Efficient disaster management involves swift decisions for the location of facilities, evacuation of casualties, provision of medical care and treatment, allocation of shelters, and distribution of humanitarian aid under a uncertain environment. The research proposes an integrated model to locate facilities, allocate demand of two types including displaced population seeking temporary accommodation and individuals wounded and thus in need of medical assistance during natural disasters. In order to consider the uncertainties in disaster environments, the research proposes a modeling framework accounting for multiple sources of uncertainty. These include uncertain number of casualties, uncertain demand levels, and potential disruption of emergency facilities as well. The current study also proposes a hybrid robust optimization method by integrating cardinality-bounded robustness with box uncertainty sets. This integration is intended to develop solutions under different potential scenarios of disaster environments. Besides, a machine learning-based clustering model with K-means++ algorithm is proposed to cluster people in terms of their locations and level of injuries. Thus, the developed multi-objective mathematical model minimizes medical consequences of delays in evacuation along with reducing total transportation times and costs involved. The current research formulates a model using ε-constraint method and applies it to a case involving the 2017 Kermanshah earthquake in Iran. Computational experiments indicate the proposed hybrid robust model yields superior results compared to the deterministic one and other robust-stochastic models. Specifically, the results demonstrate higher feasibility of proposed solutions when uncertain conditions occur. Additionally, the results show that machine learning-based clustering helps enhance the applicability of the model.