In some lateral alliances, firms coordinate their interactions in Supply Chain Management (SCM) via contracts. Successful implementation of contracts in lateral alliances remains challenging in practice because of the incomplete identification of implementation barriers by firms involved in the alliance. This paper investigates the implementation issues of lateral contracts. To identify the barriers, the literature and interview experts on the subject matter are reviewed. By adopting the novel Fuzzy Measurement of Alternatives and Ranking according to the Compromise Solution (FMARCOS) prioritization method, we evaluate the main barriers that firms face in the successful implementation of contracts discovered in our identification phase. A sensitivity analysis is conducted to demonstrate the stability and robustness of our proposed method. To check the reliability of the proposed model, a case study is solved with three methods of Multi-Criteria Decision-Making (MCDM) methods. The results show that they do not differ much from each other, which indicates the validity of this model. To validate the findings, a list of barriers is applied to assess a set of firms in the Iranian car industry, and more prepared firms are located as future partners of potential lateral alliances. The results are consistent with the common intuition toward these sample firms in the case study. The main contributions of this work include the application of the FMARCOS method in the study of the bidirectional implementation barriers, the consideration of novel aspects of implementation barriers unaddressed in the extant literature, and a real-case study in the Iranian car industry.