One of the most critical objectives in the healthcare system is maximising patient flows in the emergency care patient pathway. Patient emergency flow analysis indicates that the timetabling of a patient's movement from one activity to another through the Emergency Department (ED) is critical for treating patients. The ED deals with the patient's arrival, triage, physician assessment, imaging and laboratory studies, treatment planning, nursing procedures, and decisions to admit or discharge the patient. Any delayed activities in patient flow reduce the service level of healthcare. To address these challenges, this paper develops a stochastic ED Simulation-Optimisation approach by considering stochastic variables, such as patient interarrival times and treatment times, using statistical distributions. This type of distribution depends on two main elements: day shifts and patient categories. A hybrid evolutionary algorithm is integrated with the simulation to find a satisfactory solution for this stochastic optimisation problem in real time. Computational experiments show that the proposed approach can serve more patients in specific time windows or provide the same quality of the service with the use of fewer medical resources.