BMFP), including the BMFP with partial shared variables among followers, the so-called referential-uncooperative BMFP, the uncooperative BMFP, and the cooperative BMFP. Without losing generality, the BMFP with partial shared variables among followers will be taken as a representative to explain the universal applicability of the proposed generic interactive intuitionistic fuzzy method. Based on the theory of intuitionistic fuzzy set, the new definition of satisfactory Pareto-optimal solutions is introduced by means of membership function, non-membership function, and score function. In order to obtain satisfactory Pareto-optimal solutions of BMFP with partial shared variables among followers, a prior minimization optimization problem and a series of corresponding auxiliary maximization optimization problems are formulated, and we strictly prove that the optimal solution of the prior minimization optimization problem is not necessarily the satisfactory Pareto-optimal solutions, but at least one satisfactory Pareto optimal solution can be derived by further solving these auxiliary maximization optimization problems. Then, a detailed interactive intuitionistic fuzzy algorithm framework that consider both the balance of satisfactory degree between the leader and the followers and the balance of satisfactory degree among all followers is proposed. In the part of numerical experiments, four examples(including a linear BMFP problem with partial shared variables among followers, a BMFP model of a road network problem, an uncooperative BMFP problem, and a nonlinear BMFP problem with partial shared variables among followers) are illustrated to demonstrate the applicability, effectiveness and superior performance of the proposed technique.

Resilient and social health service network design to reduce the effect of COVID-19 outbreak.

With the severe outbreak of the novel coronavirus (COVID-19), researchers are motivated to develop efficient methods to face related issues. The present study aims to design a resilient health system to offer medical services to COVID-19 patients and prevent further disease outbreaks by social distancing, resiliency, cost, and commuting distance as decisive factors. It incorporated three novel resiliency measures (i.e., health facility criticality, patient dissatisfaction level, and dispersion of suspicious people) to promote the designed health network against potential infectious disease threats. Also, it introduced a novel hybrid uncertainty programming to resolve a mixed degree of the inherent uncertainty in the multi-objective problem, and it adopted an interactive fuzzy approach to address it. The actual data obtained from a case study in Tehran province in Iran proved the strong performance of the presented model. The findings show that the optimum use of medical centers' potential and the corresponding decisions result in a more resilient health system and cost reduction. A further outbreak of the COVID-19 pandemic is also prevented by shortening the commuting distance for patients and avoiding the increasing congestion in the medical centers. Also, the managerial insights show that establishing and evenly distributing camps and quarantine stations within the community and designing an efficient network for patients with different symptoms result in the optimum use of the potential capacity of medical centers and a decrease in the rate of bed shortage in the hospitals. Another insight drawn is that an efficient allocation of the suspect and definite cases to the nearest screening and care centers makes it possible to prevent the disease carriers from commuting within the community and increase the coronavirus transmission rate.

Designing a sustainable reverse supply chain network for COVID-19 vaccine waste under uncertainty

The vast nationwide COVID-19 vaccination programs are implemented in many countries worldwide. Mass vaccination is causing a rapid increase in infectious and non-infectious vaccine wastes, potentially posing a severe threat if there is no well-organized management plan. This paper develops a mixed-integer mathematical programming model to design a COVID-19 vaccine waste reverse supply chain (CVWRSC) for the first time. The presented problem is based on minimizing the system's total cost and carbon emission. The uncertainty in the tendency rate of vaccination is considered, and a robust optimization approach is used to deal with it, where an interactive fuzzy approach converts the model into a single objective problem. Additionally, a Lagrangian relaxation (LR) algorithm is utilized to deal with the computational difficulty of the large-scale CVWRSC network. The model's practicality is investigated by solving a real-life case study. The results show the gain of the developed integrated network, where the presented framework performs better than the disintegrated vaccine and waste supply chain models. According to the results, vaccination operations and transportation of non-infectious wastes are responsible for a large portion of total cost and emission, respectively. Autoclaving technology plays a vital role in treating infectious wastes. Moreover, the sensitivity analyses demonstrate that the vaccination tendency rate significantly impacts both objective functions. The case study results prove the model's robustness under different realization scenarios, where the average objective function of the robust model is less than the deterministic model ones’ in all scenarios. Finally, some insights are given based on the obtained results.

A mathematical model for designing a network of sustainable medical waste management under uncertainty

Medical waste generation is on the rise in most societies due to population growth, ease of access to healthcare, and wide-ranging healthcare services. Given this concern, it would be highly important to manage medical waste generated in hospitals at various stages including collection, transportation, storage, and disposal. Mismanagement in this area could seriously endanger human health and the environment. To address the sustainable location-allocation problem in medical waste management, this article proposes a multi-objective mixed-integer linear programming model under uncertainty. The suggested model primarily designs a sustainable network that locates facilities for the storage, decontamination, recycling, incineration, and disposal of waste. Additionally, it takes into account the recycling of products and electricity production from waste. The possibilistic programming is used to deal with uncertainty of key parameters and an interactive fuzzy approach is also used to solve the problem. The model is being implemented in Chaharmahal and Bakhtiari Province, Iran. The findings of implementing the model show that the income earned from recycling and waste-to-energy may offset a considerable amount of the waste management system's expenditures. Meanwhile, greenhouse gas emissions are decreasing and good social consequences are growing. The suggested model can assist medical centersand waste management organizationsin designing waste management networks that meet sustainability goals.

Designing an oil supply chain network considering sustainable development paradigm and uncertainty

This study proposes a multi-objective mathematical programming model to design an oil supply chain network at three levels: upstream, midstream and downstream. It includes oil wells, gas injection wells, production units, refineries, gas injection centers, distribution centers, export and import terminals. The proposed model optimizes all three economic, social and environmental goals at the same time. Drilling injection and production wells, transportation costs, production costs, gas injection center costs, as well as fixed and annual costs of refineries and distribution centers are all minimized in the economic dimension. The environmental dimension of sustainability reduces greenhouse gas emissions, while the social dimension of sustainability increases job opportunities. The optimization of associated petroleum gas injection operations into the reservoir is also taken into account in this study. The proposed model considers the uncertainty of critical parameters and employs a robust possibilistic hybrid approach to deal with it, as well as an interactive fuzzy approach to solve it. A case study in Iran is used to evaluate the suggested model's performance. In comparison to the single-objective economic model, the results of solving the model show that taking sustainability into account has reduced greenhouse gas emissions and increased job opportunities. The crude oil extraction potential increases in each period when gas injection optimization and reservoir pressure are taken into account. Furthermore, the cost of the supply chain grows as the amount of uncertainty in the suggested model rises. As a result, the uncertainty of system parameters must be considered.

Socially Responsible Portfolio Selection: An Interactive Intuitionistic Fuzzy Approach

In this study, we address the topic of sustainable and responsible portfolio investments (SRI). The selection of such portfolios is based, in addition to traditional financial variables, on environmental, social, and governance (ESG) criteria. The interest of our approach resides in allowing socially responsible (SR) portfolio investors to select their optimal portfolios by considering their individual preferences for each objective and simultaneous definition of the degrees of acceptance and rejection. In particular, we consider socially responsible portfolio selection as an optimization problem with multiple objectives before applying interactive intuitionistic fuzzy method to solve the portfolio optimization. The robustness of our approach is tested through an empirical study on the top 10 Stocks for ESG values worldwide.

Hybridization of an interactive fuzzy methodology with a lexicographic min-max approach for optimizing a multi-period multi-product multi-echelon sustainable closed-loop supply chain network

Here, a fuzzy multi-period multi-echelon multi-objective mixed-integer non-linear programming (MOMINLP) model is considered for a sustainable multi-product multi-site multi-distribution multi-customer supply chain in forward flow having multi-centers for collecting, checking, repairing and decomposing and multi-disposal centers in the reverse flow. Minimizing the total cost of the closed-loop supply chain (CLSC), elevating the customer satisfaction degrees, minimizing the total waiting time, minimizing the manufacturing site greenhouse gases and minimizing the CO2 emissions from vehicles are considered as the objective functions. Furthermore, integration of strategic decisions of flow allocations and vehicle routing with tactical and operational decisions such as production and workforce planning and improving upon customer satisfaction are considered. Also, we are concerned with the stability of the model and the accuracy of the obtained solution. We consider uncertainty and propose an appropriate method to develop a fair optimization of the distribution of raw materials and products to the supply chain participants. The presented solution method initially considers an adaptation of the lexicographic min–max fairness approach to finding a short delay for the delivery time of all the existing flows between every two consecutive echelons of the CLSC network. Then, a service quality measure is introduced to evaluate the uncertain delivery time considering the delay unpleasantness measure (DUM) index and measure the delay unpleasantness of all the existing delivery time delays. The model is converted to an auxiliary crisp MOMINLP problem by taking appropriate strategies, and a novel interactive fuzzy approach is proposed to find a compromised solution. The effectiveness of the algorithm is illustrated through a generated case study. The validity of the proposed method is confirmed by comparing the obtained results with the ones obtained by some other valid approaches, making use of distance and dispersion measure functions. Computational results show the proposed fuzzy method to be more efficient than other approaches. The encouraging results provide motivations for the use of our proposed fuzzy approach to solving other kinds of multi-objective mixed-integer models.

A multi-level programming for shale gas-water supply chains accounting for tradeoffs between economic and environmental concerns

This study develops a multi-level programming model for planning the shale gas-water supply chains. A set of leader-follower-interactive objectives with emphases of water consumption, economic performance, and pollutant discharge are integrated into a sequential decision-making process. Satisfactory degree is introduced to tackle the computationally challenging problem based on an interactive fuzzy approach. Operational decisions regarding water resources allocation, transportation mode selection, and pollutant discharge control would be achieved. Results reveal that the environmentally- or economically-aggressive strategies would be generated when a single goal for optimizing economic benefits or pollutant discharge. The multi-objective decisions are limited by the selected weights. However, the multi-level model would provide more comprehensive schemes due to its sequential consideration of the economic/environmental concerns. Findings from the multi-level model can facilitate (a) balancing the conflicts among different decision makers, (b) timing and siting for shale gas production, and (c) managing water resources for pollutant discharge control.

A Novel Closed-Loop Supply Chain Network Design Considering Enterprise Profit and Service Level

Increasing concerns for sustainable development have motivated the study of closed-loop supply chain network design from a multidimensional perspective. To cope with such issues, this paper presents a general closed-loop supply chain network comprising various recovery options and further formulates a multi-objective mixed-integer linear programming model considering enterprise profit and service level simultaneously. Within this model, market segmentation is also considered to meet real-world operating conditions. Moreover, an ε -constraint method and two interactive fuzzy approaches are applied to find a global optimum for this model together with the decisions on the numbers, locations, and capacities of the facilities, as well as the material flow through the network. Ultimately, numerical experiments are conducted to demonstrate the viability and effectiveness of both the proposed model and solution approaches.

Integrated forward and reverse logistics network design for a hybrid assembly-recycling system under uncertain return and waste flows: A fuzzy multi-objective programming

Abstract: This paper addresses the optimal design of a hybrid assembly-recycling network that simultaneously integrates the forward and reverse logistics among its multi-product multi-echelon superstructure. Multiple sources of raw materials including components and parts are considered at different stages of the forward assembly process. The problem investigates three recycling options for final products, semi-products and modules. Various types of uncertainties on return flow and waste flow are investigated. To optimize the dual-system superstructure, the problem is hereby modeled by a fuzzy mixed integer linear programming approach. Piecewise linear membership functions are constructed for the objectives to represent the diversified satisfactory degrees which preferably comply with the real-world decision scenarios. Further, an interactive fuzzy optimization approach is developed to solve the problem by differentiating the piece-wise sections of satisfactory degrees. Finally, an electronic assembly plant with its own recycling process is chosen as the industrial case to implement the proposed approach. Sensitivity analysis and comparison under different scenarios are presented to demonstrate the effectiveness on obtaining compromised solutions under diversified satisfactory degrees in such an uncertain environment.

A mixed resilient‐efficient approach toward blood supply chain network design

AbstractUnlike its inherent beneficial attributes, the blood supply chain is very complex due to its uncertain nature and irregular donation besides a high vulnerability to disruptions. In this regard, this study provides a multi‐objective integrated resilient‐efficient model to design a blood supply chain network under uncertainty. To evaluate the efficiency, an augmented form of the data envelopment analysis model is incorporated into the extended model. On the other hand, to improve supply chain resilience, different resiliency measures as optimization tools are introduced and inserted into the considered network. As blood donors have a main role in the blood supply chain, this paper undertakes motivational social aspects to stimulate blood donation for reducing possible shortages. Furthermore, to handle the multi‐objective problem, an interactive fuzzy approach is utilized. Finally, to indicate the applicability of the extended model and its solution approaches, a case study is provided considering realistic data. The results revealed that simultaneously considering all three measures of efficiency, resilience, and cost can assist in improvement of blood supply chain network design and a trade‐off among these three measures can be set by decision maker's preferences.

A comprehensive reverse supply chain model using an interactive fuzzy approach – A case study on the Vietnamese electronics industry

• A reverse supply chain model for electronic waste integrating risks and uncertainties is developed. • Fuzzy approach is adopted to cope with uncertain data. • The proposed model is validated by conducting a case study of an electronics company. • The results show that the proposed model can perform better than the current model established by the company. Reverse supply chains (RSCs) have gained much attention from governments, companies and scholars due to increasing levels of environmental concern, resource depletion and regulation. In Europe and other developed countries, RSCs have been imposed by regulation so that manufacturers take greater responsibility for their end-of-life products. In developing countries like Vietnam, this situation is much more complicated since there are many destinations for end-of-life products other than the take-back systems of their manufacturers. Consequently, product flow quantities to RSC facilities in Vietnam, as well as other parameters, are vague and uncertain. To help electronics companies set up more effective RSCs, this study employs a fuzzy approach to account for such uncertain parameters. Furthermore, risk factors are integrated into the proposed model to make it more comprehensive. The solution approach gives much greater flexibility for decision-makers to obtain a satisfactory solution.

Interactive iterative relative fuzzy connectedness lung segmentation on thoracic 4D dynamic MR images.

Lung delineation via dynamic 4D thoracic magnetic resonance imaging (MRI) is necessary for quantitative image analysis for studying pediatric respiratory diseases such as thoracic insufficiency syndrome (TIS). This task is very challenging because of the often-extreme malformations of the thorax in TIS, lack of signal from bone and connective tissues resulting in inadequate image quality, abnormal thoracic dynamics, and the inability of the patients to cooperate with the protocol needed to get good quality images. We propose an interactive fuzzy connectedness approach as a potential practical solution to this difficult problem. Manual segmentation is too labor intensive especially due to the 4D nature of the data and can lead to low repeatability of the segmentation results. Registration-based approaches are somewhat inefficient and may produce inaccurate results due to accumulated registration errors and inadequate boundary information. The proposed approach works in a manner resembling the Iterative Livewire tool but uses iterative relative fuzzy connectedness (IRFC) as the delineation engine. Seeds needed by IRFC are set manually and are propagated from slice-to-slice, decreasing the needed human labor, and then a fuzzy connectedness map is automatically calculated almost instantaneously. If the segmentation is acceptable, the user selects "next" slice. Otherwise, the seeds are refined and the process continues. Although human interaction is needed, an advantage of the method is the high level of efficient user-control on the process and non-necessity to refine the results. Dynamic MRI sequences from 5 pediatric TIS patients involving 39 3D spatial volumes are used to evaluate the proposed approach. The method is compared to two other IRFC strategies with a higher level of automation. The proposed method yields an overall true positive and false positive volume fraction of 0.91 and 0.03, respectively, and Hausdorff boundary distance of 2 mm.

Optimal placement of distributed generation in radial networks considering reliability and cost indices

In the current paper, the optimal placement merits of distribution generations (DGs) are investigated in the economical version of a grid-parallel mode. The proposed method is constructed based on a probabilistic approach which is called Point Estimate Method (PEM) to consider the uncertainty assoc iated with the load demand prediction error along with the variation of cost of electricity and power production of DGs. The objective functions are the total active power losses, the total emission produced and the total cost related to the grid & DGs and cost of reliability. These functions are set to be optimized that result in utilizing an interactive fuzzy approach based on improved particle swarm optimization (IPSO) to let the decision maker apply his/her preferences to the system. It is apt to mention that the application of the interactive fuzzy approach is based on the result of conflicting behaviors of the investigated objective functions. Through using the Tai-Power distribution test system the feasibility and the efficiency of the proposed method have been shown.

An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem

The consideration of this paper is given to address the straight and U-shaped assembly line balancing problem. Although many attempts in the literature have been made to develop deterministic version of the assembly line model, the attention is not considerably given to those in uncertain environment. In this paper, a novel bi-objective fuzzy mixed-integer linear programming model (BOFMILP) is developed so that triangular fuzzy numbers (TFNs) are employed in order to represent uncertainty and vagueness associated with the task processing times in the real production systems. In this proposed model, two conflicting objectives (minimizing the number of stations as well as cycle time) are considered simultaneously with respect to set of constraints. For this purpose, an appropriate strategy in which new two-phase interactive fuzzy programming approach is proposed as a solution method to find an efficient compromise solution. Finally, validity of the proposed model as well as its solution approach are evaluated though numerical examples. In addition, a comparison study is conducted over some test problems in order to assess the performance of the proposed solution approach. The results demonstrate that our proposed interactive fuzzy approach not only can be applied in ALBPs but also is capable to handle any practical MOLP models. Moreover, in light of these results, the proposed model may constitute a framework aiming to assist the decision maker (DM) to deal with uncertainty in assembly line problem.

A multi-objective healthcare inventory routing problem; a fuzzy possibilistic approach

This paper presents a new multi-objective mathematical model to address a Healthcare Inventory Routing Problem (HIRP) for medicinal drug distribution to healthcare facilities. The first part of objective function minimizes total inventory and transportation costs, while satisfaction is maximized by minimizing forecast error which caused by product shortage and the amount of expired drugs; Greenhouse Gas (GHG) emissions are also minimized. A demand forecast approach has been integrated into the mathematical model to decrease drug shortage risk. A hybridized possibilistic method is applied to cope with uncertainty and an interactive fuzzy approach is considered to solve an auxiliary crisp multi-objective model and find optimized solutions.

Multiple Objective Fuzzy Sourcing Problem with Multiple Items in Discount Environments

The selection of proper supply sources plays a vital role to maintain companies’ competitiveness. In this study a multiple criteria fuzzy sourcing problem with multiple items in discount environment is considered as a multiple objective mixed integer linear programming problem. Fuzzy parameters are demand level and/or aspiration levels of objectives. Three objective functions are minimization of the total production and ordering costs, the total number of rejected units, and the total number of late delivered units, respectively. The model is developed for the all-units discount scheme. For the incremental discount and volume discount environment, modification requirements of the model are mentioned. The previously proposed interactive fuzzy approach combined with three fuzzy mathematical models is employed to obtain most satisfactory solution which is also a nondominated one. This study provides a realistic mathematical model and promising solution strategy to multiple item-single period sourcing problem in discount environment. Consideration of fuzziness makes the obtained nondominated solution implementable for the real cases.