Sustainability of a supply chain has gained more attention from economists, environmentalists, consumers, manufacturers, government and the academia. In this paper, the literature survey has been performed on production allocation problem in a multi-echelon supply chain with carbon policies. With web-based search engines such as Scopus and Web of Science several resources such as journals, conference proceedings and books are selected and reviewed. It is observed from the literature that the mentioned problem traces the progression of carbon policies in a supply chain over the past 22 years to provide substantiation for Green Supply Chain. The research papers are then analyzed and categorized to construct the useful foundation of previous studies. Moreover, the importance of this problem in recent years needs has been highlighted by mentioning the gaps in the literature. Further, at the end of the paper, several future work directions in this area also suggested.