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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H. Zhu, J. Tang and J. Gong, "Nurse Staff Allocation in a Multi-stage Queuing System with Patients’ Feedback Flow for an Outpatient Department," iBusiness, Vol. 5 No. 3B, 2013, pp. 90-95. doi: 10.4236/ib.2013.53B019.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. J. Boucherie and N. M. VanDijk, “A hospital Queueing Network,” International Series in Operations Research & Management Science, Vol. 154, 2011, pp. 767-798.doi:10.1007/978-1-4419-6472-4_18
[2] J. R. Jackson, “Networks of Waiting Lines,” Operations Research, Vol. 5, 1957, pp. 518-521. doi:10.1287/opre.5.4.518
[3] J. R. Jackson, “Job Shop-like Queuing Systems,” Management Science, Vol. 10, 1963, pp. 131-142. doi:10.1287/mnsc.10.1.131
[4] B. Filipowicz and J. Kwiecien, Queueing Systems and Networks, Models and Applications, 56-4, 2008.
[5] S. W. M Au-Yeung, P. G. Harrison and W. J. Knottenbelt, “A Queueing Network Model of Patient Flow in an Accident and Emergency Department,” Modeling and Simulation, Vol. 4, 2006, pp. 60-67.
[6] J. Jlassi, “Networks of Queues with Multiple Customer Types: Application in Emergency Department,” International Journal of Behavioural and Healthcare Research, Vol. 1, No. 4, 2010, pp. 400-419. doi:10.1504/IJBHR.2009.032157
[7] K. Abadi, N. Hall and C. Sriskandarajah, “Minimizing Cycle Time in a Blocking Flowshop,” Production and Operation Management, Vol. 48, No. 1, 2000, pp. 177-180.
[8] S. Balsamo, V. de Nitto Persone′ and R. Onvural, Analysis of Queueing Networks with Blocking, Kluwer Academic Publishers, Boston, 2001. doi:10.1007/978-1-4757-3345-7
[9] E. El-Darzi, C. Vasilakis, T. Chaussalet, P. H. Millard, A Simulationmodeling Approach to Evaluating Length of stay, Occupancy, Emptiness and Bed Blocking in a Hospital Geriatricdepartment, Healthcare Management Science, Vol. 1, No. 2, 1998, pp. 143-149. doi:10.1023/A:1019054921219
[10] Koizumi, “Modeling Patient Flows Using a Queuing Network with Blocking,” Healthcare Management Science, Vol. 8, 2005, pp. 49-60. doi:10.1007/s10729-005-5216-3
[11] C. Osorio and M. Bierlaire, “An Analytic Finite Capacity Queueing Network Model Capturing the Propagation of Congestion and Blocking,” European Journal of Operational Research, Vol. 196, 2009, pp. 996-1007. doi:10.1016/j.ejor.2008.04.035
[12] K. M. Bretthauer, “Blocking in Healthcare Operations: A New Heuristic and An Application,” Production and Operation Management, 2011, Vol. 20, No. 3, pp. 375-391.doi:10.1111/j.1937-5956.2011.01230.x
[13] R. Hall, D. Belson, P. Murali and M. Dessouky, “Modeling Patientflows through the Healthcare System,” Patient Flow: Reducing Delay in Healthcare Delivery, Springer, New York, NY. 2006. doi:10.1007/978-0-387-33636-7
[14] J. E. Helm, S. AhmadBeygi and M. P. Van Oyen, “Design Andanalysis of Hospital Admission Control for Operational Effectiveness, Production and Operation Management, 2011, Vol. 20, No. 3, pp. 359-374. doi:10.1111/j.1937-5956.2011.01231.x
[15] C. Price, B. Golden, M. Harrington, R. Konewko, E. Wasil and W. Herring, “Reducing Boarding in A Post-anesthesia Care Unit,” Production and Operation Management, Vol. 20 No. 3, 2011, pp. 431-441. doi:10.1111/j.1937-5956.2011.01225.x
[16] J. P. Ruger, L. M. Lewis and C. J. Richter, “Identifying High-risk Patients for Triage and Resource Allocation in the ED,” American Journal of Emergency Medicine, 2007, Vol. 25, No. 7, pp. 794-798. doi:10.1016/j.ajem.2007.01.014
[17] M. A. Ahmed and T. M. Alkhamis, “Simulation Optimization for an Emergency Department Healthcare Unit in Kuwait,” European Journal of Operational Research, Vol. 198, 2009, pp. 936-942. doi:10.1016/j.ejor.2008.10.025
[18] NavidIzady and D. Worthington, “Setting Staffing Requirements for Time Dependent Queueing Networks: The Caseof Accident and Emergency Departments,” European Journal of Operational Research, Vol. 219, 2012, pp. 531-540.doi:10.1016/j.ejor.2011.10.040
[19] L. W. Robinson and R. R. Chen, “A Comparison of Traditional and Open-access Policies for Appointment Scheduling,” Manufacturing & Service Operations, 2010, Vol. 12, No. 2, pp. 330-346. doi:10.1287/msom.1090.0270
[20] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, “Optimization by Simulated Annealing,” Science, New Series, Vol. 220 (4598), 1983, pp. 671-680.
[21] A. Vasan and K. S. Raju, “Comparative Analysis of Simulated Annealing, Simulated Quenching and Genetic Algorithms for Optimal Reservoir Operation,” Applied Soft Computing, Vol. 9, No. 1, 2009, pp. 274-281. doi:10.1016/j.asoc.2007.09.002
[22] R. S. Tavares, T. C. Martins, M. S. G. Tsuzuki, “Simulated Annealing with Adaptive Neighborhood: A Case Study in Off-line Robot Path Planning,” Expert Systems with Applications, 2011, Vol. 38, No. 4, pp. 2951-2965.doi:10.1016/j.eswa.2010.08.084
[23] H. B. Zhu, J. Gong and J. F. Tang, “A Queuing Network Analysis Model in Emergency Departments,” Accepted by the 25th Chinese Control and Decision Conference, 2013, Vol. 5, pp. 27-29, Guiyang, China.

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