Recently, Ramanathan (R., Ramanathan, ABC inventory classification with multiple-criteria using weighted linear optimization, Computer and Operations Research, 33(3) (2006) 695-700) introduced a simple DEA-like model to classify inventory items on the basis of multiple criteria. However, the classification results produced by Ramanathan are not consistent with the domination concept encouraged some researchers to extend his model. In this paper, we produce the correct results and compare them to the original results and those of the extended models. We also improve this model to rank items with an optimal score of 1 using a cross-efficiency technique. The classification results are considerably different from the original results. Despite the fact that the correct results are obtained in this paper, there is no significant difference between the original model and its extensions, while the original model is more simple and suitable for the situations in which decision-maker cannot assign specific weights to individual criteria.