Abstract
Inefficient management of emergent surgeries in hospitals can, in part, be attributed to a lack of rigorous analysis appropriate to capturing the underlying uncertainties inherent to this process and a pricing mechanism to ensure its financial viability. We develop a non-preemptive multi-priority queueing model that optimally manages emergent surgeries and supports the resource allocation decision-making process. Specifically, we utilize queueing and discrete event simulation to develop empirical models for determining the required number of emergent operating rooms for a hospital surgical department. We also present algorithms that estimate the appropriate pricing for patient surgeries differentiated by priority level given the patient demand and the resources reserved to meet this demand.
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Notes
The findings might not hold if the surgery distribution did not fit a γ-type distribution (of which the Erlang is a special case), in which the distribution averages are additive.
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Appendices
Appendix A
Effect of priority transition
For highest priority customers, the expected wait time without transitions is given as:
that is, the number of Priority 1 patients in the queue and the residual time for patients in service. With transition, Priority 1 would also have to wait for all the lower priority classes that have already waited longer than the difference in survivability time between the priorities, given as 
, where Pm, n=P(wait time priority>ω
m
ω
n
), that is, the probability that priority ‘m’ has waited longer than the difference in wait time of priority ‘n’, where m>n which is strictly positive, thus the expected wait time for Priority 1 will be higher.
For priorities >1 without transition, we can decompose the expected wait time into two components: the amount of residual service time of a patient currently in service as well as all patients with the same or higher priority in the queue upon arrival. The second is all the higher priority patients arriving during the patients waiting time:
Two additional terms account for the possibility of transition of priority resulting from excessive wait time. The first concerns the presence of lower priority patients that have waited longer than the difference between the survivability times. The second addresses the fact that arriving higher priority patients will only take priority for those priority ‘i’ patients that have not waited longer than the difference in survivability times. Adding these to the above equation results in
The second term increases the expected wait time, while the addition of (1−Pi, j) to the last term decreases the expected wait time, with the net effect dependent upon system dynamics. The only exception is for the lowest priority, as the second term is zero given that there are no lower priority patients. Thus, the lowest priority will always see a decrease in their expected wait time.
Appendix B
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Paul, J., MacDonald, L. Determination of number of dedicated OR's and supporting pricing mechanisms for emergent surgeries. J Oper Res Soc 64, 912–924 (2013). https://doi.org/10.1057/jors.2012.92
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DOI: https://doi.org/10.1057/jors.2012.92