## 3 Discrete Event Simulation Model
### Simulation-Optimization Results  
For investigation of ED, we first developed an efficient simulation model that accurately reflects the operational model. Then, AWT and AS performances were analyzed through the proposed scenario. * **Result analysis of human resource adjustment scenario: Category 1** In Category 1, the objective was to explore scenarios of the actual ED resource schedule and test their impact on the weighted AWT, AS, and costs associated with the resource to be added. As demonstrated in Figures 6 and 7, 117 alternative staffing levels were generated through the addition or combination of shifts for both the short and long circuits. Thus, the VIKOR method was applied. For each scenario, we recovered the simulated performances (AWT, AS, and cost) in order to construct the decision matrix (Appendix A, Tables A1 and A2). The rows represent the scenarios and the columns represent criteria. The time unit is the minute and the cost unit is Euro. This matrix and the weight of each criterion are used as an input to the VIKOR method. Figures 6 and 7 present the final ranking of these scenarios. According the VIKOR method ranking, Scenario 6 is the best alternative to apply in the short circuit. A nurse and a caregiver must be added to the current staff with a cost of EUR 4200 in monthly salary. By doing so, the weighted AWT and AS are reduced by 26 min and 10 min, respectively, when compared with the base case. For the long circuit, the best solution was Scenario 63, where an emergency physician, a caregiver, and a nurse must be added to the staff in the 10 a.m.-10 p.m. shift. This will reduce the AWT and AS by 10 min and 3 min, respectively. Depending on the scenarios tested and the simulation results obtained, we note that in all cases, adding resources in the long circuit slightly reduces the performances in comparison to the basic model. This will be necessary to test by changing the premises, as the limit may be architectural. In the short circuit, adding an emergency physician or intern physician did not positively impact the costs and slightly reduced the AWT and AS. Thus, we notice that the resource that has the greatest impact on improving the optimized ED performances is the nurse, since it always brings the greatest gain in performances. * **Result analysis of room adjustment scenario: Category 2** In Category 2, we aim to analyze the impact of increasing and decreasing the number of rooms in the short and long circuits. Four rooms are the maximum that can be added in both circuits. The results of this strategy are follows:  
* Short circuit: Increase in the number of rooms: The number of rooms was increased from the current state of 13 rooms to 14, 15, 16, and 17 rooms. However, the biggest reduction in ED performances came from adding the third room (i.e., a total of 16 rooms), which reduced ED AWT and AS by an average of 5 min. * Short circuit: Decrease in the number of rooms: Removing 3 rooms had no impact on short circuit performances. After removing the fourth room, the waiting time increased by an average of 3 min. * Long circuit: Increase in the number of rooms: The number of rooms was increased from the current state of 14 rooms to 15, 16, 17, and 18 rooms. However, the biggest increase in ED performance came from adding the first room (i.e., a total of 15 rooms), which reduced ED AWT and AS by an average of 5 min. * Long circuit: Decrease in the number of rooms: Closing the first room resulted in waiting time increasing by an average of 5 min. Figure 6: Result of the classification of the scenarios for Category 1 (resource-related—flexible staff and shifts, short circuit). Figure 7: Result of the classification of the scenarios for Category 1 (resource-related—flexible staff and shifts, long circuit). In Category 2, the results proved that there was no significant difference between the base case and both cases when other rooms are opened or closed in the short or long circuit, as measured by the AWT and AS.