<p>Federated learning (FL) is an emerging distributed machine learning framework that preserves data privacy by sharing model parameters instead of raw data. However, conventional FL systems often randomly select clients, neglecting critical challenges such as data heterogeneity, hardware disparities, and network variability, which leads to suboptimal performance and inefficiency. Moreover, in commercial applications, minimizing the economic costs paid to clients remains a key concern. To address these issues, we propose a dynamic client selection framework for FL (DCSF-FL), which integrates Shapley value (SV) and data envelopment analysis (DEA) to optimize client selection. Specifically, the SV quantifies the contribution of each client in each communication round in FL. The DCSF-FL updates the quality and reputation metrics, while the input metrics of the dynamic slacks-based measure (SBM) model in DEA are computed through the SV, followed by the application of the SBM model to evaluate the efficiency of each client in the FL term rounds of communication, which is used to dynamically select cost-efficient clients. Experiments on multiple benchmark datasets demonstrate that DCSF-FL improves model accuracy by up to 20.3% compared to random selection methods while reducing training costs by up to 36.5%. In addition, the framework improves the efficiency of training and the reliability of the model, as evidenced by the reduced variance in performance. These results highlight DCSF-FL’s effectiveness in balancing performance, cost, and scalability in practical FL deployments.</p>