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Considering the double uncertainty caused by the ambiguity of statistical data and the ambiguity produced by the subjective assessment of decision makers, the crisp values of criteria may be insufficient to model the multi-criteria decision-making (MCDM) problem in the real world. This paper proposes a fuzzy best-worst method (FBWM) based on a dual-interval solution algorithm to extend the best-worst method (the most recent MCDM method) to fuzzy environments. The reference comparisons for the best criteria and for the worst criteria are represented by fuzzy numbers. Then, according to the BWM method, a nonlinear constrained optimization problem with fuzzy parameters is formulated. We decompose the membership function in fuzzy numbers into several interval numbers of special form and solve the aforementioned fuzzy BWM problem by compound interval algorithm to obtain fuzzy weights of different criteria. Meanwhile, an integral type-reduced method is proposed for determining the fuzzy consistency ratio in order to assess the reliability of the FBWM results. The viability of the new algorithm to expand the BWM method into fuzzy environments has been validated through three numerical examples. In contrast to the existing FBWM method, the proposed method avoids the arithmetic operation between fuzzy numbers during the solution process, directly transfers the uncertain information in the membership function corresponding to the fuzzy comparison vector to the result, and generates fuzzy weight value, which indicates that the proposed algorithm is able to obtain accurate BWM results in fuzzy environments. The results of the study provide new solution ideas for multi-criteria optimization problems under uncertainty. [ABSTRACT FROM AUTHOR]

This research addresses the Inventory-Routing Problem (IRP) with priority customers under conditions of uncertainty. The problem involves devising a plan to supply a set of customers from a facility, establishing precedence rules, and making transportation and inventory management decisions while considering uncertainty in customer demand. Priority in deliveries is assigned to customers in the health sector in accordance with government regulations. Companies must uphold product quality for health sector customers while simultaneously aiming to minimize total costs. We propose a fuzzy mixed-integer linear programming model to solve the IRP with priority customers and uncertainty in demand rates, modeled using triangular fuzzy numbers. To convert the fuzzy linear programming model into a deterministic one, an ordering method for fuzzy numbers is applied. The model is implemented using CPLEX, and a set of benchmark instances is solved. The primary results indicate that prioritizing customers leads to an increase in total costs due to visiting these customers first on each route created. Additionally, routes without priority customers exhibit higher average vehicle capacity utilization. In most cases, the solutions obtained maintain quality within the specified time limits. [ABSTRACT FROM AUTHOR]

One of the special cases of type-2 fuzzy sets is the interval type-2 fuzzy sets, which are less complicated and easier to understand than T2FSs. In this study, we explore the interval type-2 fuzzy linear programming problem with the resources vector that has imprecision of the vagueness type. These types of vagueness are expressed via membership functions. First, we review the three available methods, including the Figueroa and Sarani methods. Then, using the three ideas of Verdegay, Werners, and Guu and Wu for solving fuzzy linear programming problems with vagueness in the resources vector, we propose three new methods for solving interval type-2 fuzzy linear programming problems with vagueness in the resources vector. Finally, we demonstrate the effectiveness of our proposed methods by solving an example and comparing the results obtained with each other and with those of previous methods. [ABSTRACT FROM AUTHOR]

There are several approaches to address fuzzy linear programming problems (FLPP). However, due to using standard interval arithmetic (SIA), these methods have some limitations and are not complete solutions. This article establishes a new approach to fuzzy linear programming via the theory of horizontal membership functions and the multidimensional relative-distance-measure fuzzy interval arithmetic. Furthermore, we propose a multidimensional solution based on the primal Simplex approach that satisfies any equivalent form of FLPP. The new solutions of FLPP are also compared with the results of existing methods. Some numerical examples have been illustrated to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

An alternative new method for solving an epistemic uncertainty such as fuzzy-based linear programming problem with equality constraints has been proposed here. In this approach, the optimal solution of the considered fuzzy problem has been achieved by solving a related crisp problem. Moreover, the objective function of the crisp problem has been obtained by taking the linear combination of the fuzzified version of the original uncertain objective function. The coefficients of the linear combination are considered as strictly positive real numbers. And the constraints of the crisp problem are obtained equivalently from the equality constraints of the fuzzy problem. Triangular fuzzy numbers are considered for this analysis. Comparisons have been made with the results of Kumar et al. (Appl Math Model 35:817–823, 2011), Najafi and Edalatpanah (Appl Math Model 37:7865–7867, 2013), Ezzati et al. (Appl Math Model 39:3183-3193, 2015) and Ghoushchi et al. (Mathematics 9:2937, 2021. https://doi.org/10.3390/math9222937). [ABSTRACT FROM AUTHOR]

In this work, we propose a 3D dynamic optimization model that enables the design of an underground mine ore pass system with uncertainties. Ore transportation costs and ore pass development costs are quantified by triangular fuzzy numbers. Transportation costs are treated as production costs, and they vary over the duration of mining operation, while development costs of ore passes are treated as an investment, and they are treated as constant. The developed model belongs to the class of fuzzy 0–1 linear programming models, where the fuzzy objective cost function achieves a minimum value, with respect to given set of techno-dynamic constraints. Searching for optimal value in the fuzzy environment is a hard task, and because of that, we developed a new ranking function which transforms the fuzzy optimization model into a crisp one. A triangular fuzzy number can be presented as a triangular graph G(V,E) composed of vertices and edges. The x-coordinate of the Torricelli point of a triangular graph presents the crisp value of a triangular fuzzy number. The use of this model lets us know the optimal number of ore passes, optimal location of ore passes, and optimal dynamic ore transportation plan. [ABSTRACT FROM AUTHOR]

The necessarily optimal solution is known as the most reasonable solution to linear programming problems with interval/fuzzy objective function coefficients. As it remains optimal against the certain fluctuations of objective function coefficients, the necessarily optimal solution can be seen as a robust optimal solution. In this paper, we demonstrate that the necessary optimality degree of a non-degenerate basic feasible solution can be obtained easily by utilizing the tolerance approach. The necessary optimality degree evaluates to what extent the solution remains optimal against the fluctuations of objective function coefficients. Several types of fuzzy subsets showing the possible range of the objective function coefficient vector are considered. For each type of fuzzy subset, an efficient calculation method of necessary optimality degree is proposed. Numerical examples are given to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

The best allocation of limited resources to activities with the aim of accomplishing the desired goal, such as maximization of profit or minimization of cost, is the focus of linear programming. The relationships between activities in linear programming models satisfy the proportionality and additivity requirements since they are linear interactions. This feature of linear programming is extended to the tourism industry which is one of the major industries in the global economy with respect to invested capital and earnings of foreign currencies. In todays era of design thinking, automation, and met averse, there is a very close margin between solutions to similar real-world problems. This is where the need and demand for fuzzy and imprecise linear programming arises. The membership functions provide the model developer the freedom to grade the imprecision as per his/her preference, thereby enabling a unique solution for each problem. While considering the tourism problem a number of factors like natural resources, people, history, culture, security, accommodation, entertainment, political stability, cost of services, tour operator, tour information, and advertisement play an important role in enhancing the sector to a large extent. Combined and classified they come under the following categories like leisure tourism, therapeutic/spa tourism, conference tourism, political tourism, sports/recreational tourism, cultural tourism, social tourism, conference tourism, recreational tourism, sports tourism, religious tourism, health tourism, etc. Each of these sectors requires careful investment on the part of the Government and other stake holders for development purpose. i.e. only a proper marketing mix will ensure a better return for the state. Taking this aspect into consideration the authors decided to introduce a hypothetical LP maximization model for the tourism industry in North East. Cost and space allocation are the constraints in the model. Among the various categories, three tourism forms (heritage, eco-tourism, and pilgrimage tourism) are considered which are used to optimize the allocation of the States marketing budget in tourism in such a way that the appropriate sector provides the greatest likelihood of producing the strongest return on investment. The maximization of profit has been done using various methods, like Werner's, Verdegay's, and Zimmermans. The authors have concluded the results based on the sensitivity analysis that has been done in the process of maximizing profit along with a maximal satisfaction level. [ABSTRACT FROM AUTHOR]

In this paper, new concepts of (ˆ-feasibility and ã-efficiency of solutions for fuzzy mathematical programming problems are used, where ã is a vector of distinct satisfaction degrees. Recently, a special kind of fuzzy mathematical programming entitled Fuzzy Flexible Linear programming (FFLP) is attracted much interest. Using the mentioned concepts, we propose a two-phase approach to solve FFLP. In the first phase, the original FFLP problem converts to a Multi-Objective Linear Programming (MOLP) problem, and then in phase II a weighting technique for the reduced program is introduced. We saw that it was observed that using this concept as a generalization of the parametric approach in linear programming provides a more appropriate tool for modeling real problems and improving the solving process. Thus, by using this two-phase approach, we achieve better utilization of available resources. Further, the solution resulting from these two approaches is always an ã-efficient solution. Finally, an example in the real world is described to express this approach. [ABSTRACT FROM AUTHOR]

Demand forecasting is of crucial importance for make-to-stock companies because product demand is uncertain and it changes with time. Fuzzy linear programming (FLP) can be an optimum approach for such uncertain situations. In this study, the FLP model was used for more accurate demand forecasting in a make-to-stock company. Demand forecasting study was carried out according to the FLP method and linear programming (LP) method. Solutions of FLP and LP were compared in terms of imputed shortage cost, inventory carrying cost, and net profit. Results show that the applied FLP method is more advantageous than LP as it provides a 67% decrease in costs and a 15% increase in net profit. [ABSTRACT FROM AUTHOR]

One of the various optimization methods that addresses optimization under uncertainty is fuzzy linear programming. This model can be used when there is ambiguity in the situation because it is not precisely specified or when the problem does not require an exact value. With fuzzy linear programming, there is a range of grey between the two extremes as opposed to binary models, where an event may only be either black or white. As a result, it broadens the range of potential applications because most scenarios involve a spectrum of values rather than a bipolar state. In this article, a new FLP-based method is developed using a single MF, called modified logistics MF. The modified MF logistics and its modifications taking into account the characteristics of the parameter are from the analysis process. This MF was tested for useful performance by modeling using FLP. The developed version of FLP provides confidence in the existing IPPP application. This approach to resolving the IPPP can get feedback from the decision maker, the implementer and the analyst. In this case, this process can be called FLP interaction. FS self-assembly for MPS problems can be developed to find satisfactory solutions. The decision maker, researcher and practitioner can apply their knowledge and experience to get the best results. [ABSTRACT FROM AUTHOR]

Electrical impedance tomography (EIT) is an imaging technique that realizes the image reconstruction of conductivity distribution in the field. The existing EIT algorithms ignore the hidden fuzzy features during imaging, making the EIT technique exhibit a high degree of uncertainty, imprecision, incompleteness, and inconsistency in the actual use process, resulting in a low spatial resolution of the reconstructed images. In order to solve this problem, we introduce fuzzy linear programming into EIT imaging. On the basis of analyzing the fuzzy features of EIT in detail, a new model of fuzzy optimization is built up, whose optimal solution is obtained by using constrained coefficient fuzzy linear programming. To this end, we devise two types of simulation experiments to verify the performance of the optimization algorithm. Experimental results prove that compared with the traditional Tikhonov regularization algorithm, the correlation coefficient of the reconstructed image of the proposed algorithm is higher, the relative error value is smaller. [ABSTRACT FROM AUTHOR]

When some coefficients of the constraints are uncertain with only their possible ranges being given, a conventional linear programming (LP) problem can be generalised to the one with set-inclusive constraints. We consider the case where the possible ranges are given by fuzzy sets in this paper. The set-inclusive constraints with fuzzy coefficients have been treated by a necessity measure. However, the usual necessity measure cannot express well the decision-maker's requirement about the trade-off between the robustness level and the satisfaction level of the constraints. We extend the necessity measure to incorporate the trade-off between the robustness level and the satisfaction level of the constraints. We apply the extended necessity measure to LP problems with fuzzy coefficients. After the problem is formulated and reduced to the conventional programming problem, we propose a solution algorithm. Numerical examples are given to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

Supplier evaluation and selection (SES) problems have long been studied, leading to the development of a wide range of individual and hybrid models for solving them. However, the lack of widespread diffusion of existing SES models in the industry points to a need for simpler models that can systematically evaluate both qualitative and quantitative attributes of potential suppliers while enhancing the flexibility decision-makers need to account for relevant situational factors. Furthermore, empirical validations of existing models in SES have been few and far between. With a view to addressing these issues, this paper proposes an integrated solution framework that can be used to evaluate both tangible and intangible attributes of potential suppliers. The proposed framework combines three individual methods, namely the fuzzy analytic hierarchy process, fuzzy complex proportional assessment and fuzzy linear programming. The framework is validated through application in a Turkish textile company. The results generated using the proposed framework is compared with the actual historical data collected from the company. Additionally, a feasibility assessment is conducted on the sample supplier selection criteria employed, as well as assessment of the results generated using the proposed model. [ABSTRACT FROM AUTHOR]

In today's competitive environment, it is essential to design a flexible-responsive manufacturing system with automatic material handling systems. In this article, a fuzzy mixed integer linear programming model is designed for cell formation problems including the scheduling of parts within cells in a cellular manufacturing system (CMS) where several automated guided vehicles (AGVs) are in charge of transferring the exceptional parts. Notably, using these AGVs in CMS can be challenging from the perspective of mathematical modeling due to consideration of AGVs’ collision as well as parts pickup/delivery. This article investigates the role of AGVs and human factors as indispensable components of automation systems in the cell formation and scheduling of parts under fuzzy processing time. The proposed objective function includes minimizing the makespan and intercellular movements of parts. Due to the NP-hardness of the problem, a hybrid genetic algorithm (GA/heuristic) and a whale optimization algorithm (WOA) are developed. The experimental results reveal that our proposed algorithms have a high performance compared to CPLEX and the other two well-known algorithms, i.e., particle swarm optimization and ant colony optimization, in terms of computational efficiency and accuracy. Finally, WOA stands out as the best algorithm to solve the problem. [ABSTRACT FROM AUTHOR]

Copyright of Al-Dananeer is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Environmental concerns are on the rise around the world, as carbon emissions are increasing rapidly and which is one of the leading causes of global warming. These emissions come from different sectors but the biggest contribution comes from the transport sector. As countermeasures, countries are shifting toward electric vehicles, which are much greener modes of transportation. Currently, different types of electric vehicles are available in the market. The selection of a viable type of electric vehicle for a developing country like Pakistan needs proper evaluation. In this study, two techniques are used. Firstly, fuzzy Strength, Weaknesses, Opportunities, and Threats (SWOT) approach is used for the selection of a suitable vehicle for the future market of Pakistan. Secondly, fuzzy linear programming is used to check the viability of electric vehicles in the current market scenario. Using these techniques, hydrogen fuel cell vehicle is selected as the most advantageous vehicle for Pakistan's future market and the hybrid electric vehicle comes out as the best alternative for the current market. The techniques and the case study of Pakistan are the main novelty of this study, as no literature exists on electric vehicles with these methods on Pakistan's perspective. Based on the results, different recommendations are given to the policymakers of Pakistan. The recommended policies could make electric vehicles a prime competitor to the combustion vehicles in the current and future markets. [ABSTRACT FROM AUTHOR]

Remanufacturing can bring used or end of life products back to like-new products. The production planning of inventory control policies in a hybrid manufacturing/ remanufacturing system with different prioritizations (manufacturing vs. remanufacturing) is investigated in this study. For this production planning problem, the imprecision of customer demand, related operating costs, number of returned used components and all lead time and production times are uncertain. This uncertainty complicates the planning of the production and inventory control. The fuzzy set theory is employed due to the presence of the imprecise information, and the Fuzzy Linear Programming (FLP) is applied to optimize the model under these uncertainties. The proposed approach maximizes the most likely value of the profit, minimizes the risk of obtaining a lower profit, and maximizes the possibility of obtaining a higher profit for each production planning policy. The results show that the Priority-To-Remanufacturing (PTR) policy shows a higher profit than the policy of Priority-To-Manufacturing (PTM) and FLP can help decision makers to be aware of the risks and effects of uncertainties in their plans. As a result, they can prepare in advance for such scenarios. [ABSTRACT FROM AUTHOR]

Minimum-cost capacitated fuzzy network is formulated as a fuzzy linear programming problem. A novel fuzzy linear programming formulation for minimum-cost capacitated fuzzy network where the total resource constraints are fuzzy is proposed. The proposed model is then implemented to minimize the operations cost of American Airlines. The research is helpful to identify the most profitable destinations for the American Airlines. Twelve origin/destination pairs are taken into considerations namely Atlantic (A), Latin American (L), Pacific (P) and Domestic (D). Flight operations capacity, Available Seat Miles ASM, is taken as a measure of capacity. The goal is to minimize the flight operations cost while ensuring maximum flight operations capacities to all destinations. This is followed by perspective data analytics for "What American Airline should do to be more profitable?" Perspective analytics suggest the airline to extend flight operations capacity in certain origin/destination pairs, whereas to maintain the previous approximate average capacity for those having high operations costs. The solution of the proposed fuzzy model suggests that flight operations capacity ASM can be significantly increased by 22345148 (000) with relatively small increase 1539356 (000) USD in operations cost. The fuzzy model is superior for it emphasizes to increase flight operations capacity ASM for the origin/destination pairs with minimum flight operations costs. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Baghdad College of Economic Sciences University is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, a multi-element wind turbine blade that consists of NACA 6411 and NACA 4412 leading-edge slat design is investigated computationally. Optimum design parameters of the slatted wind turbine blade leading to maximum value of CL/CD related to the turbine power are obtained. In the optimization process, a new fuzzy logic linear programming methodology integrating with fuzzy linear regression and 2D CFD analysis is proposed. The aerodynamic characteristics of the slatted blade are computed by using Incompressible Navier–Stokes equations and k-omega turbulence modeling. Results are compared with the results of linear programming method and direct search optimization method. The computational results reveal that the proposed methodology for performance optimization is more effective than other methods to obtain high-performance value of the CL/CD. The maximum value of the CL/CD is obtained as 25.1 leading the maximum efficiency of 0.52. [ABSTRACT FROM AUTHOR]

The parameters of decision models are not clearly known and they are not exact for most real-life problems. Therefore, this article presents a model of linear programming with grey interval numbers for right-hand-side parameters under an uncertainty case. The purpose of this article is to compare the results of a fuzzy linear programming model and those of four proposed grey linear programming models and to find effective solutions for alternative production planning. The results produced a more effective plan to use as an industrial solution according to a fuzzy linear programming model. The objective function value is about 3% more effective than with the fuzzy linear programming method, and the customer satisfaction of total demand is about 25% more effective for the number of served customers. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of determining the optimal production quantity under uncertainties. The treated problem has a critical effect on the achievement of business goals, which further propagates to the competitive advantage of manufacturing company. The considered problem is stated as the fuzzy linear programming task. The objective function is defined as the maximization of all profit over the time period. The set of constraints consists of constraints deriving from the enterprise (available capacities) and from the market (demand). The fuzzy rating coefficient values of objective function of each pair of the considered products are described by linguistic expressions which are modelled by triangular fuzzy numbers. Handling of uncertainties of the stated fuzzy pair-wise comparison matrix is performed by using the extent analysis. The right-hand-side values of the capacity constraints are determined by decision makers and modelled by the triangular fuzzy numbers. The market constraint values are given according to evidence data. Determination of the optimal quantities of considered products for each time period is based on the concept of equal possibilities. The proposed model is illustrated by an example with real-life data. [ABSTRACT FROM AUTHOR]

Although assembly lines are designed to be highly efficient and very cost effective, they have been criticised for their effects on workers. Assembly workers usually perform repetitive tasks and sit or stand for long periods of time, therefore they are at high risk of work-related injuries such as musculoskeletal disorders. In this study, we present a new assembly line balancing problem that incorporates not only task precedence and processing times but also physical workloads in order to reduce work-related injuries. We consider the physical workload of a task as a fuzzy concept and propose a fuzzy linear programming model. The proposed model is applied to an assembly line balancing problem in a textile company and to some of the benchmark problems in order to illustrate the effects of physical workloads. [ABSTRACT FROM AUTHOR]

To achieve carbon neutrality, the power structure is bound to usher in fundamental transformations. In this study, an energy–carbon–water nexus (F-ECWN) system model is developed to assess trade-offs among different decision-making objectives within a power system under varying policy orientations. The model incorporates forecast data derived from various global climate models, leverages neural network prediction, draws upon multi-criteria decision-making theory, and incorporates fuzzy theory. Moreover, to effectively handle a multitude of fuzzy parameters within the model, a novel dual-interval algorithm for solving fuzzy linear programming is proposed. The F-ECWN model has the capability to derive the fuzzy membership function for each variable within the model ensuring that errors remain below 1 %, reflecting the uncertainty stemming from diverse policy orientations and technology choices. Various scenarios were formulated to gauge the impact of policy orientation on the allocation decisions of regional energy systems. Additionally, sensitivity analysis has been conducted to assess the effects of uncertain parameters on modeling outputs. The results of the applied research in Fujian Province have revealed that the presence of uncertainties in the energy system's parameters can significantly influence model outputs and decision-making processes. Furthermore, the modeling results demonstrate the region's substantial potential for reducing carbon emissions. Under optimal policy guidance and climate conditions, the total carbon emissions can be reduced by 65 %, with a 36.14 % increase in the total system cost. These findings are anticipated to provide valuable support for formulating optimal decisions regarding regional energy-carbon-water nexus system and related environmental policies. [Display omitted] • A new algorithm for solving fuzzy multi-objective programming problems is proposed. • A robust fuzzy number reduction algorithm based on probabilistic integration is proposed. • E -C-W nexus in Fujian Province under different policy orientations is quantified. • Incorporation of CMIP6 forecast data into renewable energy parameters construction. • Carbon and water synergy effects in regional power system optimization are observed. [ABSTRACT FROM AUTHOR]

Copyright of Proceedings of the Faculty of Economics & Business in Zagreb / Zbornik Ekonomskog Fakulteta u Zagrebu is the property of Ekonomski Fakultet u Zagrebu and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Many companies established a closed-loop supply chain to increase their supply chain profit and sustainability. The goal of this study is to design a faucet closed-loop supply chain network, in which forward supply chain is explained is aimed to increase the profit and environmental savings, and used faucet exchange plan is presented in the reverse chain. A mixed integer linear programming model under demand uncertainty is developed. A single-objective, multi-product and multi-period model is proposed for this network. The objective function maximizes the total profit along with optimization of the flow within facilities. Moreover, a fuzzy linear programming and fuzzy stochastic linear programming model describes the proposed network's decisions. Finally, to validate the proposed model, a real case study is performed on Tehrandoosh Company and the model solutions are analyzed. The obtained results show the performance of the presented network. In which, considering the exchange plan would lead to 58 percent increase in the total profit of the supply chain. Furthermore, this study provided efficient and reliable managerial solutions for the faucet industry decision makers. [ABSTRACT FROM AUTHOR]

Abstract Traditional games theory is based on the idea of having a set of deterministic payoffs to represent actions taken by homogeneous individuals (interaction among players) while in several real scenarios, social and business conflicts are handled by groups of actors with different technical/social skills. This way, a group-game problem can be seen as to two-groups of players who individually select a strategy to win, so the information given by every player in their group affects the payoffs of such game. Sometimes, deterministic payoffs are not available, and even when they can be obtained from negotiation between players, they are not clearly defined. Indeed within groups, individual players could have different perceptions of the payoffs for which we propose a uncertain based matrix games model involving Interval-valued fuzzy payoffs. [ABSTRACT FROM AUTHOR]

In this paper we focus on a polynomial order even penalty function for solving a fuzzy linear programming problem and develop an algorithm which gives a better rate of convergence to achieve the optimal solution to the problem in hand. Some numerical examples are included to exhibit the efficiency of the new algorithmic procedure developed by us. [ABSTRACT FROM AUTHOR]

In this article, we consider some well-known approaches for solving fuzzy linear programming (FLP) problems. We present some of the difficulties of these approaches. Then, crisp linear programming problems are suggested for solving FLP problems. A new algorithm is also given. The proposed approach has advantages over the other methods. For example, we can achieve higher membership degrees for objective function and constraints. Moreover, we show that the fuzzy optimal solutions obtained by the proposed approach are efficient enough. Also, we see that unlike the previous methods, our method finds efficient solutions by solving only one crisp linear problem instead of solving two or three crisp problems. Finally some numerical examples are presented to show the efficiency of the given approach over the other approaches. [ABSTRACT FROM AUTHOR]

The operation of bidirectional V2G participating in ancillary services markets is particularly challenging due to various uncertainties. This work proposes an algorithm to optimize the uncertain operation of bidirectional V2G for an electric vehicle (EV) aggregator. The proposed algorithm maximizes the profits of the aggregator while providing additional system flexibility and low charging costs to the EV owners. The proposed algorithm considers electricity market and EV mobility uncertainties using fuzzy linear programming. These uncertainties include those of the regulation and responsive reserve prices, deployment signals, and the energy used for EV trips. Unlike other works in the literature, the proposed algorithm is capable of considering a large number of uncertain parameters without greatly impacting the problem's complexity or simulation time. Also, the algorithm does not result in conservative solutions. The simulation results show the superiority of the proposed fuzzy algorithm over its deterministic counterpart in terms of higher realized profits. Also, the proposed approach results in lower real-time penalties, which ensures its superiority to provide the EVs with the required trip energy at the required time. In addition, it results in lower battery degradation costs, which helps increase the life time of the EVs. [ABSTRACT FROM AUTHOR]

An innovative solution to provide a demand response for power system is proposed in this paper by considering the feasibility of two-way direct load control (TWDLC) of central air conditioning chiller system for wide-area in real-time manner. Particularly, the proposed TWDLC scheme is designed to tackle the load shedding ratio optimization problem for all under-controlled customers, aiming to satisfy the target load curtailment defined in each scheduling step. Another notable contribution of this work is the utilization of constraint loosening concept on actual load, curtailed to overcome the uncertainties of load reduction during TWDLC. Given the presence of fuzzy constraints, the proposed load shedding ratio optimization problem can be tackled using fuzzy linear programming. A delicate strategy is then formulated to transform the proposed fuzzy linear programming problem into a regular linear programming problem. A selection scheme used to obtain the feasible candidates set for load shedding at every sampling interval of TWDLC is also designed along with the fuzzy linear programming. [ABSTRACT FROM AUTHOR]

In this paper, steelmaking-continuous casting (SCC) scheduling problem is investigated and a mixed integer linear programming model is developed. Since the technical constraints in the mathematical model are not defined exactly, fuzzy sets are used to present them. With using fuzzy constraints, a compromise between different criteria is made based on expert’s ideas in steel industry. Since the mathematical model is suitable only for small size problems, a hybrid algorithm is developed to solve the SCC scheduling problem. The proposed algorithm is based on a combination of particle swarm optimization and fuzzy linear programming (FLP) methods. In this algorithm, the process of generating a solution consists of two phases. In the first phase, assigning and sequencing the charges on machines is done, while in the second phase, a FLP model is applied to determine start time of charges on assigned machines. To evaluate the proposed procedure, it is compared with an algorithm reported in the literature through solving different problems. Numerical results show that the proposed algorithm can obtain very good solutions for SCC scheduling problem. The results also reveal the higher efficiency of the proposed approach in decreasing waiting time of charges between processing. [ABSTRACT FROM AUTHOR]

We know that the linear programming model (LPM) is one of the most approach used in operation research and decision making, it represent a mathematical model for finding optimum allocation of resources, to satisfy certain objective, like maximize profit or minimize cost. In (LPM), we consider all coefficients of operation function and constraints are real but in real life problem, the wright hand side of (LP), and coefficients of variables of operation function may be a fuzzy number, so this research deals with explaining fuzzy linear programming model with definitions of required and with operation on fuzzy number, then how to solve fuzzy linear programming. [ABSTRACT FROM AUTHOR]

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness. [ABSTRACT FROM AUTHOR]

Energy and energy management is one of the most important subjects which concerns all the countries around the world. As fossil fuels are depleted, attention toward other energy sources increases. Renewable energy sources have become one of the popular topics in this field. Although these sources are renewable by nature, several difficulties are faced when countries attempt to implement these systems. One of these problems is the changing efficiency of renewable energy sources due to availability and quality of the sources such as sunlight intensity, wind speed, and so on. This study considers various renewable energy sources and different needs in a country. Next, a linear programming model is used to optimize the problem in deterministic form. After that, because efficiency of RES is not deterministic, in this article, we use fuzzy linear programming to handle these difficulties. To achieve this, we transform our linear model to fuzzy linear programming using theorems from literature. In this study, we used six RES plus nuclear energy to meet different electricity demand. In the end to test our FLP model, a case study in Iran, which bifurcates this country to east and west sections, each with different energy potentials, is done and the results are presented. © 2017 American Institute of Chemical Engineers Environ Prog, 36: 953-966, 2017 [ABSTRACT FROM AUTHOR]

The Berth Allocation Problem (BAP) in a maritime terminal of containers is defined as the feasible berth allocation of incoming vessels. In this work a model of fuzzy optimization for the BAP continuous and dynamical is developed. It is assumed that the time of arrival of the vessels is imprecise, in the sense that the vessels arrive early or late until a permissible tolerance. To represent the imprecision in the arrival of the vessels fuzzy set are used. For the solution of the model the α- cut method is applied. The proposed model has been coded in CPLEX and it has been evaluated for different instances. The obtained results show that the proposed model is useful to the managers of a maritime terminal of containers since they have at hand some berth plans with different degrees of earliness and delay allowed, optimized with regard to the waiting time and with the feature that, while greater the possibility of earliness or delay of a vessel is, a berth time is assigned to it supporting that possibility. [ABSTRACT FROM AUTHOR]

In this paper we analyze a special case of Fuzzy Linear Programming (FLP) in which its constraints are composed by fuzzy numbers contained into an interval. The binary relation between crisp constraints and fuzzy coefficients is analyzed, and the membership degree of a random realization of fuzzy parameters is de fined. An application example is presented and solved. [ABSTRACT FROM AUTHOR]

Short-term production plans are the basis for operational mine production schedules. They concentrate on making long-term mine plans operationally feasible. It ensures a steady flow of product for meeting blending targets. Due to the quality variation of material, blend optimization is an uncertainty based optimization problem. There are different approaches toward uncertainty management and the current paper investigates a portfolio optimization model in order to minimize the risks in short-term plans. In this paper, a fuzzy linear programming model is formulated to provide a set of options for the mine plan. These blending options are treated as portfolios. Then a model for the optimal selection of a portfolio is introduced. The objective of the model is to maximize the expected return of the portfolio under constraints limiting its variance. The model is applied in a limestone mine complex. [ABSTRACT FROM AUTHOR]

As the retailing industry becomes more customer oriented, it struggles with integrating the voice-of-customers into quality development policies, determining accurate customer expectations, and understanding how to incorporate the required store attributes in retailing activities. The aim of this study is to provide managers with a more decisive and sustainable framework to fulfill customer satisfaction by determining the most essential customer needs and gain a competitive advantage by applying a benchmarking process for the whole retailing activities. To essentially support managers in determining and implementing required store attributes, this study develops a sustainable linear programming (LP) based Quality Function Deployment (QFD) methodology under IVIF-environment. The proposed method determines more accurate customer expectations (CEs) and related service requirements (SRs). Accordingly, while "Clothing Quality", Price Policy", and "Staff Behavior" are determined as the most important CEs, "Design of Customer Persona", "Production Cost", and "Marketing Applications" are obtained as the most affecting SRs. Since no specific study in the literature addresses uncertainty in CEs and SRs in the apparel retailing industry, we developed an LP-based QFD under the IVIF-environment framework, which reflects the ambiguity and vagueness of the evaluations better. Thus, this study contributes to the literature by proposing a sustainable framework for managers to make decisions that are more effective and take sustainable actions. The companies who want to get the advantage in the apparel retailing industry should follow the methodology provided within this study by adding their business specific dimensions. Lastly, to represent the validity and feasibility of the proposed approach sensitivity and comparison analysis are conducted. The results of comparison show that the LP based QFD method is as consistent as other method but more effective in terms of handling ambiguity and fuzziness of expert evaluations, comprehensively. [ABSTRACT FROM AUTHOR]