Improving Emergency Department patient throughput by considering providers' inpatient rates: a mathematical programming approach
20191011_SEAS_RandD_KNZR_FINAL_COMPLETE.pdfImproving Emergency Department patient throughput by considering providers' inpatient admission rates: a mathematical programming approach
Kelly N. Z. Rickard, M.P.H. | Johan René van Dorp, D.Sc. | Jesse M. Pines, M.D., M.B.A., M.S.C.E. | Kenneth W. McKinley, M.D.
Scheduling Emergency Department doctors’ work shifts by aligning their practice patterns to patient arrival patterns may alleviate crowding in the inpatient unit. This creates bed availability for admissions, thereby creating space for new patients in the Emergency Department.
Updates
Please follow this project's progress here; we will occasionally post updates!
This project is a part of Kelly Rickard's doctoral dissertation in Systems Engineering & Operations Research.
More on next steps:
On our GWU R&D 2019 poster we show a SMORE plot (box-and-whisker plot with confidence intervals around the mean and quartiles) of what happens when the staffing (scheduling)1 configuration from the notional case (based on Hospital 17's forecasting) is applied to Children's National Medical Center (CNMC): it does not work. The 'best' configuration from the notional case is worse than the 'worst' configuration! We ran preliminary data from CNMC in our Integer Program (IP) and into our Discrete-Event Simulation (DES) (built in Simio v.10.165) to find CNMC's optimal scheduling configuration and verify the two models against one another. We used each model to find the optimized scheduling configurations: for the IP we ran the Evolutionary solving method in Excel 2013's Solver (built-in optimization algorithms), and for the DES we ran Simio's OptQuest Add-In. However, it is trivial to enumerate all 393 viable schedule configurations in simulation, so we did that too.
Interestingly, CNMC's Emergency Department (ED) seems to be an edge case: it is so sensitive to a high admission rate that having even one day with an admission rate at the 75th percentile will throw off the entire week! This results in the 'chance' or 'evenly distributed' configuration being the 'best' configuration! At least with only three possible admission rate values there is no way to improve upon the schedule... just 392 (minus a handful) ways to make it worse.
The MMMMMMM case has the least variation, the LMHHHLL case has the most. On its best day, the 'evenly distributed' configuration (MMMMMMM) has 29-30 beds in use (on average), and the 'worst' configuration (LMHHHLL) has 18-19 beds in use (on average). This kind of smoothing is highly desirable in hospitals!
Comparing all 393 scenarios, on a Monday, traditionally the busiest day in the ED (click to enlarge):
The 'chance', or 'evenly distributed' configuration (MMMMMMM) has the same admission rate on every day (M = medium = 14%). It is the 'best' configuration, or is equivalent to the other best configurations. Another candidate for 'best' configuration (MMMMMLH) has a high admission rate on Sundays (H = high = 20%), a low rate on Saturdays (L = low = 8%), and a medium rate the rest of the week. The confidence intervals overlap so we cannot say one is better than the other, we only know this configuration is not worse.
The 'worst' configuration (LMHHHLL, which is, rather, one of the worst configurations) has a high admission rate on Wednesdays, Thursdays, and Fridays, with a low rate on Saturdays, Sundays, and Mondays, and a medium rate on Tuesdays. This SMORE plot shows us that the 'evenly distributed' configuration, on the worst day of the week, sees about 35-36 inpatient beds in use (on average) and that the 'worst' configuration, on the worst day of the week, sees about 49-50 inpatient beds in use.
Not surprising, the least busy days of the week are nearly oppositely ranked:
The repeating pattern is largely an artifact of the method we used to generate all the configurations, but happens to group Mondays somewhat usefully for visual inspection.
Thursdays are a bit more visually consistent (click to enlarge):
Saturdays are a bit more chaotic (click to enlarge):
Background
(1) Scheduling is accomplished in four parts:
1. Forecasting (determining demand)
2. Staffing (determining number of workers necessary to meet demand)
3. Shift Scheduling (structuring the schedule into shifts)
4. Rostering (assigning individuals to shifts)
This project deals with the staffing component and will be used to develop recommendations for the rostering component.