Multi-objective Linear Fractional Programming Problem Research Articles

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

In the field of operation research, both linear and fractional programming problems have been more encountered in recent years because they are more realistic in expressing real-life problems. Fractional programming problem is used when several rates need to be optimized simultaneously such as resource allocation planning, financial and corporate planning, healthcare, and hospital planning. There are several techniques to solve the multiobjective linear fractional programming problem. However, because of the use of scalarization, these techniques have some limitations. This paper proposed two new mean and median techniques to solve the multiobjective linear fractional programming problem by overcoming the limitations. After utilizing mean and median techniques, the problem is converted into an equivalent linear fractional programming problem; then, the linear fractional programming problem is transformed into linear programming problem and solved by the conventional simplex method or mathematical software. Some numerical examples have been illustrated to show the efficiency of the proposed techniques and algorithm. The performance of these solutions was evaluated by comparing their results with other existing methods. The numerical results have shown that the proposed techniques are better than other techniques. Furthermore, the proposed techniques solve a pure multiobjective maximization problem, which is even impossible with some existing techniques. The present investigation can be improved further, which is left for future research.

On application of linear fractional programming problem using e-education system

This article focuses on an area of nonlinear programming problems known as linear fractional programming problems with multiple objectives. When tackling real-world linear fractional optimization problems, ambiguity and uncertainty in decision-making are inherent. This research aims to present a simple and computationally quick approach to solving multiple objective linear fractional programming problems with all decision variables and parameters described in terms of crisp. The proposed solution algorithm is based primarily on the fuzzy-based technique, and a membership function strategy. To resolve the multi-objective linear fractional programming problem, first consider the problem as a single objective function and along with the fuzzy programming model obtain the optimal solution using LINGO software. LINGO is a software application primarily used for solving linear, nonlinear, and integer optimization problems Moreover, an e-education setup problem demonstrates the steps of the proposed method.

Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems

Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic. This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function. Fuzzy goal programming is used to solve the MOLPP that has been obtained. Finally, the usefulness of the proposed technique is established using two mathematical models.

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

Solving neutrosophic multi-objective linear fractional programming problem using central measures

In this article, we present different kind of mean technique to solve Multi-Objective Linear Fractional Programming Problem (MOLFPP) in Neutrosophic Environment. Here in these mean techniques the MOLFPP is converted into Single Objective Linear Programming problem(SOLPP) and then we obtained the optimal solution by simplex method in Neutrosophic Environment. The proposed method is illustrated with the help of a numerical example.

Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem

Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem

Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems

An iterative technique based on the use of parametric functions is proposed in this paper to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem (MOLFPP). Each fractional objective is transformed into a non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively calculated and the intuitionistic fuzzy optimization method is used to solve a multi-objective linear programming problem. Also, some basic properties and operations of an intuitionistic fuzzy set are considered. The development of the proposed algorithm is based on the principle of optimal decision set achieved by the intersection of various intuitionistic fuzzy decision sets which are obtained corresponding to each objective function. Additionally, as the intuitionistic fuzzy optimization method utilizes the degree of belonging and degree of non-belonging, we used the linear membership function for belonging and non-belonging to see its impact on optimization and to get insight into such an optimization process. The proposed approaches have been illustrated with numerical examples.

A new efficient approach to tackle multi objective linear fractional problem with flexible constraints

<p style='text-indent:20px;'>Finding efficient solutions for the multi-objective linear fractional programming problem (MOLFPP) is a challenging issue in optimization due to the fact that more than one objective must be taken into consideration by the decision maker. For this class of optimization problems, we deal with the concept of efficient solutions. The set of efficient solutions could be an infinite set especially when the objectives are in conflict. In this paper, we present a new methodology to address the MOLFPP with flexible constraints i.e. the constraints with fuzzy right hand sides. In the method, firstly, the concept of the <inline-formula><tex-math id="M1">\begin{document}$ \alpha- $\end{document}</tex-math></inline-formula>cuts and ranking of fuzzy numbers are utilized to transform the original problem into the MOLFPP with fixed right hand sides. Secondly, a new MOLFPP is constructed based on the membership functions of the objectives. Afterward this new problem is changed into a single objective programming problem using the weighted sum approach. Finally, the global optimal solution of this single objective programming is obtained by taking into account a finite number of linear programming problems (LPPs). It is proven that the obtained solution is efficient for the main problem. Numerical examples are given to illustrate the method and comparisons are made to show the accuracy.</p>

Multi-level multi-objective linear fractional programming problem: a solution approach

Multi-level multi-objective linear fractional programming problem: a solution approach

Multi-level multi-objective linear fractional programming problem: A solution approach

Multi-level multi-objective linear fractional programming problem: A solution approach

Solving Multi-Objective Linear Fractional Programming Problems by Novel Methods

In this paper, we suggested two new techniques for transforming multi-objective linear fractional programming problems into single-objective linear fractional programming problems (SOLFPP) and then solving them by methods of SOLFPP. Illustrative numerical examples are presented for demonstration purposes. Also, the obtained results are compared with another method studied previously.

Modify Symmetric Fuzzy Approach to Solve the Multi-Objective Linear Fractional Programming Problem

The property of fuzzy sets is approached as an instrument for the construction and finding of the value of the multi-objective linear fractional programming problem (MOLFPP), which is one of the systems of decision problems that are covered by fuzzy dealings. The paper introduces an approach to convert and solve such a problem by modifying the symmetric fuzzy approach, suggesting an algorithm, and demonstrating how the fuzzy linear fractional programming problem (FLFPP) can be answered without raising the arithmetic potency. Also, it introduces a technique that uses an optimal mean to convert MOLFPP to a single LFPP by modifying the symmetric fuzzy approach. A numeric sample is provided to clarify the qualification of the suggested approach and compare the results with other techniques, which are solved by using a computer application to test the algorithm of the above method, indicating that the results obtained by the fuzzy environment are promising.

An Application of Fully Intuitionistic Fuzzy Multi-objective Linear Fractional Programming Problem in E-education System

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

Tackling the fuzzy multi-objective linear fractional problem using a parametric approach

Finding efficient solutions for the multi-objective linear fractional programming problem (MOLFPP) is a challenging issue in optimization because more than one target has to be taken into account. For the problem, we face the concept of efficient solutions which is an infinite set especially when the objectives are in conflict. Since a classical method generally comes out with only one efficient solution, thus introducing new efficient approaches is helpful and beneficial for the decision makers to make their decisions according to more possibilities. In this paper, we aim to consider the MOLFPP with fuzzy coefficients (FMOLFPP) where the concept of α - cuts is utilized so as to transform the fuzzy numbers into closed intervals and rank the fuzzy numbers as well. Consequently, the fuzzy problem is changed into an interval valued multi-objective linear fractional programming problem (IV-MOLFPP). Subsequently, the IV-MOLFPP is further changed into linear programming problems (LPPs) using a parametric approach, weighted sum and max-min methods. It is demonstrated that the solution obtained is at least a weakly ɛ - efficient solution, where the value of ɛ helps a decision maker (DM) to make his decision appropriately i.e. DMs chose more likely the solutions with the lowest value of ɛ. Numerical examples are solved to illustrate the method and comparison are made to show the accuracy, and the reliability of the proposed solutions.

Application of fuzzy random-based multi-objective linear fractional programming to inventory management problem

This research article aims to study a multi-objective linear fractional programming (FMOLFP) problem having fuzzy random coefficients as well as fuzzy pseudorandom decision variables. Initially, the FMOLFP model is converted to a single objective fuzzy linear programming (FLP) model. Secondly, we show that a fuzzy random optimal solution of an FLP problem is resolved into a class of random optimal solution of relative pseudorandom linear programming (LP) model. As a result, some of theorems show that a fuzzy random optimal solution of a fuzzy pseudorandom LP problem is combined with a series of random optimal solutions of relative pseudorandom LP problems. As an application, the developed approach is implemented to an inventory management problem by taking the parameters as trapezoidal fuzzy numbers, ultimately resulting in a new initiative for modelling real-world problems for optimization. In the last, some numerical examples are introduced to clarify the obtained results and their applicability.

A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables

A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables

Study on multi-objective linear fractional programming problem involving pentagonal intuitionistic fuzzy number

In this paper, we have suggested an alternative approach to solve intuitionistic fuzzy multi objective linear fractional programming problems (IFMOLFPP). Here, the cost of the objective function, the resources and the technological coefficients are taken to be pentagonal intuitionistic fuzzy numbers. In the proposed method, we have transformed (IFMOLFPP) to intuitionistic fuzzy multi objective linear programming problem (IFMOLPP) and then the resultant (IFMOLPP) is converted into crisp multi objective linear programming problem (CMOLPP) under well defined accuracy function. We have established some theorems to show that the efficient solution of (CMOLPP) is also an efficient solution of (IFMOLPP) and (IFMOLFPP). Then by using Zimmermann’s technique under suitable non linear membership functions, we have reduced (CMOLPP) to a single objective LPP which can be easily solved by any LPP algorithm or software. We have illustrated the proposed approach by Numerical examples.

Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and find its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

Solution procedure for multi-objective fractional programming problem under hesitant fuzzy decision environment

For the three last decades, the multi-objective fractional programming problem has attracted the attention of many researchers due to various applications in production planning, financial field, and inventory management, and so on. The main aim of this study is to introduce a new application of hesitant fuzzy sets in real-life modeling. We intend to model multi-objective linear fractional programming problems under a hesitant fuzzy environment and present a procedure to solve them. the increasing applications of multi-objective linear fractional programming problems and the lack of research papers in this field under a hesitant fuzzy environment are the main motivations of this study. In a hesitant fuzzy set, the membership degree of an element belongs to the set can be represented by several possible values in [0,1]. These values can be chosen by different experts that cannot reach a single opinion in determining a membership degree. so, in our model several evaluations for each of goals established by decision makers based on their attitudes. The generalization of the fuzzy decision-making principle and some new concepts provide an effective solution procedure for the problem. Finally, a practical example is extended to illustrate the applicability of the proposed method.

A New Method to Solve Multi-Objective Linear Fractional Problems

Background: In the literature, there exists several approaches to address the multi-objective linear fractional programming problem (MOLFPP). However, there is a drawback to these methods. Aim: This paper presents an efficient method treating the MOLFPP. Methodology: To construct our approach,the membership functions of the objectives, suitable non-linear variable transformations, and max-min technique are used. Results: In our proposed method, the MOLFPP is finally changed into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an efficient solution for the MOLFPP. Conclusion: Numerical examples are solved, and the results demonstrate that our method with less computational expenses and cost reach the efficient solutions.