Fractional Transportation Problem Research Articles

Linear fractional transportation problem in bipolar fuzzy environment

This article proposes a solution methodology for the Linear Fractional Transportation Problem (LFTP) by incorporating bipolar fuzzy sets (BFSs) to accommodate both positive and negative judgmental perspectives. The approach explores Zimmermann's extension within bipolar fuzzy environment to compare outcomes. In this context, the cost function and constraint coefficients are depicted using interval-valued trapezoidal bipolar fuzzy numbers (IVTrBFNs) and defuzzified by (s, t)-cut. The initial approach employs the simplex method and fuzzy optimization method, renowned for its effectiveness in obtaining optimal solutions. In the alternative method, Bipolar fuzzy programming approach (BFPA) is utilized for better outcome. In this method the LFTP is altered to a Multi-Objective Transportation Problem (MOTP), and BFPA extends Zimmermann's technique under suitable positive and negative membership functions, converting MOTP to a one-objective transportation problem (TP) and solved using LINGO software. Supporting this proposed method some theorems are formulated to demonstrate that the most effective solution of the single-objective TP is a Pareto optimal solution for the corresponding MOTP. A quantitative example is provided for better understanding of the proposed BFPA method alongside two other approaches.

Investigation of Markovian Process in Server Break-down

In day to day life goods produced at a number of places are consumed at different locations and then the problem faced by producer or dealer is to transfer goods from numerous places of origin to various places of consumption such that cost of transportation, time required, damages to the product etc. are optimum. This is called classical transportation problem. In this study we have studied transportation problem solve by Markov Decision Process. Introduction to the operations research is made along with over view of optimization techniques of single objective transportation problem. For literature review in the subject of multi objective fractional as well as linear multi objective transportation problems. In basic concepts of Markov Decision Process are given for further usage in the thesis work. We have stated algorithms for solving different types of multi objective programming problems. In entire work we have used basically linear membership functions, hyperbolic membership function and exponential membership function. These membership functions are Markov Decision Process. In case of linear membership function weighted arithmetic mean, weighted quadratic mean, geometric mean is used to find compromise solution. Almost everywhere we have found that the compromise solutions are fairly close to optimal solution when the problem is solved as single objective function. We have solution procedure for multi objective linear transportation is given using Markov Decision Process. Introduction to fractional programming is made and solutions of multi objective linear fractional programming problems are discussed. We have solutions of multi objective linear fractional transportation problem. In this topic fractional objective functions are approximated as linear functions using Taylor’s theorem and then applied method to solve the multi objective linear transportation problem discussed earlier. We focus on solution to fractional transportation problem with Markov Process coefficients. To multi objective fractional transportation problem with goal programming approach. We deal with general integer programming problem along with fractional transportation problems. The main result of this thesis is a characterization of increasing Marko processes satisfying certain conditions. At the end bibliography and research papers published by authors are given. Keywords: Markov Process, Transportation, Queen analyses Server system.

A new iterative fuzzy approach to the multi-objective fractional solid transportation problem with mixed constraints using a bisection algorithm

A new iterative fuzzy approach to the multi-objective fractional solid transportation problem with mixed constraints using a bisection algorithm

Navigating uncertain distribution problem: a new approach for resolution optimization of transportation with several objectives under uncertainty

Amidst uncertainty, decision-making in manufacturing becomes a central focus due to its complexity. This study explores complex transportation constraints and uses novel ways to guide manufacturers. The Multi-objective Stochastic Linear Fractional Transportation Problem (MOSLFTP) is a crucial tool for managing supply chains, manufacturing operations, energy distribution, emergency routes, healthcare logistics, and other related areas. It adeptly addresses uncertainty, transforming efficiency and effectiveness in several domains. Stochastic programming is the process of converting theoretical probabilities into concrete certainties. The artistic compromise programming technique acts as a proficient mediator, reconciling opposing objectives and enabling equitable decision-making. This novel approach also addresses the Multi-objective Stochastic Linear plus Linear Fractional Transportation Problem (MOSLPLFTP), which involves two interconnected issues. The effectiveness of these principles is clearly shown with the help of the LINGO® 18 optimization solver. This study uses a ranking method to compare the similar methods to solve the current problems. A meticulously designed example acts as a significant achievement, shedding light on our method in a practical setting. It serves as a distinctive instrument, leading manufacturers through the maze of uncertainty and assisting them in determining the most advantageous course of action. This journey involves subtle interactions between complexity and simplicity, uncertainty is overcome by decisiveness, and invention is predominant.

Solving a multi-choice solid fractional multi objective transportation problem: involving the Newton divided difference interpolation approach

<abstract> <p>Multi-objective transportation problems (MOTPs) are mathematical optimization problems that involve simultaneously considering multiple, often conflicting objectives in transportation planning. Unlike traditional transportation problems, which typically focus on minimizing a single objective such as cost or distance, MOTPs aim to balance multiple objectives to find the optimal solution. These problems appear in various real-world applications such as logistics, supply chain management, and transportation, where decision-makers need to consider multiple criteria when designing transportation networks, routing vehicles, or scheduling deliveries. The primary challenge lies in the uncertainty in real-world transportation scenarios, where logistics involve factors beyond cost and distance. We investigated a multi-choice solid fractional multi-objective transportation problem (MCSF-MOTP) based on supply, demand, and conveyance capacity, where the coefficients of the objective functions were of the multi-choice type due to uncertainty. To address this uncertainty, the proposed model employed the Newton divided difference interpolation polynomial method, and the suitability of this model was validated through a numerical illustration employing a ranking approach.</p> </abstract>

An aspect of bilevel interval linear fractional transportation problem with disparate flows: a fuzzy programming approach

An aspect of bilevel interval linear fractional transportation problem with disparate flows: a fuzzy programming approach

On solving fully rough multi-objective fractional transportation problem: development and prospects

On solving fully rough multi-objective fractional transportation problem: development and prospects

Multi-choice fractional stochastic multi-objective transportation problem

Multi-choice fractional stochastic multi-objective transportation problem

On Fuzzy Linear Fractional Programming Problems via α-Cut-Based Method with Application in Transportation Sector

The article provides an α-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using α-cut of fuzzy numbers wherein the α- and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of r∈(0,1] are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique.

An improved solution approach for solving multi-objective linear and linear fractional transportation problem

This work shows a transportation problem (TP) that can be thought of as the sum of a linear function and a linear fractional function. Here, the linear function shows the total transportation cost, and the linear fractional function shows the proportion of damaged objects and the transport profit. We aim to set up a transportation plan that reduces the total transportation cost and the proportion of total damage to the object to the total profit. Here we are discussing three types of objective functions as: linear plus linear fractional, linearfractional, and linear separately. We formulated a TP using the three objective functions for the solution. We solve all three objective functions for different weights with the proposed method and get a compromise solution.

A new solution procedure for multi-objective linear fractional transportation problem with rough parameters

In this article, we are discussing a rough multi-objective linear fractional transportation problem (RMOLFTP). In Day-to-day life, we frequently encounter many situations where the transportation problems are represented by a rough set. The main aim of our research article is to solve the RMOLFTP where the transportation cost and profit, of the product as rough interval coefficients. Here a new logic is introduced by us to solve RMOLFTP that diversifies the form of Nomani et. al., (2016). To demonstrate the recommended algorithm, a rough numeric problem with two objective functions is offered. A weighted model is presented in this approach for the solutions.

An approach for solving fully fuzzy linear fractional transportation problem with the using of splitting technique

An approach for solving fully fuzzy linear fractional transportation problem with the using of splitting technique

Flexible fractional transportation problem with multiple goals: a pentagonal fuzzy concept

We present the framework of the multiobjective fractional transportation problem in the form of pentagonal fuzzy supply and demand. The ideal transportation model is set up to match the decision makers’ preferences in competing for the criteria, and transportation costs, delivery time, degradation, environmental and social concerns are the objectives. We employed flexible fuzzy goal programming to handle the Model’s complexity to improve the reasonable compromise. The real-world problem of wind turbine blades is used to validate the superiority and effectiveness of the technique.

A novel iterative method to solve a linear fractional transportation problem

The linear fractional transportation problem (LFTP) is widely encountered as a particular type of transportation problem (TP) in real-life. In this paper, a novel algorithm, based on the traditional definition of continuity, is presented to solve the LFTP. An iterative constraint is constructed by combining the objective function of the LFTP and the supply-demand condition since the fractional objective function is continuous at every point of the feasible region. By this constraint obtained, LFTP is converted into an iterative linear programming (LP) problem to reach the optimum solution. In this study, the case of asymptotic solution for LFTP is discussed for the first time in the literature. The numerical examples are performed for the linear and asymptotic cases to illustrate the method, and the approach proposed is compared with the other existing methods to demonstrate the efficiency of the algorithm. Also, an application had environmentalist objective is solved by proposed mathematical method using the software general algebraic modeling system (GAMS) with data set of the real case. Finally, some computational results from tests performed on randomly generated large-scale transportation problems are provided.

Time variant multi-objective linear fractional interval-valued transportation problem

Time variant multi-objective linear fractional interval-valued transportation problem

Bilevel transportation problem in neutrosophic environment

In the current times of the predominance of COVID-19, almost all the countries are conducting inoculation drives. Given the market’s inability to compute how much to manufacture, how to transport and the frequently changing demand, the cost of safely and timely transporting the vaccines from factory to syringe is currently indeterminate. In this paper, we formulate this situation using a bilevel transportation problem with neutrosophic numbers (BLTP-NN). The problem comes from a vaccine manufacturing company where the vaccine is produced and then transported to different distribution centres from where it is further transported to various health centres for the conduction of their vaccination drive. The authors have tried to perceive this situation from two perspectives by formulating two different problems. The first problem is a bilevel linear fractional transportation problem which aims at minimizing the transportation cost in proportion to per unit maximization of quantity transported. The second problem is a bilevel indefinite quadratic transportation problem which aims at minimizing the transportation cost and depreciation cost. In both problems, cost coefficients are neutrosophic numbers along with availabilities and demands in the constraint set. These formulated bilevel transportation problems in neutrosophic environment are solved using goal programming strategy to arrive at a satisfactory solution. The relevance of this work is to help the decision makers in budgeting their finances related to the transportation by strategic disbursement leading to a smooth administration of vaccination program.

Solving multi-objective linear fractional transportation problem under neutrosophic environment

We are discussing multi-objective linear fractional transportation problem (MOLFTP) under neutrosophic environment in the present paper. In proposed methodology, we characterize each objective of our MOLFTP in three different ways such that truth membership; indeterminacy membership and falsity membership functions. Proposed methodology gives us best neutrosophic compromise programming model under the given membership functions. In the given approach, we convert MOLFTP model into the non-linear integer programming model using proposed approach and solve it using MATLAB. To support the theory a numerical example is also discussed.

Fractional transportation problem under interval-valued Fermatean fuzzy sets

<abstract><p>The concept of an interval-valued Fermatean fuzzy set (IVFFS), an extension of Fermatean fuzzy sets, is a more resilient and reliable tool for dealing with uncertain and incomplete data in practical applications. The purpose of this paper is to define a triangular interval-valued Fermatean fuzzy number (TIVFFN) and its arithmetic operations. Fractional transportation problems (FTPs) have important implications for cost reduction and service improvement in logistics and supply management. However, in practical problems, the parameters in the model are not precise due to some unpredictable factors, including diesel prices, road conditions, weather conditions and traffic conditions. Therefore, decision makers encounter uncertainty when estimating transportation costs and profits. To address these challenges, we consider a FTP with TIVFFN as its parameter and call it an interval-valued Fermatean fuzzy fractional transportation problem (IVFFFTP). A new method for solving this IVFFFTP is proposed without re-transforming the original problem into an equivalent crisp problem. Illustrative examples are discussed to evaluate the precision and accuracy of the proposed method. Finally, the results of the proposed method are compared with those of existing methods.</p></abstract>

Application of Water Cycle algorithm to Stochastic Fractional Programming Problem

This paper presents an application of Water Cycle algorithm (WCA) in solving stochastic programming problems. In particular, Linear stochastic fractional programming problems are considered which are solved by WCA and solutions are compared with Particle Swarm Optimization, Differential Evolution, and Whale Optimization Algorithm and the results from literature. The constraints are handled by converting constrained optimization problem into an unconstrained optimization problem using Augmented Lagrangian Method. Further, a fractional stochastic transportation problem is examined as an application of the stochastic fractional programming problem. In terms of efficiency of algorithms and the ability to find optimal solutions, WCA gives highly significant results in comparison with the other metaheuristic algorithms and the quoted results in the literature which demonstrates that WCA algorithm has 100% convergence in all the problems. Moreover, non-parametric hypothesis tests are performed and which indicates that WCA presents better results as compare to the other algorithms.

Uncertain Multi Level Four Dimensional Multi Item Fractional Transportation Problem

Uncertain Multi Level Four Dimensional Multi Item Fractional Transportation Problem