During a medical emergency in the USA, critical medical supplies such as medications, vaccines, gloves, masks and ventilators, are delivered to one location within each state. The state and local governments are responsible for delivering the supplies from this location, called the receiving, staging and storage (RSS) site to the points of dispense (PODs). The supplies can be sent from the RSS to PODs directly or via regional distribution nodes (RDNs). We develop two mixed-integer programming models for this emergency logistics network (ELN) problem. These two models are simplified to obtain equivalent models that lead to the same results, but with fewer constraints. The equivalent models are much less complex and have lower computational memory and time requirements. We optimise the required number and locations of RSSs and RDNs needed to satisfy the demands at the PODs within the required time windows. Experiments are conducted to illustrate how the proposed models can be applied to a real life problem.