This study presents a novel approach that integrates Discrete Event Simulation (DES) with Design of Experiments (DOE) techniques, framed within a stochastic optimization context and guided by a multi-objective goal programming methodology. The focus is on enhancing the operational efficiency of an emergency department (ED), illustrated through a real-world case study conducted in a Chilean hospital. The methodology employs Response Surface Methodology (RSM) to explore and optimize the impact of four critical resources: physicians, nurses, rooms, and radiologists. The response variable, formulated as a goal programming function, captures the aggregated patient flow time across four representative care tracks. The optimization process proceeded iteratively: early stages relied on linear approximations to identify promising improvement directions, while later phases applied a central composite design to model nonlinear interactions through a quadratic response surface. This progression revealed complex interdependencies among resources, ultimately leading to a local optimum. The proposed approach achieved a 50% reduction in the aggregated objective function and improved individual patient flow times by 7% to 26%. Compared to traditional metaheuristic methods, this simulation–optimization framework offers a computationally efficient alternative, particularly valuable when the simulation model is complex and resource-intensive. These findings underscore the value of combining simulation, RSM, and multi-objective optimization to support data-driven decision-making in complex healthcare settings. The methodology not only improves ED performance but also offers a flexible and scalable framework adaptable to other clinical environments seeking resource optimization and operational improvement.