We propose a Discrete Event Simulation (DES) model for an emergency department (ED). The model is developed in close collaboration with the French hospital Saint Camille, and is validated using real data. The objective of this model is to help ED managers better understand the behavior of the system and to improve the ED operations performance. The most essential features of an ED are considered in the model. A case study is conducted in order to allow decision makers select the most relevant investment in the human staffing budget. A simulation-based optimization algorithm is adopted to minimize the average Length of Stay (LOS) under a budget constraint. We conduct a sensitivity analysis on the optimal average LOS as a function of the staffing budget, and derive useful recommendations to managers on how the budget can impact the performance of the system.