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An effective green supply chain (GSC) can help an enterprise obtain more benefits and reduce costs. Therefore, developing an effective evaluation method for GSC performance evaluation is becoming increasingly important. In this study, the advantages and disadvantages of the current performance evaluations and algorithms for GSC performance evaluations were discussed and evaluated. Based on these findings, an improved five-dimensional balanced scorecard was proposed in which the green performance indicators were revised to facilitate their measurement. A model based on Rough Set theory, the Genetic Algorithm, and the Levenberg Marquardt Back Propagation (LMBP) neural network algorithm was proposed. Next, using Matlab, the Rosetta tool, and the practical data of company F, a case study was conducted. The results indicate that the proposed model has a high convergence speed and an accurate prediction ability. The credibility and effectiveness of the proposed model was validated. In comparison with the normal Back Propagation neural network algorithm and the LMBP neural network algorithm, the proposed model has greater credibility and effectiveness. In practice, this method provides a more suitable indicator system and algorithm for enterprises to be able to implement GSC performance evaluations in an uncertain environment. Academically, the proposed method addresses the lack of a theoretical basis for GSC performance evaluation, thus representing a new development in GSC performance evaluation theory

New Algorithm for Evaluating the Green Supply Chain Performance in an Uncertain Environment