Environmentally Sustainable Multi-Stage Multi-Objective Multi-Item Fixed-Charge Solid Fractional Hesitant Fuzzy Transportation Problem

Document Type : Primary Research paper


PG & Research Department of Mathematics, Holy Cross College (Autonomous) Affiliated to Bharathidasan University, Tiruchirappalli, India


This paper presents the creative study on environmentally sustainable multi-stage multi-objective multi-item fixed-charge solid fractional hesitant fuzzy transportation problem (MSMOMISFHFTP). Emission of greenhouse gas from the vehicle plays vital role in environmental pollution and global warming. This study helps to control such pollution and gives the optimal solution to lead the green supply chain. The objective of the problem is to minimise the ratio of cost and profit, deterioration rate and emission. This paper provides the proper plan of distribution of multi items from production plants to the customers in three stages. Here all the parameters of multi-stage multi-objective multi-item fixed-charge solid fractional transportation problem are treated as trapezoidal hesitant fuzzy numbers. Hesitant TOPSIS method is introduced to solve MSMOMISFHFTP which provides the better solution than the other existing methods. Finally numerical problem is solved using proposed methodology with the help of LINGO package.