IHP 640 Module 7 Capacity Modeling Paper Example

Is the Recovery Room the Bottleneck? Queueing and Simulation at Highland Valley

[Student Name]

Southern New Hampshire University

IHP 640: Measurement, Analysis, & Models for Performance Improvement

Module Seven Paper

[Instructor Name]

[Date]

The organization, setting and figures below are a composite written as a model document. No real employer, client, colleague or patient is described.

Is the Recovery Room the Bottleneck? Queueing and Simulation at Highland Valley

Operating room nurses at Highland Valley Medical Center report that patients sometimes stay in the room after surgery because the recovery unit cannot take them. Each hold delays cleaning and the next case, adding to the overtime examined in earlier milestones. The recovery unit manager says the problem is rare and requests more nurses; surgeons say the unit is simply slow. This paper uses two modeling approaches to settle the question and test solutions.

The System

The recovery unit has 16 bays, but staffing, not space, limits capacity: nurses care for two patients each, and six nurses cover the core daytime shift, allowing 12 patients at once. About 45 patients arrive each weekday. Arrivals peak between 10:00 a.m. and 2:00 p.m. at about seven an hour, and stays average 85 minutes with a standard deviation of 40. Operating room records show about 1.4 holds longer than ten minutes per day, averaging 22 minutes each.

Why Averages Hide Congestion

Green (2006) explained that queueing theory relates arrival rates, service times, the number of servers and variability to expected delays, and that delays rise steeply as utilization approaches full capacity. A unit that looks comfortably staffed on average can be congested at peaks, and variability in arrivals and service times increases waiting even when average capacity is adequate. She also noted that pooling resources reduces delays and that target occupancy levels should reflect acceptable waiting rather than a fixed percentage.

A Queueing Estimate

At the midday peak, offered load equals the arrival rate times average stay: seven an hour times about 1.42 hours, or about 9.9 patients in the unit on average. With capacity for 12, utilization is about 83%. A standard multi-server queueing model, which assumes random arrivals and highly variable stays, predicts that about 43% of peak arrivals would find no staffed space immediately. With seven nurses, capacity of 14, utilization falls to 71% and that probability to about 17%. Most such waits would be brief, and the model's assumptions overstate variability, but the estimate shows the unit operates in the zone where small changes have large effects.

Why Simulate

Queueing formulas assume steady conditions, but the recovery unit's arrivals depend on the operating room schedule, which changes through the day. Simulation can represent that schedule directly. Reviewing hospital simulation studies, Günal and Pidd noted strong uptake for single-unit capacity problems (Günal & Pidd, 2010) and warned that many models are complex, used once and never validated against reality. The model here is kept deliberately small and checked against observed holds.

Building the Simulation

The model represents each of the 14 operating rooms running its actual schedule for a sample of 60 weekdays, with case durations and recovery stays drawn from each service's observed distributions. When a case ends and no staffed bay is free, the patient waits in the operating room. The model tracks holds, their length and nurse workload. Run 200 times, it produced an average of 1.3 holds over ten minutes per day, close to the 1.4 observed, which gives confidence in its structure.

Options Tested

Four options were tested. Adding a seventh nurse from 10:00 a.m. to 2:00 p.m. addresses the peak directly. Reducing average stays by ten minutes, through earlier discharge criteria, shortens occupancy. Resequencing cases changes when patients arrive. And staggering first-case starts, with half the rooms starting at 7:30 a.m. and half at 8:00 a.m., spreads the midday wave.

Evidence on Sequencing and Peaks

Marcon and Dexter (2006) used simulation to show that the order in which surgeons sequence their cases affects recovery unit staffing needs, because some sequences concentrate arrivals and others spread them. Dexter and Tinker (1995) analyzed strategies to reduce recovery unit costs and found that staffing requirements are driven largely by peak admission rates, so smoothing arrivals can matter as much as shortening stays. Both findings suggest the schedule itself is a capacity tool.

Results

Adding a midday nurse cut holds from 1.3 to 0.3 per day. Resequencing, placing longer cases first in rooms with several short procedures, cut holds to 0.6. Staggered starts reduced holds to 0.7 but slightly lengthened the operating day in affected rooms. A ten-minute shorter stay reduced holds to 0.8. Combining resequencing with shorter stays achieved 0.4 without new staff.

Table 1. Simulated Recovery Room Holds Under Each Option

Note. Averages of 200 runs over 60 simulated weekdays; composite data.

Interpreting the Results

The recovery unit is a genuine but modest contributor to operating room delays: holds consume about 7,000 operating room minutes a year, less than first-case tardiness but concentrated in the busiest hours. Both sides of the dispute were partly right. A midday nurse is the surest fix at about $80,000 a year, while resequencing and shorter stays achieve most of the benefit at no staffing cost but depend on surgeon and nurse cooperation.

Sharing Results With Stakeholders

Model results persuade only if people trust them. The analyst presented the simulation to the recovery unit manager, two surgeons and the anesthesia chief, showing first that it reproduced the holds they recognized before showing any options. Surgeons questioned the sequencing assumption, so the team ran a version in which only half of eligible surgeons changed their order; holds still fell to 0.9 per day. That sensitivity test, and the transparency of the model's inputs, helped move the discussion from blame toward choosing among options.

Limitations

The model does not include rare events such as emergencies arriving midday or staff breaks, which would increase holds, and it assumes surgeons would follow resequencing guidance. Its results depend on the observed distributions, which may shift as case mix changes.

Conclusion

Queueing analysis shows the recovery unit runs close to the point where delays climb steeply at midday, and simulation confirms that holds are real but modest. A combination of case resequencing and faster discharge could nearly eliminate holds without new staff, with a midday nurse as a fallback, and both options will feed into the improvement plan.

References

Dexter, F., & Tinker, J. H. (1995). Analysis of strategies to decrease postanesthesia care unit costs. Anesthesiology, 82(1), 94-101. https://doi.org/10.1097/00000542-199501000-00013

Günal, M. M., & Pidd, M. (2010). Discrete event simulation for performance modelling in health care: A review of the literature. Journal of Simulation, 4(1), 42-51. https://doi.org/10.1057/jos.2009.25

Green, L. (2006). Queueing analysis in healthcare. In R. W. Hall (Ed.), Patient flow: Reducing delay in healthcare delivery (pp. 281-307). Springer. https://doi.org/10.1007/978-0-387-33636-7_10

Marcon, E., & Dexter, F. (2006). Impact of surgical sequencing on post anesthesia care unit staffing. Health Care Management Science, 9(1), 87-98. https://doi.org/10.1007/s10729-006-6282-x