Search

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]

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 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]

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]

Network planning is an important design-step wherein various network resources are provisioned at different network locations. Traffic demand for all node pairs in the network is an important determining factor for network planning, and typically, a static traffic demand matrix consisting of long-term average traffic values for all node pairs is employed. However, assessment of traffic demand matrix may not be accurate (precise). In this paper, we propose an optimization framework to minimize traffic congestion in a wavelength-routed wavelength-division multiplexing WDM optical backbone network using such approximate traffic demands. Modeling such a network is constrained by limited network resources, and can be formulated in general as a fuzzy optimization problem. Moreover, decision maker might want to relax traffic congestion goal by a small margin in presence of approximate traffic demand matrix, so as to reach some aspiration level, rather missing the crisp target by a very small amount. We use the network planning model to minimize traffic congestion so as to achieve an aspiration level of traffic congestion. We use Zimmermann's fuzzy programming technique to explore mixed integer linear programing based optimization model incorporating fuzzified constraints and objective function. All related constraints, such as traffic and lightpath routing, wavelength selection, restriction due to average propagation delay, lightpath degree and maximum hop count constraints are taken into consideration. Following the proposed model, under fuzzy environment, we implement reliable and efficient network planning and traffic provisioning, and estimate traffic congestion more accurately. [ABSTRACT FROM AUTHOR]

In this manuscript, three contributions are proposed. First contribution is proposing a good evaluation between the fuzzy and neutrosophic approaches using a novel fuzzy-neutrosophic transfer. Second contribution is introducing a general framework for solving the neutrosphic linear programming problems using the advantages of the method of Abdel-Basset et al. and the advantages of Singh et al.'s method. Third contribution is proposing a new neutrosophic exterior point simplex algorithm NEPSA and its fuzzy version FEPSA. NEPSA has two paths to get optimal solutions. One path consists of basic not feasible solutions but the other path is feasible. Finally, the numerical examples and results analysis show that NEPSA more than accurate FEPSA. [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]

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]

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, α -cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately. [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]

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]

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]

Abstract Recycling aims at preventing rapid depletion of natural resources while transforming produced waste into value for economy. However, this process becomes a major challenge in automotive industry, which requires cooperative engagement of multiple players within a complex supply chain. In line with the essence of the topic, government agencies around the world issue directives drawing regulatory frameworks for designing recycling operations comprising various activities such as collection of end-of-life vehicles (ELVs), recovery of reusable components, shredding ELV's body, recycling valuable materials and disposal of the hazardous waste. In general, the amount of returned product in a reverse logistics network is highly uncertain, and the ELV market in Turkey is no exception to this. For that purpose, this study aims developing a fuzzy mixed integer location-allocation model for reverse logistic network of ELVs conforming to the existing directives in Turkey. Accordingly, this study uses a novel approach and assumes that ELV supply in the network is uncertain. The merit of the proposed mathematical model is proved on a real world scenario addressing the reverse logistics design problem for ELVs generated in metropolitan area of Istanbul. The network generated specifies that recycling process is not profitable under the existing circumstances with the given level of supplied ELV and the returned product records per capita in Istanbul are far beyond the EU averages. Consequently, sensitivity analyses question the reliability of the obtained results. [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]

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]

The growing awareness about the adverse effects of fossil fuels and the ensuing pollution has encouraged and promoted the use of renewable energies throughout the world. This in turn has encouraged governments and investors to show more interest in generation of renewable energy through construction of facilities such as wind farms. The novelty of this research work is the budget constraints consideration for the first time in wind energy projects. This work is done for the Khorasan provinces of Iran. This study is based on regional and municipal data pertaining to the year 2016, and uses the fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to deal with the uncertainty of the data. The fuzzy TOPSIS method is used to evaluate and rank the candidate cities, and the results are then used to develop a budget-constrained model by fuzzy linear programming with the Maxmin objective function. The resulting mathematical model is optimised with GAMS software. The modelling results show that in the presence of budget constraints, of 10 Khorasan cities considered as candidate locations, Afriz, Rudab, and Fadashk exhibit the best conditions for the construction of wind farms. [ABSTRACT FROM AUTHOR]

This paper proposes a new energy management scheduling model for optimizing operation costs of a non-isolated micro-grid. It's assumed that the micro-grid includes some renewable energy resources like wind turbines and photovoltaic panels, fuel cell, and energy storage systems, and is connected to the macro-grid through a distributed transmission line with limited capacity. Different possible uncertainties associated with different elements of the micro-grid like forecasted outputs of renewable resources, a maximum capacity of the fuel cell and batteries, a maximum capacity of distributed line and hourly demands are considered in the proposed model. Fuzzy sets concept is used to model these uncertainties in the micro-grid and a three stage optimization method is applied to find the optimal scheduling of the micro-grid under the uncertainties. The proposed method is implemented to a real case study. Impacts of variations in each element of the micro-grid and its associated uncertainty on the results are investigated through a sensitivity analysis. [ABSTRACT FROM AUTHOR]

Fuzzy linear regression analysis helps to produce successful assumptions in situations with uncertainty between variables and provides researchers with a flexible perspective. In this study, 305 days milk yield estimation studies were carried out using partial lactation records of Jersey cattle with the fuzzy linear regression method. Calving age, number of lactation, days of milk, calving season, and the first four milk test days records were used as the independent variables in the study. Also,305 days milk yield was used as the dependent variable. Reliability of the obtained estimates was discussed using graphical representations of h values and three different statistical error criteria (RMSE, MAPE and R). In addition, the estimated values obtained were compared with the observed values. The fuzzy linear regression equations developed for 10 different h values shows that the equations obtained for the h = 0.4 and h = 0.5 values are the closest observed values to305 days milk yield. The difference between the predicted values and the observed values was statistically insignificant (p>0.05). These results show that the fuzzy linear regression method can be successfully used to predict 305 days milk yield at the beginning of the lactation. [ABSTRACT FROM AUTHOR]

In this paper, efforts are made to find the fuzzy optimal solutions for electric tomography imaging (ETI) process. Most of the conventional ETI methods depend on an optimization process with a deterministic objective function and constraint conditions. The effective application of these methods requires the availability of measured data. However, in practical ETI possess, the assessable data are uncertain, imprecise, incomplete, and characterized by fuzziness. In this paper, the fuzzy characteristics hidden in the ETI process are extracted, and a new model of fuzzy optimization is built up, whose optimal solution is obtained by using fuzzy linear programming (FLP). The FLP model can provide a robust methodology to boost the ETI spatial resolution. Thus it creates a new and promising research direction for the optimization of the ETI process. Experimental results prove that compared with other existing ETI algorithms, the proposed method is more effective in reconstructing complex and discretely distributed objects. [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]

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]

Most of the existing methods for solving fully fuzzy mathematical programs are based on the standard fuzzy arithmetic operations and/or Zadeh's extension principle. These methods may produce questionable results for many real-life applications. Due to this fact, this paper presents a novel method based on the constrained fuzzy arithmetic concept to solve fully fuzzy balanced/unbalanced transportation problems in which all of the parameters (source capacities, demands of destinations, transportation costs etc.) as well as the decision variables (transportation quantities) are considered as fuzzy numbers. In the proposed method, the requisite crisp and/or fuzzy constraints between the base variables of the fuzzy components are provided from the decision maker according to his/her exact or vague judgments. Thereafter, fuzzy arithmetic operations are performed under these requisite constraints by taking into account the additional information while transforming the fuzzy transportation model into crisp equivalent form. Therefore, various fuzzy efficient solutions can be generated by making use of the proposed method according to the decision maker's risk attitude. In order to present the efficiency/applicability of the proposed method, different types of fully fuzzy transportation problems are generated and solved as illustrative examples. A detailed comparative study is also performed with other methods available in the literature. The computational analysis have shown that relatively more precise solutions are obtained from the proposed method for “risk-averse” and “partially risk-averse” decision makers. The proposed method also successfully provided fuzzy acceptable solutions for “risk seekers” with high degree of uncertainty similar to the other existing methods in the literature. [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]

For power system decision makers, they should decide a reasonable wind capacity or target penetration level considering the balance of wind curtailment, investment, system reliability and social benefit. Assessing wind curtailment under different wind capacity, considering the wind resource uncertainty, is therefore necessary for utilizing wind power effectively. In this paper, fuzzy wind capacity factor is proposed to analyze and propagate the uncertainty of wind resources based on the wind speed distribution. By investigating the maximal wind power output that can be accepted in candidate system nodes, a fuzzy linear programming problem is proposed to decide the required wind capacity considering the fuzzy wind capacity factor. Based on the cumulative distribution function of wind capacity resulting from large number of simulations, the relationship between wind capacity and wind curtailment is determined. The effectiveness of the proposed model is validated by its application in two power grids. The results demonstrate that the proposed model and method are capable of describing the possibilistic uncertainty of wind resources and assessing wind curtailment under different wind capacity. Compared with previous research, this method can aid power system planners to allocate wind capacity considering the possibilistic uncertainty of wind resources. [ABSTRACT FROM AUTHOR]

Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving interval-valued trapezoidal fuzzy numbers for the transportation costs and values of supplies and demands. We propose a fuzzy linear programming approach for solving interval-valued trapezoidal fuzzy numbers transportation problem based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To illustrate the proposed approach an application example is solved. It is demonstrated that study of interval-valued trapezoidal fuzzy numbers transportation problem gives rise to the same expected results as those obtained for TP with trapezoidal fuzzy numbers. [ABSTRACT FROM AUTHOR]

Fuzzy Linear Programming is among the best and most studied topics in the Fuzzy Sets and Systems area. In this paper, the author describes the main developments, results and solution methods achieved in this topic throughout the last 35 years, from a personal point of view. Short descriptions on different Fuzzy Linear Programming problems are provided and future research lines are briefly pointed out. [ABSTRACT FROM AUTHOR]

Here This paper focuses on solving the transportation problems with neutrosophic data for the first time. The indeterminacy factor has been considered in Transportation Problems (TP). The two methods of linear programming - Fuzzy Linear Programming (FLP) and Crisp Linear Programming (CLP) are discussed with reference to neutrosophic transportation problems. The first method uses the membership, non-membership and indeterminacy degrees separately to find the crisp solution using the Fuzzy Programming Technique and then the optimal solution is calculated in terms of neutrosophic data with the help of defined cost membership functions. The satisfaction degree is then calculated to check the better solution. The second method directly solves the TP to find crisp solution considering a single objective function. The cost objective function is taken as neutrosophic data and the methods have been used as such for the first time. Both the methods have been illustrated with the help of a numerical example and these are then applied to solve a real life multi - objective and multi-index transportation problem. Finally the results are compared. [ABSTRACT FROM AUTHOR]

The first researchers to publish an operationalization of the Bellman and Zadeh's original approach to “Decision making in a fuzzy environment” [1] were H. Tanaka and K. Asai in their 1973 article [2] which was published in English in 1974 [3] . These two researchers developed many fundamental theories and methods including novel concepts of fuzzy operations research [4] with their collaborators. They went beyond the original proposal for fuzzy optimization set forth by Bellman/Zadeh. They are important founders of fuzzy optimization. This paper gives an overview of their great contributions to fuzzy optimization. [ABSTRACT FROM AUTHOR]

Abilities of fuzzy models in more adaptations with the real world phenomena causes that in this paper, we remodel semi-infinite linear programming problems as fuzzy problems which contained the crisp objective function and the infinite number of fuzzy constraints. Then, we introduce a new hybrid solution method for these fuzzy semi-infinite linear programming problems. This solution technique is a kind of cutting plane algorithm in which its sub-problems were solved by using the Zimmermann-method. Convergence of the presented algorithm is proved, and some numerical test examples are given and also the obtained results are compared. [ABSTRACT FROM AUTHOR]

Selecting a suitable outsourcing provider is one of the most critical activities in supply chain management. In this paper, a new fuzzy linear programming method is proposed to select outsourcing providers by formulating it as a fuzzy inhomogeneous multi-attribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information. In this method, the decision maker's preferences are represented as trapezoidal fuzzy numbers (TrFNs), which obtained through pair-wise comparisons of alternatives. Based on the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS), the fuzzy consistency and inconsistency indices are defined by the relative closeness degrees in TrFNs. The attribute weights are estimated by solving the proposed fuzzy linear programming. And then the selection ranking is determined by the comprehensive relative closeness degree of each alternative to the FPIS. An industrial IT outsourcing provider selection example is analyzed to demonstrate the implementation process of this method. [ABSTRACT FROM AUTHOR]

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

In recent years various attempts have been made to study the solution of fuzzy variable linear programming problems by introducing and solving certain auxiliary problems or directly by the use of dual simplex method based on a certain linear ranking function. But these methods are not applicable for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, as a natural extension of the results in crisp linear programming and based on a certain linear ranking function we obtain some new results leading to a new method to overcome this shortcoming. To show the application of our method a real life problem is solved by using the proposed method. Also, one application of this approach in solving maximum flow problem with fuzzy capacity is dealt with. [ABSTRACT FROM AUTHOR]

This paper proposes a novel meta-heuristic based algorithm which provides the optimal solution for several different degrees of feasibility for fuzzy linear and nonlinear programming problems. The proposed method has got the ability for solving those problems in which all coefficients of the objective function and constraints are represented by LR fuzzy numbers with linear and/or non-linear membership function. To solve the fuzzy problems, this paper provides a new hybrid genetic algorithm accompanied by a new proposed method of simulating fuzzy coefficients which 1) eliminates the need of applying defuzzification methods and/or expected interval methods, and 2) allows dealing with different types of fuzzy numbers, properly. In order to show the performance of the proposed method, it is compared with 'M. Jiménez, M. Arenas, A. Bilbao and M.V. Rodríguez, Linear programming with fuzzy parameters: An interactive method resolution, European Journal of Operational Research 177 (2007), 1599-1609.'. Computational results reveal that the proposed method is superior to the Jiménez et al. [13] method from the viewpoint of feasibility and optimality. [ABSTRACT FROM AUTHOR]

Companies stick to particular plans and programs in manufacturing in order to use resources productively to increase revenues. Linear programming approach is one of the effective solutions to production planning issues. In this study, real data have been obtained from a bedstead manufacturer in furniture industry to develop a fuzzy linear programming model in order to solve production planning problem. In this study, Zimmermann approach has been used for the fuzzification of the objective function, total machine time, lower and upper demand levels. [ABSTRACT FROM AUTHOR]

Fuzzy linear programming is used widedly for the problems of uncertain system's optimization, but the optimization solutions or satisfactory solution are often not "immune" to parameters, that is if the parameters are changed, initial optimal solution is no longer optimal or even infeasible. First of all, for the λ-cut level of fuzzy linear programming, λ-robust optimization solutions are put forward; then article indicates the definition of λ-robust solution by fuzzy structured element, and obtains the solving model. Solution can achieve the degree requirements are different due to the different decision makers, therefore, the measure constraints which can reflect the decision-makers risk preferences are added to the model, the solution of this model is γ-robust solution, and the solution not only has the robustness and optimization, but also reflects the degree of risk preference of the decision makers. By an example, it is found that the optimization robust solutions with measurement are immune to parameters, which are more useful for decision-makers and reflect a better practical value. [ABSTRACT FROM AUTHOR]

To formulate fuzzy linear programming, Gaussian membership functions rather than triangular or trapezoidal ones are usually recognized as more reasonable descriptions for fuzziness. However, the strong nonlinearity of Gaussian membership functions is readily to cause increasing difficulties in achieving optimum solutions accordingly. Motivated by this challenge, we introduce a novel piecewise linear membership function-based decomposition-coordination algorithm, which can initially decompose a fuzzy linear programming problem with Gaussian membership functions into several crisp linear programming models and then coordinate solutions of the sub-models to eventually achieve an overall optimum one. In this paper, detailed algorithmic procedures are presented along with corresponding theoretical analysis. In addition, an application of production planning programming in a workshop of an oil refinery is provided to demonstrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]