Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem

José Luis Verdegay,Sankar Kumar Roy,Ali Ebrahimnejad,Shyamali Ghosh

doi:10.1007/s40747-020-00251-3

Abstract

During past few decades, fuzzy decision is an important attention in the areas of science, engineering, economic system, business, etc. To solve day-to-day problem, researchers use fuzzy data in transportation problem for presenting the uncontrollable factors; and most of multi-objective transportation problems are solved using goal programming. However, when the problem contains interval-valued data, then the obtained solution was provided by goal programming may not satisfy by all decision-makers. In such condition, we consider a fixed-charge solid transportation problem in multi-objective environment where all the data are intuitionistic fuzzy numbers with membership and non-membership function. The intuitionistic fuzzy transportation problem transforms into interval-valued problem using (alpha ,beta )-cut, and thereafter, it reduces into a deterministic problem using accuracy function. Also the optimum value of alternative corresponds to the optimum value of accuracy function. A numerical example is included to illustrate the usefulness of our proposed model. Finally, conclusions and future works with the study are described.

Highlights

In the last few decades, the traditional transportation problem (TP) considers only single objective function
Apart from the transportation cost, a fixed cost, sometimes called set-up cost, is taken only when solution appears with positive level and such a problem is termed as fixedcharge transportation problem (FCTP) and it is associated with 0-1 variable
We have considered an multi-objective fixed-charge solid transportation problem (MOFCSTP)

Summary

Introduction

In the last few decades, the traditional transportation problem (TP) considers only single objective function. When a homogeneous product is transferred from a source to different destinations in competitive economic condition, there exist more than single criterion such as the transportation. Apart from the transportation cost, a fixed cost, sometimes called set-up cost, is taken only when solution appears with positive level and such a problem is termed as fixedcharge transportation problem (FCTP) and it is associated with 0-1 variable. There exist landing fees at an airport, toll charges on a highway, renting cost of a vehicle, set up cost for machines in manufacturing environment, etc. FCTP corresponds with two types of cost, one is direct cost and another is fixed-charge where fixed-charge occurs for transportation activity in source–destination pair which is independent on transportation amount, and for direct cost, it is dependent on transportation amount for each source to each destination.

Methods

Results

Discussion

Conclusion