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

Joshi, Vishwas Deep; Naharwar, Saurabh Singh; Singh, Jagdev; Nisar, K. S.

doi:10.47974/JIM-1652

Open Access Research Article

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

Vishwas Deep Joshivdjoshi.or@gmail.comDepartment of MathematicsJaipur, RajasthanJECRC University JaipurIndia0000-0001-8134-0282View full profile → , Saurabh Singh Naharwarsaurabhsinghnaharwar@gmail.comDepartment of MathematicsJaipur, RajasthanJECRC University JaipurIndiaView full profile → , Jagdev Singhjagdevsinghrathore@gmail.comDepartment of MathematicsJaipur, RajasthanJECRC University JaipurIndiaView full profile → , ^*K. S. NisarCorresponding authorn.sooppy@psau.edu.saAffiliation 1Department of MathematicsCollege of Sciences and Humanities in AlkharjAlkharj 11942Prince Sattam bin Abdulaziz UniversitySaudi ArabiaAffiliation 2School of TechnologyHyderabad 502345, TelanganaWoxsen UniversityIndiaView full profile →

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pp. 133–143Vol. 26Issue 1January 2023DOI: 10.47974/JIM-1652XML

Published Online:: 31 Jan 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1652
Pages:: 133–143

Abstract

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.

Keywords

Linear plus linear fractions Fractions Transportation problems Weighted sum approach Multi-objective linear plus linear fractional-transportation problem (MOLPLFTP)

Subject Classifications

90C3290B0690C29

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