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Staff assignment policies for a mass casualty event queuing network

  • Applications of OR in Disaster Relief Operations
  • Published:
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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.

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Notes

  1. Although doctors are perfectly capable of treating patients with minor injuries, we assume that their unique skills are reserved for patients with serious or critical injures.

  2. There are queuing models where servers with the same skill sets can work collaboratively to process a single customer; but the scenario considered here is very different. In existing collaborative models, customers can be served by one or more servers, where more servers increases the collective service rate. In this paper, the servers that work together have different skills and their combined skills are required in order for service to take place.

  3. We say “at most” because the transition equations can take multiple states in period t to the same state in period \(t+1\). Thus the number of states in Eq. (12) includes some duplicates.

  4. The five possible sequences in which the three queues can be prioritized are 3–2–1, 2–3–1, 2–1–3, 1–3–2, and 1–2–3. Recall that 3–2–1 and 3–1–2 are equivalent as described in the explanation of the Priority Sequence column of Table 5.

  5. Technically, \(b^* > 0\) for 21 of the 24 experiments. Although the best buffer size for the CQ3B rule is \(b^* = 1\) for experiment 17, the resulting average cost only improves upon the \(b=0\) solution by 0.43%. Also, the average costs are statistically equivalent (at 99% confidence level), which means that \(b=0\) is also a pseudo-optimal buffer size.

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Authors and Affiliations

  1. Culverhouse College of Commerce and Business Administration, The University of Alabama, Tuscaloosa, AL, 35487, USA

    Emmett J. Lodree & Robert A. Cook

  2. Driehaus College of Business, Depaul University, Chicago, IL, 60604, USA

    Nezih Altay

Authors
  1. Emmett J. Lodree
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  2. Nezih Altay
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  3. Robert A. Cook
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Correspondence to Nezih Altay.

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Lodree, E.J., Altay, N. & Cook, R.A. Staff assignment policies for a mass casualty event queuing network. Ann Oper Res 283, 411–442 (2019). https://doi.org/10.1007/s10479-017-2635-8

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