Optimizing Healthcare Delivery: A Model for Staffing, Patient Assignment, and Resource Allocation

The healthcare industry has recently faced the issues of enhancing patient care, streamlining healthcare operations, and offering high-quality services at reasonable costs. These crucial issues include general healthcare administration, resource allocation, staffing, patient care priorities, and effective scheduling. Therefore, efficient staff scheduling, resource allocation, and patient assignments are required to address these challenges. To address these challenges, in this paper, we developed a mixed-integer linear programming (MILP) model employing the Gurobi optimization solver. The model includes staff assignments, patient assignments, resource allocations, and overtime hours to minimize healthcare expenditures and enhance patient care. We experimented with the robustness and flexibility of our model by implementing two distinct scenarios, each resulting in two unique optimal solutions. The first experimental procedure yielded an optimal solution with an objective value of 844.0, with an exact match between the best-bound score and the objective value, indicating a 0.0% solution gap. Similarly, the second one produced an optimal solution with an objective value of 539.0. The perfect match between this scenario’s best-bound score and objective value resulted in a 0.0% solution gap, further affirming the model’s reliability. The best-bound scores indicated no significant differences in these two procedures, demonstrating that the solutions were ideal within the allowed tolerances.