Abstract
Nowadays, the transportation problem is a multiobjective decision-making problem. It involves deciding to determine the ideal transportation setup that matches the decision maker’s preferences while taking into account competing objectives/criteria such as transportation cost, transportation time, and environmental and social concerns. This study presents a general framework of the multiobjective fractional transportation problem (MOFTP) to deal with such complex scenarios. This paper’s major goal is to propose a solution methodology to solve the MOFTP based on a neutrosophic goal programming (NGP) approach. By obtaining the optimal compromise solution using three memberships, namely, truth membership, indeterminacy membership, and falsity membership, the suggested technique gives a novel insight into solving the MOFTP. A real-world problem such as selling wind turbine blades’ problem and a numerical example are used to demonstrate the efficacy and superiority of the proposed method.
Highlights
Transportation problems (TPs) are formulated to transport different types of products to different locations for lower cost, lower transport time, lower production cost, and more
En, the neutrosophic goal programming (NGP) problems are solved using LINGO software. e obtained solution is compared with the solutions of Goal programming (GP), fuzzy goal programming (FGP), and intuitionistic fuzzy goal programming (IFGP) methods which is shown in Tables 2 and 3 for the numerical example and case study problems
A neutrosophic programming framework is developed in this study to obtain an optimal compromise solution for the multiobjective fractional transportation problem (MOFTP)
Summary
Transportation problems (TPs) are formulated to transport different types of products to different locations for lower cost, lower transport time, lower production cost, and more. Suppose a distribution center seeks to determine the transportation plan to transport identical goods from M sources to N locations. Each source has materials to deliver to different locations, and each destination has a forecast request of products to be sourced from sources. Us, when a TP problem is proposed, it tries to determine the optimal volumes to carry from each source to each destination by minimizing the cost of production, transportation cost, and delivery time. Hitchcock invented the traditional transportation problem [1]. Based on the primal simplex transportation technique, Dantzig and apa [2] proposed the simplex method to solve the TP. Ezekiel and Edeki [3] developed a new method to solve the TP which is called modified Vogel’s approximation method
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