Robust capacity planning for accident and emergency services
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1757-1773.

Accident and emergency departments (A&E) are the first place of contact for urgent and complex patients. These departments are subject to uncertainties due to the unplanned patient arrivals. After arrival to an A&E, patients are categorized by a triage nurse based on the urgency. The performance of an A&E is measured based on the number of patients waiting for more than a certain time to be treated. Due to the uncertainties affecting the patient flow, finding the optimum staff capacities while ensuring the performance targets is a complex problem. This paper proposes a robust-optimization based approximation for the patient waiting times in an A&E. We also develop a simulation optimization heuristic to solve this capacity planning problem. The performance of the approximation approach is then compared with that of the simulation optimization heuristic. Finally, the impact of model parameters on the performances of two approaches is investigated. The experiments show that the proposed approximation results in good enough solutions.

DOI : 10.1051/ro/2019112
Classification : 49, 90
Mots-clés : Health-care modelling, capacity planning, accident and emergency services, queuing theory, simulation optimization, robust optimization
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Gökalp, Elvan. Robust capacity planning for accident and emergency services. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1757-1773. doi : 10.1051/ro/2019112. http://archive.numdam.org/articles/10.1051/ro/2019112/

[1] M.A. Ahmed and T.M. Alkhamis, Simulation optimization for an emergency department healthcare unit in Kuwait. Eur. J. Oper. Res. 198 (2009) 936–942. | DOI | Zbl

[2] E. Alfonso, X. Xie, V. Augusto and O. Garraud, Modelling and simulation of blood collection systems: improvement of human resources allocation for better cost-effectiveness and reduction of candidate donor abandonment. Vox Sang. 104 (2013) 225–233. | DOI

[3] A.O. Allen, Probability, Statistics, and Queueing Theory. Academic Press (2014). | MR | Zbl

[4] M.H. Alrefaei and A. Diabat, Modelling and optimization of outpatient appointment scheduling. RAIRO: RO 49 (2015) 435–450. | DOI | Numdam | MR | Zbl

[5] M. Asaduzzaman, T.J. Chaussalet and N.J. Robertson, A loss network model with overflow for capacity planning of a neonatal unit. Ann. Oper. Res. 178 (2010) 67–76. | DOI | MR | Zbl

[6] Audit General for Scotland: Emergency Departments. Tech. Rep., Audit General for Scotland (2010). Available from: http://www.audit-scotland.gov.uk/uploads/docs/report/2010/nr_100812_emergency_departments.pdf.

[7] C. Bandi and D. Bertsimas, Tractable stochastic analysis in high dimensions via robust optimization. Math. Program. 134 (2012) 23–70. | DOI | MR | Zbl

[8] P. Bonami, M. Kilinç and J. Linderoth, Algorithms and software for convex mixed integer nonlinear programs. In: Mix. integer nonlinear Program, Springer, New York (2012). | DOI | MR | Zbl

[9] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press (2004). | DOI | MR | Zbl

[10] K.M. Bretthauer, H.S. Heese, H. Pun and E. Coe, Blocking in healthcare operations: a new heuristic and an application. Prod. Oper. Manag. 20 (2011) 375–391. | DOI

[11] I. Castillo, A. Ingolfsson and T. Sim, Social optimal location of facilities with fixed servers, stochastic demand, and congestion. Prod. Oper. Manag. 18 (2009) 721–736. | DOI

[12] T.L. Chen and C.C. Wang, Multi-objective simulation optimization for medical capacity allocation in emergency department. J. Simul. 10 (2016) 50–68. | DOI

[13] J.K. Cochran and K.T. Roche, A multi-class queuing network analysis methodology for improving hospital emergency department performance. Comput. Oper. Res. 36 (2009) 1497–1512. | DOI | Zbl

[14] Computational Infrastructure for Operations Research: Bonmin (2018). Available from: https://www.coin-or.org/Bonmin/index.html.

[15] A.X. Costa, S.A. Ridley, A.K. Shahani, P.R. Harper, V. De Senna and M.S. Nielsen, Mathematical modelling and simulation for planning critical care capacity. Anaesthesia 58 (2003) 320–327. | DOI

[16] S. Creemers and M. Lambrecht, An advanced queueing model to analyze appointment-driven service systems. Comput. Oper. Res. 36 (2009) 2773–2785. | DOI | Zbl

[17] V. De Angelis, G. Felici and P. Impelluso, Integrating simulation and optimisation in health care centre management. Eur. J. Oper. Res. 150 (2003) 101–114. | DOI | Zbl

[18] H. Eskandari, M. Riyahifard, S. Khosravi and C.D. Geiger, Improving the emergency department performance using simulation and MCDM methods. In: Proc. winter Simul. Conf. Winter Simulation Conference (2011) 1211–1222.

[19] S. Flessa, Where efficiency saves lives: a linear programme for the optimal allocation of health care resources in developing countries. Health Care Manag. Sci. 3 (2000) 249–267. | DOI

[20] A. Fletcher, D. Halsall, S. Huxham and D. Worthington, The DH Accident and Emergency Department model: a national generic model used locally. J. Oper. Res. Soc. 58 (2007) 1554–1562. | DOI

[21] S. Fomundam and J.W. Herrmann, A Survey of Queuing Theory Applications in Healthcare. University of Maryland, College Park (2007).

[22] F. Fruggiero, A. Lambiase and D. Fallon, Computer simulation and swarm intelligence organisation into an emergency department: a balancing approach across ant colony optimisation. Int. J. Serv. Oper. Inf. 3 (2008) 142–161.

[23] K. Ghanes, M. Wargon, O. Jouini, Z. Jemai, A. Diakogiannis, R. Hellmann, V. Thomas and G. Koole, Simulation-based optimization of staffing levels in an emergency department. Simulation 91 (2015) 942–953. | DOI

[24] M. Gourgand, N. Grangeon and N. Klement, Activities planning and resources assignment on distinct places: a mathematical model. RAIRO: OR 49 (2015) 79–98. | DOI | Numdam | MR

[25] R. Govind, R. Chatterjee and V. Mittal, Timely access to health care: customer-focused resource allocation in a hospital network. Int. J. Res. Mark. 25 (2008) 294–300. | DOI

[26] L.V. Green, P.J. Kolesar and W. Whitt, Coping with time-varying demand when setting staffing requirements for a service system. Prod. Oper. Manag. 16 (2007) 13–39. | DOI

[27] S. Gul, B.T. Denton and J.W. Fowler, A progressive hedging approach for surgery planning under uncertainty. Inf. J. Comput. 27 (2015) 755–772. | DOI | MR | Zbl

[28] E.D. Güneş and H. Yaman, Health network mergers and hospital re-planning. J. Oper. Res. Soc. 61 (2010) 275–283. | DOI | Zbl

[29] V. Gupta and T. Osogami, On Markov-Krein characterization of the mean waiting time in M / G / K and other queueing systems. Queueing Syst. 68 (2011) 339–352. | DOI | MR | Zbl

[30] P.R. Harper, N.H. Powell and J.E. Williams, Modelling the size and skill-mix of hospital nursing teams. J. Oper. Res. Soc. 61 (2010) 768–779. | DOI | Zbl

[31] X. Hu, S. Barnes and B. Golden, Applying queueing theory to the study of emergency department operations: a survey and a discussion of comparable simulation studies. Int. Trans. Oper. Res. 25 (2018) 7–49. | DOI | MR

[32] P.J.H. Hulshof, M.R.K. Mes, R.J. Boucherie and E.W. Hans, Tactical planning in healthcare using approximate dynamic programming. Tech. Rep.. University of Twente (2013).

[33] I.M. Ibrahim, C.Y. Liong, S.A. Bakar, N. Ahmad and A.F. Najmuddin, Estimating optimal resource capacities in emergency department. Indian J. Public Heal. Res. Dev. 9 (2018).

[34] N. Izady and D. Worthington, Setting staffing requirements for time dependent queueing networks: the case of accident and emergency departments. Eur. J. Oper. Res. 219 (2012) 531–540. | DOI | Zbl

[35] J. Köllerström, Heavy traffic theory for queues with several servers. I. J. Appl. Probab. 11 (1974) 544–552. | DOI | MR | Zbl

[36] C. Lakshmi and S.A. Iyer, Application of queueing theory in health care: a literature review. Oper. Res. Heal. Care 2 (2013) 25–39. | DOI

[37] B. Lunenfeld and P. Stratton, The clinical consequences of an ageing world and preventive strategies. Best Pract. Res. Clin. Obstet. Gynaecol. 27 (2013) 643–659. | DOI

[38] S. Mahar, K.M. Bretthauer and P.A. Salzarulo, Locating specialized service capacity in a multi-hospital network. Eur. J. Oper. Res. 212 (2011) 596–605. | DOI

[39] L. Mayhew and D. Smith, Using queuing theory to analyse the government’s 4 h completion time target in accident and emergency departments. Health Care Manag. Sci. 11 (2008) 11–21. | DOI

[40] Z. Mingzhu and Q. Ershi, A multi-type queuing network analysis method for controlling server number in the outpatient. Open Autom. Control Syst. J. 8 (2016). | DOI

[41] S. Mohiuddin, J. Busby, J. Savović, A. Richards, K. Northstone, W. Hollingworth, J.L. Donovan and C. Vasilakis, Patient flow within UK emergency departments: a systematic review of the use of computer simulation modelling methods. BMJ Open 7 (2017) e015007. | DOI

[42] A. Mortimore and S. Cooper, The “4-hour target”: emergency nurses’ views. Emerg. Med. J. 24 (2007) 402–404. | DOI

[43] W. Munir, Critical analysis of the 4-hour A&E policy’s impact on elderly patients. Br. J. Nurs. 17 (2008) 1188–1192.

[44] NHS England: AE Waiting times and activity. Tech. Rep. NHS England, London (2018). Available from: https://www.england.nhs.uk/statistics/statistical-work-areas/ae-waiting-times-and-activity/ae-attendances-and-emergency-admissions-2018-19/.

[45] NHS England: Commissioning Committee Report to Board. Tech. Rep. NHS England (2018). Available from: https://www.england.nhs.uk/wp-content/uploads/2018/11/13i-pb-28-11-18-commissioning-committeee-report-to-board-24-october.pdf.

[46] NHS UK: Hospital Accident and Emergency Activity, 2017–18, Provider Level Analysis. Tech. Rep., National Health Services UK (2018). Available from: https://digital.nhs.uk/data-and-information/publications/statistical/hospital-accident–emergency-activity/2017-18.

[47] NHS UK: Pay for Doctors (2019). Available from: https://www.healthcareers.nhs.uk/explore-roles/doctors/pay-doctors.

[48] NHS UK: Urgent and Emergency Care: When to go to A&E (2019). Available from: https://www.nhs.uk/using-the-nhs/nhs-services/urgent-and-emergency-care/when-to-go-to-ae/.

[49] NHS UK: OptQuest (2019). Available from: https://www.opttek.com/products/optquest/.

[50] C. Pehlivan, V. Augusto, X. Xie and C. Crenn-Hebert, Multi-period capacity planning for maternity facilities in a perinatal network: a queuing and optimization approach. In: Autom. Sci. Eng. (CASE). 2012 IEEE Int. Conf. IEEE (2012) 137–142. | DOI

[51] F. Rico, E. Salari and G. Centeno, Emergency departments nurse allocation to face a pandemic influenza outbreak. In: In: Proc. 39th Conf. Winter Simul. IEEE Press (2007) 1292–1298.

[52] Royal College of Nursing: NHS pay scales 2017–18 (2019). Available from: https://www.rcn.org.uk/employment-and-pay/nhs-pay-scales-2017-18.

[53] S. Saghafian, G. Austin and S.J. Traub, Operations research/management contributions to emergency department patient flow optimization: review and research prospects. IIE Trans. Healthc. Syst. Eng. 5 (2015) 101–123. | DOI

[54] P. Santibáñez, G. Bekiou and K. Yip, Fraser Health uses mathematical programming to plan its inpatient hospital network. Interfaces (Providence) 39 (2009) 196–208. | DOI

[55] C. Stummer, K. Doerner, A. Focke and K. Heidenberger, Determining location and size of medical departments in a hospital network: a multiobjective decision support approach. Health Care Manag. Sci. 7 (2004) 63–71. | DOI

[56] S.S. Syam and M.J. Côté, A location allocation model for service providers with application to not-for-profit health care organizations. Omega 38 (2010) 157–166. | DOI

[57] The Telegraph: One in three hospital patients admitted as an emergency to be sent home without an overnight stay (2019). Available from: https://www.telegraph.co.uk/news/2019/03/08/one-three-hospital-patients-admitted-emergency-sent-home-without/.

[58] H.C. Tijms, M.H. Van Hoorn and A. Federgruen, Approximations for the steady-state probabilities in the M / G / c queue. Adv. Appl. Probab. 13 (1981) 186–206. | DOI | MR | Zbl

[59] S.J. Weng, B.C. Cheng, S.T. Kwong, L.M. Wang and C.Y. Chang, Simulation optimization for emergency department resources allocation. In: Proc. 2011 Winter Simul. Conf. (WSC). IEEE (2011) 1231–1238. | DOI

[60] J.L. Wiler, R.T. Griffey and T. Olsen, Review of modeling approaches for emergency department patient flow and crowding research. Acad. Emerg. Med. 18 (2011) 1371–1379. | DOI

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