Humanitarian logistics aims to save lives and alleviate human suffering in disasters. Furthermore, humanitarian supplies are essential items for humanity (such as water and food), and their lack can have a great impact. However, the available resources may not be enough to meet the beneficiaries needs. The deprivation cost quantifies the suffering caused to disaster victims by the lack of these items. Thus, this paper aims to analyze the effect of including deprivation costs in disaster relief supplies inventory management. To reach the proposed goal, the research analyzes the state of the art of its modeling through a systematic review of the academic literature. An inventory management model considering deprivation costs is then formulated as a two-stage stochastic model. Furthermore, the various deprivation cost functions found in the literature are analyzed. Finally, the model is empirically validated through a two case studies. The results suggest that the choice of the deprivation function can impact up to a 99.9 per cent difference in the total costs of inventory management. The service level generated also has a high amplitude when the different functions are compared. It is concluded that the functions generate different service levels, and it is up to the decision-makers to choose which one best suits the studied problem. As a practical contribution, we highlight that the proposed inventory management model considering the cost of deprivation may help decision-makers and reduce the suffering of people affected by disasters. As an academic contribution, the study analyzes and compares the main deprivation functions proposed in the literature, which can help to propose new models.