The increasing adoption of Deep Learning (DL)-based Object Detection (OD) models in smart manufacturing has opened up new avenues for optimizing production processes. Traditional industries facing capacity constraints require noninvasive methods for in-depth operations analysis to optimize processes and increase revenue. In this study, we propose a novel framework for capacity constraint analysis that identifies bottlenecks in production facilities and conducts cycle time studies using an end-to-end pipeline. This pipeline employs a Convolutional Neural Network (CNN)-based OD model to accurately identify potential objects on the production floor, followed by a CNN-based tracker to monitor their lifecycle in each workstation. The extracted metadata are further processed through the proposed framework. Our analysis of a real-world manufacturing facility over six months revealed that the bottleneck station operated at only 73.1% productivity, falling to less than 40% on certain days; additionally, the processing time of each item increased by 53% during certain weeks due to critical labor and materials shortages. These findings highlight significant opportunities for process optimization and efficiency improvements. The proposed pipeline can be extended to other production facilities where manual labor is used to assemble parts, and can be used to analyze and manage labor and materials over time as well as to conduct audits and improve overall yields, potentially transforming capacity management in smart manufacturing environments.