Analysis of MOFTP using Modern Zero Suffix Method

Abstract

In this paper, a new algorithm is introduced for dealing with the Multi-Objective Fuzzy Transportation Problem (MOFTP) where all parameters such as transportation cost, demand and supply are in triangular fuzzy numbers. The approach involves modern zero suffix method using Harmonic Mean. First the Multi-objective fuzzy transportation problem is converted into a crisp value by using a Robust’s Ranking Method. Then the crisp value is solved by Modern Zero Suffix method. The effectiveness of the data is examined by a numerical example.

Introduction

I. INTRODUCTION

The transportation problem is a special type of linear programming problem, where the objective is to minimize the cost of distributing a product from a number of sources to a number of destinations. To obtain the initial basic feasible solution, there are several methods as North West Corner method (NWC), Least Cost method (LC) and Vogel’s Approximation method (VAM). The transportation problem in this case is aimed as a single objective. But often in real life problem, there are multiple objectives needed to achieve while making the transportation operation. The transportation problem typically arises from a singular objective, whether its minimizing transportation time or cost, as developed by Hitchcock [10]. Diaz [3] developed an alternative algorithm to obtain all non-dominated solutions for MOTP and it depends on the satisfaction level regarding how closely a compromise solution aligns with the ideal solution. Diaz [4] expanded a procedure to obtain all non-dominated solution for MOTP. Ringuest et. al.,[14] developed two iterative algorithms to solve MOTP. Bit et.al., [2] examined a k-objective transportation problem incorporating fuzzy numbers and used α -cut to formulate the fuzzy transportation problem in linear programming terms. The first foraging ant system was developed using the notation in Maniezzo et.at., [12]. Dorigo et. al., [5] described ACO as a probabilistic method for locating optimum pathways. Shyu et.al., [15] presented a real-world problem by utilizing both existing ant traits and brand-new ones.  Kaur et.al., [11] presented to obtain the best compromise solution of linear MOTP. To solve the minimum spanning tree problem and the TP, we use modified ACA which was introduced by Ekanayake et.al., [6]. Ambadas Deshmukh et.al., [1] presented a new ranking method to order any two fuzzy triangular number. Hebasayed et.al [9] presented a new summation method for solving MOTP. Goel et.al., [8] developed a new row maxima method to solve MOTP using C programme. K.P.O. Niluminda et.al., [13] developed a novel alternative algorithm that uses geometric mean and penalty technique to address MOTP. E.M.U.S.B. Ekanayake [7] expanded an ant colony technique to solve a MOTP.

Conclusion

In this paper we have analysed a transportation problem using an alternative method for applying fuzzy MOTP, namely modern zero suffix method, which provides the best solution of the multi-objective transportation system as often as possible. Multi-objective Transportation Problems are those where more than one objective needs to be optimized. Several methods have been put forward in the literature to solve MOTP. Instead of utilizing traditional methods, the harmonic mean with the modern zero suffix method is applied in this study to solve a MOTP. This method is also simple and easily understandable for effective solutions.

References

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Copyright

Copyright © 2024 F. Cathrine Leema, A. Sahaya Sudha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.