A New Solution Technique for Fuzzy Transportation Problem Using Novel Ranking Functions on Heptagonal Fuzzy Numbers: A Case Study of Regional Shipment

Balasundaram Baranidharan; Ghanshaym Singha Mahapatra

doi:10.47852/bonviewJCCE42023253

Authors

Balasundaram Baranidharan Department of Mathematics, National Institute of Technology Puducherry, India https://orcid.org/0009-0003-0491-8695
Ghanshaym Singha Mahapatra Department of Mathematics, National Institute of Technology Puducherry, India https://orcid.org/0000-0002-5225-0445

DOI:

https://doi.org/10.47852/bonviewJCCE42023253

Keywords:

heptagonal fuzzy numbers, centroid of centroid, alpha-cut, ranking function, transportation problem

Abstract

This paper presented a fuzzy transportation problem to represent the uncertainty of transportation in parameters to produce an appropriate solution. In addition to making reliable solutions for real-world decision-making problems, the objective of transportation problem cost, demand, and supply parameters are demonstrated using heptagonal fuzzy numbers (HFN). The multiplication and division operations are presented with an example to make the inner performance of any two HFNs. A new ranking technique has been derived to defuzzify the linear HFN using an alpha-cut-based ranking technique, and it has been compared with the existing ranking technique. Furthermore, a generalized ranking heptagonal fuzzy method (GRHFM) algorithm is framed by incorporating defined operations and ranking techniques to solve the heptagonal fuzzy regional shipment problem. The effectiveness of our proposed method is demonstrated through a numerical example of an adopted case study. It determines the feasible shipment cost for vegetable transportation from the regional markets utilizing HFNs, which further compare solutions obtained through various algorithms. The conclusion section discusses the suggested GRHFM and alpha-cut ranking efficiency, outcomes, decision management, and future directions based on the existing transportation study.

Received: 26 April 2024 | Revised: 15 July 2024 | Accepted: 22 July 2024

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data available on request from the corresponding author upon reasonable request.

Author Contribution Statement

Balasundaram Baranidharan：Conceptualization, Software, Validation, Investigation, Data curation, Writing – original draft, Visualization. Ghanshaym Singha Mahapatra：Methodology, Software, Formal analysis, Resources, Data curation, Writing – review & editing, Visualization, Supervision.