Advertisement

Annals of Operations Research

, Volume 283, Issue 1–2, pp 411–442 | Cite as

Staff assignment policies for a mass casualty event queuing network

  • Emmett J. Lodree
  • Nezih AltayEmail author
  • Robert A. Cook
Applications of OR in Disaster Relief Operations

Abstract

We study parallel queuing systems in which heterogeneous teams collaborate to serve queues with three different prioritization levels in the context of a mass casualty event. We assume that the health condition of casualties deteriorate as time passes and aim to minimize total deprivation cost in the system. Servers (i.e. doctors and nurses) have random arrival rates and they are assigned to a queue as soon as they arrive. While nurses and doctors serve their dedicated queues, collaborative teams of doctors and nurses serve a third type of customer, the patients in critical condition. We model this queueing network with flexible resources as a discrete-time finite horizon stochastic dynamic programming problem and develop heuristic policies for it. Our results indicate that the standard \(c \mu \) rule is not an optimal policy, and that the most effective heuristic policy found in our simulation study is intuitive and has a simple structure: assign doctor/nurse teams to clear the critical patient queue with a buffer of extra teams to anticipate future critical patients, and allocate the remaining servers among the other two queues.

Keywords

Humanitarian logistics Medical emergency Stochastic dynamic programming Monte Carlo simulation 

References

  1. Ahn, H. S., & Righter, R. (2006). Dynamic load balancing with flexible workers. Advances in Applied Probability, 38(3), 621–642.CrossRefGoogle Scholar
  2. Altay, N., & Green, W. G. (2006). OR/MS research in disaster operations management. European Journal of Operational Research, 175(1), 475–493.CrossRefGoogle Scholar
  3. Anaya-Arenas, A. M., Renaud, J., & Ruiz, A. (2014). Relief distribution networks: A systematic review. Annals of Operations Research, 223(1), 53–79.CrossRefGoogle Scholar
  4. Andradóttir, S., Ayhan, H., & Down, D. G. (2001). Server assignment policies for maximizing the steady-state throughput of finite queueing systems. Management Science, 47(10), 1421–1439.CrossRefGoogle Scholar
  5. Andradóttir, S., Ayhan, H., & Down, D. G. (2003). Dynamic server allocation for queueing networks with flexible servers. Operations Research, 51(6), 952–968.CrossRefGoogle Scholar
  6. Andradóttir, S., Ayhan, H., & Down, D. G. (2011). Technical notequeueing systems with synergistic servers. Operations Research, 59(3), 772–780.CrossRefGoogle Scholar
  7. Argon, N. T., Ding, L., Glazebrook, K. D., & Ziya, S. (2009). Dynamic routing of customers with general delay costs in a multiserver queuing system. Probability in the Engineering and Informational Sciences, 23(02), 175–203.CrossRefGoogle Scholar
  8. Arumugam, R., Mayorga, M. E., & Taaffe, K. M. (2009). Inventory based allocation policies for flexible servers in serial systems. Annals of Operations Research, 172(1), 1–23.CrossRefGoogle Scholar
  9. Bassamboo, A., Randhawa, R. S., & Mieghem, J. A. V. (2012). A little flexibility is all you need: On the asymptotic value of flexible capacity in parallel queuing systems. Operations Research, 60(6), 1423–1435.CrossRefGoogle Scholar
  10. Bell, S. L., Williams, R. J., et al. (2001). Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy. The Annals of Applied Probability, 11(3), 608–649.CrossRefGoogle Scholar
  11. Bostick, N. A., Subbarao, I., Burkle, F. M., Hsu, E. B., Armstrong, J. H., & James, J. J. (2008). Disaster triage systems for large-scale catastrophic events. Disaster Medicine and Public Health Preparedness, 2(S1), S35–S39.CrossRefGoogle Scholar
  12. Cohen, I., Mandelbaum, A., & Zychlinski, N. (2014). Minimizing mortality in a mass casualty event: Fluid networks in support of modeling and staffing. IIE Transactions, 46(7), 728–741.CrossRefGoogle Scholar
  13. Elsharkawi, H., Jaeger, T., Christensen, L., Rose, E., Giroux, K., & Ystgaard, B. (2010). Mobile field hospitals in the Haiti earthquake response: A red cross model. Humanitarian Exchange Magazine, 48, 10–13.Google Scholar
  14. Fine, C. H., & Freund, R. M. (1990). Optimal investment in product-flexible manufacturing capacity. Management Science, 36(4), 449–466.CrossRefGoogle Scholar
  15. Gaver, D. P., & Jacobs, P. A. (1999). Servicing impatient tasks that have uncertain outcomes. Tech. rep., DTIC Document.Google Scholar
  16. Glazebrook, K., Ansell, P., Dunn, R. T., & Lumley, R. R. (2004). On the optimal allocation of service to impatient tasks. Journal of Applied Probability, 41(01), 51–72.CrossRefGoogle Scholar
  17. Gong, Q., & Batta, R. (2006). A queue-length cutoff model for a preemptive two-priority m/m/1 system. SIAM Journal on Applied Mathematics, 67(1), 99–115.CrossRefGoogle Scholar
  18. Gupta, S., Starr, M. K., Farahani, R. Z., & Matinrad, N. (2016). Disaster management from a POM perspective: Mapping a new domain. Production and Operations Management, 25(10), 1611–1637.CrossRefGoogle Scholar
  19. Hick, J. L., Barbera, J. A., & Kelen, G. D. (2009). Refining surge capacity: Conventional, contingency, and crisis capacity. Disaster Medicine and Public Health Preparedness, 3(S1), S59–S67.CrossRefGoogle Scholar
  20. Hirshberg, A., Stein, M., & Walden, R. (1999). Surgical resource utilization in urban terrorist bombing: A computer simulation. Journal of Trauma and Acute Care Surgery, 47(3), 545–550.CrossRefGoogle Scholar
  21. Holguín-Veras, J., Pérez, N., Jaller, M., Van Wassenhove, L. N., & Aros-Vera, F. (2013). On the appropriate objective function for post-disaster humanitarian logistics models. Journal of Operations Management, 31(5), 262–280.CrossRefGoogle Scholar
  22. Jacobson, E. U., Argon, N. T., & Ziya, S. (2012). Priority assignment in emergency response. Operations Research, 60(4), 813–832.CrossRefGoogle Scholar
  23. Kilic, A., Dincer, M. C., & Gokce, M. A. (2014). Determining optimal treatment rate after a disaster. Journal of the Operational Research Society, 65(7), 1053–1067.CrossRefGoogle Scholar
  24. Lerner, E. B., Schwartz, R. B., Coule, P. L., Weinstein, E. S., Cone, D. C., Hunt, R. C., et al. (2008). Mass casualty triage: An evaluation of the data and development of a proposed national guideline. Disaster Medicine and Public Health Preparedness, 2(S1), S25–S34.CrossRefGoogle Scholar
  25. Mayorga, M., Lodree, E. J., & Wolczynski, J. (2017). The optimal assignment of spontaneous volunteers. Journal of the Operational Research Society, 68(9), 1106–1116.CrossRefGoogle Scholar
  26. Mayorga, M. E., Taaffe, K. M., & Arumugam, R. (2009). Allocating exible servers in serial systems with switching costs. Annals of Operations Research, 172(1), 231–242.CrossRefGoogle Scholar
  27. Merin, O., Ash, N., Levy, G., Schwaber, M. J., & Kreiss, Y. (2010). The israeli field hospital in Haiti—Ethical dilemmas in early disaster response. New England Journal of Medicine, 362(11), e38.CrossRefGoogle Scholar
  28. Mills, A. F. (2012). Patient prioritization and resource allocation in mass casualty incidents. Chapel Hill: University of North Carolina at Chapel Hill.Google Scholar
  29. Sacco, W. J., Navin, D. M., Fiedler, K. E., Waddell, I., Robert, K., Long, W. B., et al. (2005). Precise formulation and evidence-based application of resource-constrained triage. Academic Emergency Medicine, 12(8), 759–770.CrossRefGoogle Scholar
  30. Saghafian, S., Van Oyen, M. P., & Kolfal, B. (2011). The W network and the dynamic control of unreliable flexible servers. IIE Transactions, 43(12), 893–907.CrossRefGoogle Scholar
  31. Sethi, A. K., & Sethi, S. P. (1990). Flexibility in manufacturing: A survey. International Journal of Flexible Manufacturing Systems, 2(4), 289–328.CrossRefGoogle Scholar
  32. Van Mieghem, J. A. (2008). Operations strategy: Practices and principles. Belmont, MA: Dynamic Ideas.Google Scholar
  33. Wang, X., Andradóttir, S., & Ayhan, H. (2015). Dynamic server assignment with task-dependent server synergy. IEEE Transactions on Automatic Control, 60(2), 570–575.CrossRefGoogle Scholar
  34. Xiang, Y., & Zhuang, J. (2016). A medical resource allocation model for serving emergency victims with deteriorating health conditions. Annals of Operations Research, 236(1), 177–196.CrossRefGoogle Scholar
  35. Yang, R., Bhulai, S., & Van der Mei, R. (2011). Optimal resource allocation for multiqueue systems with a shared server pool. Queueing Systems, 68(2), 133–163.CrossRefGoogle Scholar
  36. Yang, R., Bhulai, S., & van der Mei, R. (2013). Structural properties of the optimal resource allocation policy for single-queue systems. Annals of Operations Research, 202(1), 211–233.CrossRefGoogle Scholar
  37. Zayas-Caban, G., & Lodree, E. J. (2017). Optimal control of volunteer convergence. Working paper.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Culverhouse College of Commerce and Business AdministrationThe University of AlabamaTuscaloosaUSA
  2. 2.Driehaus College of BusinessDepaul UniversityChicagoUSA

Personalised recommendations