Title: Optimisation of fuzzy transportation problem using new ranking approach with fuzzy numbers

Authors: Jay Chandra Yadav; Mohammad Rizwanullah

Addresses: Department of Mathematics and Statistics, Manipal University Jaipur, Ajmer Highway, Dahmi Kalan, Jaipur-303007, Rajasthan, India ' Department of Mathematics and Statistics, Manipal University Jaipur, Ajmer Highway, Dahmi Kalan, Jaipur-303007, Rajasthan, India

Abstract: Transportation problem is one of the sub-classes of allocation problem of operations research. Optimisation (max or min) of transportation problems under fuzzy environment, under different constraints are increasing approach of the researchers now a days. Conventional transportation problem is using crisp data as cost, time, and distance as parameter. Decision-making problems, data analysis, and socio-economic systems all are highly dependent on ranking fuzzy numbers. Numerous models of transportation problems based on ranking fuzzy number have been developed monotonously. Most of the approaches that have been suggested so far do not discriminate in terms of optimisation of transportation problems. In this paper, the fuzzy transportation problem is transformed into a crisp valued problem using a novel ranking mechanism. The transformed problem is solved by Vogel approximation method using TORA Software to obtain the fuzzy optimal solution. It can be seen from numerical examples using a noble approach of triangular fuzzy number, pentagonal fuzzy number and hexagonal fuzzy number with the fuzzy ranking method provides a better solution. The proposed ranking method mapped the fuzzy numbers directly into the real line and proved that it is a powerful tool for addressing fuzzy type of the transportation problems. It is simple, efficient, and easy to apply for solving fuzzy-based transportation problem.

Keywords: optimisation; pentagonal fuzzy number; hexagonal fuzzy number; ranking function; fuzzy transportation problem.

DOI: 10.1504/IJMOR.2025.150942

International Journal of Mathematics in Operational Research, 2025 Vol.32 No.4, pp.536 - 550

Received: 26 Oct 2023
Accepted: 18 Jan 2024
Published online: 05 Jan 2026 *

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