29 - Using Queuing Theory to Determine Optimal Obstetrical Bed Numbers

Poster Number: 29
Publication Number: 29.338

Caroline N. Jackson, University of Louisville School of Medicine, Louisville, KY, United States; Scott D. Duncan, University of Louisville, Louisville, KY, United States; Yana Feygin, University of Louisville School of Medicine, Louisville, KY, United States; Sagnik Bhadury, University of Louisville School of Medicine, Louisville, KY, United States; Liza M. Creel, University of Louisville School of Public Health and Information Sciences, Louisville, KY, United States; Maiying Kong, University of Louisville, Louisville, KY, United States; Kahir S. Jawad, University of Louisville School of Medicine, Louisville, KY, United States

Background: In Kentucky, obstetrical (OB) bed capacity and utilization data is publicly reported by hospital and Area Developmental District (ADD). Per ACOG, the recommended number of obstetrical beds is determined by using 75% utilization. An alternative model for determining the number of required beds is derived from queuing theory, wherein the probability of a non-zero wait time is < 0.01.

Objective: To estimate current and target capacity and utilization of obstetrical beds in the ADDs and Kentucky, applying queuing theory.

Design/Methods: Data examined is from publicly reported 2019 Kentucky Annual Hospital Utilization and Services Report. The number of OB beds, OB inpatient days, and births across the ADDs and state were input values for queuing calculations. For each ADD and the state, optimal bed number was defined using 75% capacity utilization. Subsequently, a sensitivity analysis was performed to determine the optimal bed number, using the Erlang-C formula to estimate the probability that a patient must wait for a bed. The number of beds were then stratified by 75% utilization, < 10%, < 5%, and < 1% probability of a non-zero wait time. If a patient was delayed, the average delay was calculated, as represented by Wq (Figure 2).

Results: In Kentucky, capacity utilization in 2019 was 44.5%, ranging 18.9-62.6% in the ADDs. With 75% capacity utilization, the probability of a positive wait time is between 0-28.6%, with wait times as long as 556 minutes. When calculating the number of beds such that there is a < 10% probability of a delay, wait times vary from 28-68 minutes; with a < 5% probability of a delay, wait times range from 10-31 minutes; with a < 1% probability of a delay, wait times decrease to 1-3 minutes. The current and calculated number of beds is noted in Table 1.Conclusion(s): This analysis suggests there is an excess of obstetrical beds in Kentucky. Through the utilization of queuing theory, there is potential to impact public policy, where capacity could be adjusted based on calculated need assessment. This is especially applicable in a Certificate of Need state such as Kentucky. At the hospital level, such calculations can be used to assess and adjust staffing needs. Limitations to this analysis include the self-reported data set and the use of number of births vs. actual OB admissions. Applying queuing theory as part of operations research can shape policy and operations, impacting access and costs incurred in caring for the maternal infant dyad.
Caroline Jackson CVJackson CV.pdf
Figure 2: Wait Time Formula