Mass casualty incidents caused by unpredictable and devastating disasters result in significant property loss and pose serious threats to human life. In such crises, the ethical priority of emergency responders is to save as many lives as possible, despite limited medical resources. Effective delivery of emergency medical services is crucial in managing life-threatening events. The severe shortage of medical support during these disasters requires each medical professional to treat multiple patients simultaneously. Additionally, professionals should also promote the overall effectiveness of treatment by preventing "tying" themselves to one patient. This research introduces a scheduling model that integrates multitasking into patient treatment plans. The model aims to minimize time-related objectives to ensure a rapid medical response in time-critical scenarios, allowing all patients to benefit from more efficient prioritization schemes. To proactively evaluate the proposed model and treatment plans without incurring actual risks, a comprehensive solution framework has been developed. This framework includes asymptotically optimal heuristics, a well-designed branch-and-bound algorithm for exact solutions, and an improved memetic algorithm. The results demonstrate the effectiveness and robustness of the framework across various problem scales. By analyzing the structures of various solutions, managers gain valuable insights that inform policy decisions and guide emergency response planning.