This study examines the fully fuzzy multi-objective linear fractional programming problem (FFMOLFPP), whereby both the objective functions and restrictions incorporate fuzzy parameters represented as triangular fuzzy numbers (TFN), without converting them into crisp values. A hybrid solution approach is presented to tackle the intrinsic nonlinearity and uncertainty. Initially, the imprecise numbers are transformed into parametric representations via the y- cut method. A first-order Taylor series expansion is subsequently utilized to linearize each fractional objective function around a fuzzy decision point. The linearized objectives are then consolidated by the weighted sum approach, transforming the multi-objective fuzzy model into a single-objective linear program. Numerical examples validate the strategy and demonstrate the improved accuracy and efficiency of the proposed methodology.

An adaptive branch-and-bound algorithm for minimax linear fractional programming

Linear fractional programming problems in an interval environment

The real world optimization problems in hierarchical decision making systems, often encounter multiple functions in fractional forms with uncertain parameters. To tackle such situation of uncertainty, this paper proposes a novel methodology to find a compromise solution of a bi-level multi-objective linear fractional programming problem which is designed in a fuzzy environment with its parameters expressed as intuitionistic triangular fuzzy numbers. Based on the concept of intuitionistic fuzzy (α, β)-cuts and some theoretical aspects, the bi-level intuitionistic fuzzy model is formulated into an equivalent bi-level optimization with multiple interval valued fractional functions. The method proposed by Chakraborty and Gupta, is utilized to compute the individual compromise solution of each interval valued fractional objective function. Subsequently, the upper and lower level compromise solutions are computed to ascertain the aspiration values of the multiple interval valued fractional functions and the decision variables controlled at the upper level. Goal programming approach using a proposed modified linearization technique for fractional functions, is implemented to derive the compromise solution of the bi-level fuzzy optimization model. An existing numerical example, a practical problem in production sector are solved and the comparative discussion on result analysis is incorporated to demonstrate the feasibility and efficiency of the proposed approach.

Performing the efficient global optimization algorithm for generalized linear fractional programs (GLFPs) is a very desirable goal in the field of optimization. As the problem's size increases, this goal is becoming increasingly difficult to achieve, although there have been some advances in recent years. In this paper, we present an efficient outcome space branch-and-bound algorithm for globally solving large-scale GLFPs. First, we convert the GLFP into its equivalent problem (EP) by introducing new variables. Second, a hybrid relaxation strategy (a convex envelope and a second-order cone) is used to derive a series of new linear relaxation problems (LRPs) that approximate the EP's optimal value. Meanwhile, a new region reduction method is presented, where the branching operation is performed in an outcome space. A novel branch-and-bound algorithm is then provided to solve GLFPs by computing a lower bound from the LRPs. Subsequently, the algorithm's convergence and worst-case iteration count are also reported. We conclude with numerical experiments illustrating the proposed algorithm's efficacy, especially when solving large-scale GLFPs.

An Efficient Algorithm for Solving Linear Fractional Programming Problems with Flexible Branching Technique

An important planning tool is linear fuzzy fractional programming, it is used in various fields such as business, engineering, and others. We are trying to get one of the direct and effective methods that contain some arithmetic operations to obtain the optimal real values through which a multi-objective fuzzy linear programming problem (MOFLFPP) is transformed into a linear programming problem (LPP) through the use of α-cut and MaxMin technique. The field of application is Iraqi Light Industries Company and chose the best products that must be protected which achieved a possible greatest profit ratio to less cost, Where the paper will include two sections, the first is concerned with describing the data and building the mathematical model for the problem (MOFLFPP) related to the research problem. The second section deals with trying to solve the model as well as finding the optimal solution, which represents determining the best and optimal production mix that achieves maximum profits at the lowest costs in light of the restrictions imposed on the production process, which may limit the company’s ability to provide products in the required quantity and the right time. The proposed methodology proved effective in solving multi-objective linear fractional programming problems with fuzzy coefficients (MOLFPP). While the previous approach produced results between (0.19904, 0.3406), our technique improved them to (0.2087, 0.3431), demonstrating higher reliability and efficiency with an ε-optimal unique solution.

Linear fractional programming inadequately captures the complexities of real-world scenarios due to its inherent linearity and sensitivity to parameter variations. In contrast, non-linear fractional programming (NLFP) offers versatility in modelling nonlinear relationships. Yet, existing literature lacks a comprehensive treatment of NLFP with interval uncertainties associated with both coefficients and decision variables. This paper introduces the Non-linear Enhanced Interval Fractional Programming Problem ( NLEIFP ), which extends NLFP to accommodate interval uncertainties. A parametric approach is proposed to address NLEIFP , transforming it into a deterministic model by leveraging the parametric representation of intervals. This approach enables more precise solutions that account for interval uncertainties in both the objective function and constraints. The efficacy of the proposed methodology is demonstrated through illustrative numerical examples, highlighting its applicability in diverse real-world contexts.

A Linearization to the Fully Fuzzy Linear plus Linear Fractional Program

Production optimization under resource constraints can be effectively modeled using Linear Fractional Programming (LFP), where the objective function is defined as a profit-to-cost ratio. This study applies the Hasan–Acharjee method to optimize production planning in a household-scale bakery enterprise in Indonesia, considering four product types and three resource constraints (materials, labor, and equipment). The model was reformulated as a single linear program and solved using LINGO 21.0. Validation against the classical Charnes–Cooper transformation confirmed identical optimal solutions, demonstrating the robustness of the Hasan–Acharjee approach. Sensitivity and trade-off analyses further revealed how variations in costs and production capacity influence profitability. The results highlight both the theoretical relevance of the Hasan–Acharjee method in fractional programming and its practical applicability to small and medium-sized enterprises seeking efficient resource utilization under limited conditions.

Fuzzy stochastic optimization has emerged as an effective approach for dealing with probabilistic and imprecise uncertainties, which makes it useful for problems when data is simultaneously impacted by vagueness and randomness. When these uncertainties involve in decision making problem where, it is required to determine the relative merits between different alternatives, we have often used the fuzzy stochastic fractional programming problem. This paper developed a new approach to derive the acceptable range of objective values for a Multi-objective fuzzy stochastic linear fractional programming problem (MOFSLFPP). In this problem, the fuzzy random variables coefficient is involved as the parameters of the objective function as well as system constraints. The proposed method constructs an expectation model based on the mean of the fuzzy random variable. For the satisfaction level of decision-makers, the level set properties of the fuzzy set are applied in the objective function. The chance-constrained programming method is utilized to transform the MOFSLFPP into its equivalent crisp form. For validation of the proposed methodology, an existing numerical has been solved, and the comparison of the proposed methodology has been discussed with the existing one. Also to demonstrate the practical application of this methodology, an inventory management problem has been discussed.

The revised harmonious fuzzy technique (RHFT) is a method used to solve fuzzy optimization problems. It was capitalized as an extension of the classical linear programming technique to handle constraints and objectives that are fuzzy. The harmonious fuzzy technique HFT aims to find a solution that satisfies the uncertain restraints and optimizes the uncertain objectives while taking into account the uncertainty or fuzziness of the problem parameters. This work demonstrates how the RHFT can be utilized to dexterously solve “fully fuzzy multi-goal linear fractional programming (FFMOLFP) problems”. Initially, the FFMOLFP problem can be converted to “single goal linear fractional programming (SOLFP) problems” consuming the modified brittle linear technique. Second, the RHFT is applied to converted brittle problems into linear programming problem, which follow, “the single-goal problem” is made on so on applied the revised harmonious fuzzy for apiece level. at the end, the obtained LPP will be solved by applied the simplex algorithm. To illustrate the application of this method, two examples will be provided. Also, the numerical results are simulated by comparing between proposed method and efficient ranking function methods for fully fuzzy linear fractional programming problems FFLFPP

Fuzzy Triangular Linear Fractional Programming Problem (FTLFPP) is one in which the objective function is a linear fractional function, while the constraints are in the form of linear inequalities. This paper meticulously implements the proposed conversion technique without compromising the original objective functions and constraints. The standard methods are quite complex and tedious. Here we propose a novel conversion technique that converts the given FTLFPP into FTLPP, which helps us smoothly solve the FTLFPP. This is illustrated with the help of some numerical examples.

A note on “Study on multi-objective linear fractional programming problem involving pentagonal intuitionistic fuzzy number”

Process analysis-based industrial production modelling with uncertainty: A linear fractional programming for joint optimization of total caron emissions and emission intensity

Unmanned aerial vehicle (UAV)-assisted visible light communication (VLC) plays an essential role in night communication and lighting. Nevertheless, the restricted payload capacity of UAVs, coupled with user demands for high communication quality, brings new challenges to UAV communication. This research explores a rate-splitting multiple access (RSMA)-enabled UAV-VLC network considering jittering effects with imperfect channel state information (CSI) and successive interference cancellation (SIC). Then, a multi-objective optimization problem is proposed to minimize energy consumption and maximize the transmission rate. Due to its non-convexity and high computational complexity, the problem is decomposed into two sub-problems: path planning and power allocation. For the path planning problem, a hover point fine-tuning algorithm is proposed considering the field of view (FoV) constraint, and then a simulated annealing (SA) algorithm is utilized to obtain an optimized trajectory. For the power allocation problem, linear fractional programming (LFP) and successive convex approximation (SCA) are employed to convert the power allocation issue into a convex one. Finally, simulation results demonstrate the effectiveness of the proposed algorithm in RSMA power allocation and UAV path planning.

A fuzzy approach for the intuitionistic multi-objective linear fractional programming problem using a bisection method

In this article, we propose a new method for solving Linear Fractional Programming (LFP) problems with bounded variables. The proposed algorithm passes from a support feasible solution to a better one following the feasible direction proposed in [K. Djeloud, M. Bentobache and M. O. Bibi, A new method with hybrid direction for linear programming, Concurrency and Computation, Practice and Experience 33 (1), 2021]. Optimality and suboptimality criteria which allow to stop the algorithm when an optimal or suboptimal solution is achieved were stated and proved. Then, a new method called a Hybrid Direction Method (HDM) is described and a numerical example is given for illustration purpose. In order to compare our method to the classical approaches, we develop an implementation with the Matlab programming language. The obtained numerical results on solving 120 randomly generated LFP test problems show that HDM with long step rule is competitive with the primal simplex method and the interior-points method implemented in Matlab.

Fuzzy Goal Programming Approach for Solving Linear Fractional Programming Problems with Fuzzy Conditions

A novel technique for solving bi-level linear fractional programming problems with fuzzy interval coefficients