Nurse Staff Allocation in a Multi-stage Queuing System with Patients’ Feedback Flow for an Outpatient Department

A general multi-stage queuing system model with patients’ feedback flow is developed to address the behavior of patients’ flow in an Outpatient Department (OD) in a hospital. The whole process includes registration, diagnosis, chemical examination, payment, and medicine-taking. Focusing on nurse resources, the formulas of performance indicators such as patient waiting times and nurse idle times are derived by using the system parameters. A mathematical programming model is developed to determine how many nurses should be allocated to each stage to minimize the total costs of patient waiting times and nurse idle times. The neighborhood search combined Simulated Annealing (NS-SA) is developed to solve the model, which is essentially a natural number decomposition problem. Numerical experiments are conducted to analyze the discipline of nurse allocation and the impact of patient arrival rates and the probability of patient’s feedback flow on the system costs. The research results will be helpful for hospital managers to make decisions on allocation of nurse staff in practice.

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