The deprivation cost quantifies the suffering of disaster victims owing to the lack of relief supplies. We compare different deprivation functions by considering deprivation costs in the inventory management of disaster relief supplies. For this purpose, we formulate an inventory management model that considers deprivation costs using two-stage stochastic modeling. We then analyze seven deprivation cost functions found in the literature. Finally, the model is empirically validated using a real-world case. The results suggest that the chosen deprivation function can result in a difference of up to 99.9% in the total inventory management cost. When different functions are compared, the service level also has a high amplitude. We conclude that the functions lead to different service levels. As a practical contribution, this study shows that the deprivation cost provides relevant information to the decision-maker about distribution coverage and the operational cost involving disbursement. As an academic contribution, this study compares different deprivation functions and connects academics and practitioners by demonstrating how different formulations of deprivation costs impact the service level of relief items delivered to the population.