Emergency department overcrowding is a global issue that poses a great threat to patient health and safety. The timeliness of medical services provided to patients is crucial to emergency departments as it directly impacts the mortality and morbidity of urgent patients. However, critical resources (e.g., doctors and nurses) are typically constrained due to the limited financial budget. Thus, hospital administrators may need to investigate solutions to improve the efficiency of the emergency department. In this work, we study the dynamic problem of scheduling patients to doctors, aiming at minimizing the total weighted tardiness. We propose a simple reoptimization heuristic based on multiple queues of patients in accordance with their urgency levels, and then combine it with an effective variable neighborhood search. We also propose a scenario-based planning approach that uses sampled scenarios to anticipate future events and the variable neighborhood search to schedule patients. The methods are adapted to handle a problem variant where information on arrival time and urgency level of some patients can be received in advance by the emergency department. With a comprehensive computational study on two sets of realistic instances from Hong Kong SAR of China and Italy, we validate the performance of the proposed methods, evaluating the benefits of having more doctors and receiving early information.