This study determines the potential barriers to achieving circularity in dairy supply chains; it proposes a framework which covers big data driven solutions to deal with the suggested barriers. The main contribution of the study is to propose a framework by making ideal matching and ranking of big data solutions to barriers to circularity in dairy supply chains. This framework further offers a specific roadmap as a practical contribution while investigating companies with restricted resources. In this study the main barriers are classified as ‘economic’, ‘environmental’, ‘social and legal’, ‘technological’, ‘supply chain management’ and ‘strategic’ with twenty-seven sub-barriers. Various big data solutions such as machine learning, optimization, data mining, cloud computing, artificial neural network, statistical techniques and social network analysis have been suggested. Big data solutions are matched with circularity focused barriers to show which solutions succeed in overcoming barriers. A hybrid decision framework based on the fuzzy ANP and the fuzzy VIKOR is developed to find the weights of the barriers and to rank the big data driven solutions. The results indicate that among the main barriers, ‘economic’ was of the highest importance, followed by ‘technological’, ‘environmental’, ‘strategic’, ‘supply chain management’ then ‘social and legal barrier’ in dairy supply chains. In order to overcome circularity focused barriers, ‘optimization’ is determined to be the most important big data solution. The other solutions to overcoming proposed challenges are ‘data mining’, ‘machine learning’, ‘statistical techniques’ and ‘artificial neural network’ respectively. The suggested big data solutions will be useful for policy makers and managers to deal with potential barriers in implementing circularity in the context of dairy supply chains.