Increasing customization has driven manufacturers to develop more flexible manufacturing systems. In these systems, different models of the same part are able to share the same production line. For parts that need multiple operations, different models are combined in some operations and separated in others. To achieve this, it is crucial to accurately send every part to its next operation site. Tag-based methods have been commonly used to sort parts, but they cannot be used when the tags may be damaged in certain operations. In these situations, vision-based methods are preferable. Traditional machine vision methods require manual feature definition and may not be suitable in complex situations. Therefore, in this article, we propose a convolutional neural networks (CNNs) based visual sorting system. To support this, a cloud-edge computing environment is developed for fast computation and continuous service maintenance and upgradation. A CNN-based element segmentation method is proposed for accurate part model classification. The prototype system shows that the proposed method can provide high classification accuracy within an acceptable time.