By deploying mobile power sources and using their network topology effectively, electric utilities can enhance resilience during power outages. This paper develops an outage management approach for power distribution systems in which loads equipped with electricity-dependent medical devices are considered as critical loads. Load criticality is determined by the distance of the load from shelters, the type of medical device, the socio-economic status of the customers, and the average age of the customers at medically vulnerable load points. The optimization model based on mixed-integer linear programming optimizes network reconfiguration, the installation of mobile power sources, and the curtailing of minimum critical loads. The model includes the constraints for a three-phase network configuration for practical grid representation. Optimal restoration schemes are obtained by maximizing restored weighted loads during restoration. In order to deal with uncertainty and imprecise judgments, a fuzzy modification of the analytical hierarchical process (FAHP) is used to prioritize the loads during restoration. The proposed method is tested on the modified IEEE 34-bus distribution test system under several scenarios. The outcome of this study can provide a strategy for power distribution grid operators to manage outages in the presence of loads with electricity-dependent medical devices.