The Emergency Department $($ED$)$ in the Middletown General Hospital sees about $200$ patients each day. On average, $150$ of these are discharged to home after being seen; but about $50$ of the patients seen need to stay overnight in a hospital bed. About $20$ percent of these are on $$observation$$ status, meaning that an admission decision has not yet been made, pending some test results or the result of an overnight observation stay. The remaining $80$ percent are admitted directly. Currently all patients who stay overnight $($whether admitted or on observation status$)$ are put into an inpatient bed $($see Figure $1).$ That is$,$ there is no separate observation area in which patients can be boarded. Observation patients stay on observation status for an average of $1\mathrm{.}2$ days before either being discharged or upgraded to an inpatient bed. Patients admitted to the hospital stay an average of $5\mathrm{.}8$ days before discharge.

Question $1$

What is the average census of observation patients in the hospital?

Extra Credit

If $80$ percent of observation patients are discharged to home, and $20$ percent are upgraded to inpatient status $($and these then stay an average of $5\mathrm{.}8$ days$),$ what is the average census of admitted patients in the hospital? If there are $270$ inpatient beds in Middletown General, what is the utilization of the beds $($occupancy rate in percentage of beds filled$)?($Hint: The flow of admitted patients will be those

admitted directly from the ED plus those admitted from observation status, and both of these stay an average $5\mathrm{.}8$ days.$)$

For the remainder of this case we will ignore the flows from observation status to admitted status, and work with an approximate model of two types of patients as suggested by Figure $1.$

Question $2$

Given the current patient flows, how large should the ED observation unit be to achieve a target utilization of $80$ percent? Assume that the average observation patient represents about $$3,300$ in profits to the hospital$*,$ and the average admitted patient represents about $$3,500$ in profits $($Figure $1).$

Question $3$

Currently, what is the profit flow per day resulting from patients who enter the hospital through the ED on either observation or admitted status?

If an observation unit of your recommended size $($question $2)$ is built, then most of the observation patients could be kept there $($except for days with very high variability about the mean arrival rate of patients$).$ Observation beds are less costly to construct and staff than inpatient beds due to differing code requirements and patient characteristics. In addition, in Certificate of Need states, increasing licensed

inpatient bed capacity incurs additional administrative hurdles relative to increasing observation bed capacity. Assume that if an observation unit is available, the average profit per observation patient will be $$3,700($Figure $2).$

Question $4$

What is the profit increase to the hospital, $($the difference between the new day and old profit per day$)$ if the observation unit is built? What is the profit boost per year?

The answer to question $4$ may underestimate the value of the observation unit, because in addition to reducing the cost for $20$ percent of the ED patients going on observation status, the construction of an observation unit removes these patients from inpatient beds. These now$-$empty beds can be backfilled with new patients.

Question $5$

Assume that all vacated beds are backfilled by admitted patients. How many new patients per day can be admitted? Assume that all of these new patients come in on admitted status and stay an average of $5\mathrm{.}8$ days. $($Hint: Use Little$$s Law, I $=$ RT$,$ where you know I and T from the above information$)$

Question $6$

There is a critical assumption front and center in question $5.$ What is it$?$ How would you check on whether that assumption is justified at Middletown General?

Question $7$

If your calculations in question $5$ are accurate, and each patient in the new flow of patients represents $$3,500$ in profits to the hospital, what is the total benefit to the hospital for having the observation unit $($including cost reductions and backfill patients$)?$

The answer to question $7$ should be compared with the construction and equipment costs to get the observation unit built and operational. Typically these costs are one$-$time up$-$front costs, and then the changed cash flows $($that you computed$)$ occur every day after the unit is operational. Standard financial

metrics $($e$.$g$.,$ net present value, payback period, internal rate of return$)$ can be computed from these data.