Multi-Objective Multi-Index Transportation Model for Crude Oil Using Fuzzy NSGA-II

Abstract

The import and export of crude oil are vastly affected by the economy of a developing country. It can be useful for the production of petroleum products. Likewise, the developing country, India is completely relying on the import of crude oil from Gulf countries. Thus, there is a need for optimization of routes and modes of transportation. This article presents a two-stage cost and time minimizing fuzzy business restricted multi−objective multi−index transportation problem, in which supplies, demands, and requirements are triangular fuzzy numbers. A business restricted constraints using binary variables are added in the developed supply chain of crude oil in India. The proposed model helps the decision-maker to choose the source country for the import of crude oil. The model is solved by using our proposed fuzzy non−dominated sorting genetic algorithm (NSGA)−II. The performance of the proposed algorithm is analyzed by using a simulation technique for uncertainty level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \in [{0, 1}]$ </tex-math></inline-formula> . Also, the Pareto decision space for formulated business restricted transportation problem is discussed using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha -$ </tex-math></inline-formula> cut technique. For the superiority of the proposed methodology, we have implemented this on real-world case study viz., Daya case study. Based on the results we claim that the methodology is superior.