DDHA 8203 Week 4 Capacity Model Example

Twenty Beds, Counted in Bed-Hours, With Two Evening Hours Left Uncovered on Purpose: An Hour-by-Hour Capacity Model for an Emergency Department Observation Unit

Student Name

Walden University

DDHA 8203: Advanced Healthcare Operations Management

Instructor Name

Month Day, Year

Twenty Beds, Counted in Bed-Hours, With Two Evening Hours Left Uncovered on Purpose: An Hour-by-Hour Capacity Model for an Emergency Department Observation Unit

The Question the Model Answers

The emergency department at a composite 340-bed hospital I will call Brookhollow Regional runs a protocol-driven observation unit for patients who need more than an emergency visit and less than an inpatient admission: chest pain awaiting serial testing, syncope, transient ischemic attack, asthma or COPD flares and a few other protocols. The unit has 16 beds. Leadership is planning a renovation and has asked how many beds it should have. The usual answer, a single daily number such as "about 17 patients a day," cannot settle that question, because it says nothing about when the beds are needed or how often the unit is allowed to be full. This model answers it hour by hour, in one counting unit, against a stated service level, and it names the hours it chooses not to cover.

Observation units matter beyond their own walls. Ross et al. (2013), studying protocol-driven observation units in emergency departments, found that patients in these units had shorter stays and fewer inpatient admissions than comparable patients managed without them, which is part of why the unit's size affects the whole hospital.

Converting Demand Into the Unit Capacity Is Counted In

Demand arrives as patients, and capacity is counted in beds. The two cannot be set beside each other until both are expressed in bed-hours, the number of hours a bed is held by a patient or by the work of turning it over. Table 1 converts the unit's demand, using six months of placements from the case data.

The mean of about 16 occupied beds explains why the current 16-bed unit is busy, but it would mislead if used to size the new unit. A unit built to the mean is full half the time.

Table 1

Observation Demand Converted to Bed-Hours per Weekday

Bed-hours divided by 24 give a mean occupied-bed count of about 16.2 across the day.

Demand Across the Hours of a Weekday

Placements do not arrive evenly. Requests from the emergency department follow its own arrival pattern, with one peak in the late morning and early afternoon and a second in the evening, and discharges cluster in the late morning and afternoon, after test results return. Table 2 lays the resulting census across the day in two-hour blocks, showing both the mean and the 90th percentile of occupied beds over the six months.

The two request peaks have different consequences. The midday peak arrives while morning discharges are freeing beds, so the census barely rises. The evening peak arrives after most discharges have finished for the day, and it stacks on top of patients who will not leave until the next morning. Smoothing these into one daily curve would hide the only window that drives the bed count.

Table 2

Placement Requests and Occupied Beds by Two-Hour Block, Weekdays

Requests show two peaks, 12:00 to 14:00 and 20:00 to 22:00; the census peaks in the evening because daytime placements stay overnight while evening ones keep arriving.

The Service Level the Unit Is Built to Hold

The bed count depends less on any calculation in this model than on one choice: how often the unit is allowed to be full when a patient needs it. I chose the 90th percentile of occupied beds in each block. In plain terms, on nine weekdays in ten, every patient the emergency department places should find a bed waiting.

This choice should be defended rather than assumed. De Bruin et al. (2010), modeling hospital wards as loss systems, showed that a single occupancy target applied to every unit gives poor results, because the occupancy a unit can sustain without turning patients away depends on its size and on how much refusal the hospital is willing to accept. Green (2006) makes the related point that waiting rises steeply as a service nears full use, so the last few percentage points of occupancy are paid for in delay. For an observation unit, the cost of a full unit falls on the emergency department, where a patient waiting for an observation bed occupies a treatment bay. A 95th-percentile standard would remove more of that cost, and I consider it below.

Sizing the Unit and Reporting the Residual at Every Hour

Table 3 sets a proposed bed count of 20 against the 90th percentile census in each block and reports what is left over, including where the remainder is negative.

At 20 beds, the unit holds its service level in every block except the evening, when the 90th percentile census exceeds capacity by up to two beds between 20:00 and 22:00 and by one bed until midnight. Covering those two hours as well would require 22 beds.

Table 3

Proposed 20 Beds Against the 90th Percentile Census

Negative residuals mark the hours the proposed unit is not built to cover at the stated service level.

Why the Two Evening Hours Are Left Uncovered

Two additional beds would be occupied at the 90th percentile level for roughly four hours a day and would sit empty or lightly used for most of the remaining twenty. Staffing them around the clock would add roughly 2.4 nursing full-time equivalents at the unit's ratio of one nurse to five patients, and the renovation would lose space that the plan currently gives to a family waiting area and a procedure room. Spending that money to cover four evening hours would buy less than the alternatives the hospital has for it.

Leaving the hours uncovered has a cost, and the model should state it. On the case data, the evening census exceeded 20 beds on about one weekday in four. On those days, one or two patients would wait in an emergency treatment bay, usually for between one and two hours, until an evening discharge or a transfer to an inpatient bed freed space. That is two to four bay-hours lost to the emergency department on a busy evening, and it falls during the department's own evening peak.

Two operating changes would reduce that cost without adding beds. The first is an evening discharge round at 19:00 for patients whose final test results have returned, which the case data suggest would release one bed on most evenings. The second is a rule that patients whose expected stay exceeds 24 hours are admitted directly rather than placed in observation, since the longest-stay protocols in Table 1 hold beds through two evening peaks. Neither change is assumed in the 20-bed figure; both are reasons the uncovered window may prove smaller than the model shows.

Limits of the Model

The model uses weekday data only, and weekend patterns differ. It treats the next six months as if they will resemble the last six, although the emergency department's volume has grown by about 4% a year. It assumes turnover takes 45 minutes, a figure from the case that has not been timed in this unit. Finally, the 90th percentile standard is a judgment rather than a finding, and a hospital that places a higher cost on waiting in the emergency department should run the same tables at the 95th percentile, which gives 22 beds.

Conclusion

Counted in bed-hours, laid across the weekday in two-hour blocks and sized against a 90th percentile service level, the observation unit needs 20 beds. At that size, the unit is short in the evening on about one weekday in four, and that decision costs the emergency department a few bay-hours on those evenings. The model states the choice openly so that leadership can decide whether those evening hours are worth two more beds.

References

de Bruin, A. M., Bekker, R., van Zanten, L., & Koole, G. M. (2010). Dimensioning hospital wards using the Erlang loss model. Annals of Operations Research, 178(1), 23-43. https://doi.org/10.1007/s10479-009-0647-8

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

Ross, M. A., Hockenberry, J. M., Mutter, R., Barrett, M., Wheatley, M., & Pitts, S. R. (2013). Protocol-driven emergency department observation units offer savings, shorter stays, and reduced admissions. Health Affairs, 32(12), 2149-2156. https://doi.org/10.1377/hlthaff.2013.0662