This study focuses on the challenging problem of labeling a collection of objects with inherent morphological and positional dependencies, where instances may be missing or duplicated. We integrate principles of assignment theory in the design of a convolutional neural network to find the optimal label set given pairwise geometrical features extracted from the candidate objects. The objective function aims to minimize the distance between the one-hot encoded labels of the objects and the scores produced by the model, with added emphasis on the scores corresponding to the optimal assignment plan. We tested our solution in the dental domain on the task of finding the teeth labels given a set of candidate instances. The study database included 1200 dental casts of upper and lower jaws from 600 patients. The model reached identification accuracies of 0.952 and 0.968 for the lower and upper jaws, respectively. Moreover, we presented a solution for generating teeth candidates using a multi-step pipeline consisting of coarse and fine segmentations. The algorithm was tested on a database consisting of 600 dental casts, reaching an F1 score of 0.968.