Halvering Valley Hospital: Operations Case Study with Answer

Patients walk out when they wait too long, and they wait when demand at some step in the patient flow exceeds that step's capacity. So I would map the flow (triage, room, provider, tests, disposition), measure demand and capacity at each step by hour of day, and find the bottleneck. Only then would I compare fixes on cost, size of impact and speed.

Before any data, I would hold four hypotheses: more patients are arriving, the ED has fewer staff, each patient takes longer somewhere in the flow, or something outside the ED (such as full inpatient beds) is holding ED resources.

• Demand: arrivals per hour by time of day, acuity mix, admit rate, trend vs 2024.
• Capacity by step: triage nurses, providers, treatment rooms, CT and lab; each as units x patients per unit per hour.
• Time per patient at each step, split by discharged vs admitted patients, including boarding.
• Bottleneck: the step with the highest utilization at the peak hours, not on the daily average.
• Fixes: cost, one-time investment, impact on walkouts and revenue, time to impact, and risks such as patient safety.

What the interviewer is looking for

• Good: a demand vs capacity structure built around the ED patient flow, not a generic revenue and cost tree.
• Strong: insists on looking at the peak hours rather than the daily average, and lists boarding or inpatient beds as a possible cause outside the ED.
• Excellent: frames the goal as finding the single binding constraint, since adding capacity anywhere else does not reduce waits.

Push-back: The ED director is sure the answer is more doctors. Why not just test that first?

Daily arrivals grew from 140 to 150, only 7%. Walkouts went from about 2.8 a day (2% of 140) to about 12.1 a day (8.1% of 150), more than four times as many. Demand growth alone cannot explain that, so capacity must have fallen or each patient must be taking longer.

The walkouts are concentrated at the peak: the noon to 8 p.m. block, where 8 patients arrive per hour, produces about 8.3 walkouts a day, or 69% of the total. Overnight, at 3.5 arrivals per hour, almost nobody leaves. This is a peak-hour capacity problem.

What the interviewer is looking for

• Good: computes daily arrivals and notices visits grew far less than walkouts.
• Strong: converts rates into walkouts per day by block and shows most of them happen noon to 8 p.m.
• Excellent: concludes that volume is not the story and that the next question is what reduced effective capacity at the peak.

Push-back: Visits are up 7%. Isn't a 7% busier ED enough to tip it over the edge?

The average patient now occupies a room for 4.3 hours, up from 3.32 hours (0.8 x 3.0 + 0.2 x 9.5 vs 0.8 x 2.9 + 0.2 x 5.0). Of that 0.98-hour rise, 0.9 hours, about 92%, comes from boarding: admitted patients now wait 6.0 hours for an inpatient bed instead of 1.5. Care itself has barely changed.

Total demand for rooms rose from about 465 to 645 room hours a day. Only about 33 of the extra 180 hours come from more visits; about 147 come from longer room time. Boarders alone now use 180 room hours a day, a quarter of the ED's 720 available room hours. The cause sits upstairs: inpatient occupancy hit 96% and most inpatients are discharged after 3 p.m., exactly when the ED peaks.

What the interviewer is looking for

• Good: computes the weighted average room time for both years and sees boarding jump from 1.5 to 6.0 hours.
• Strong: splits the rise in room demand into volume and time per patient, and shows time per patient explains about 80% of it.
• Excellent: links boarding to the 96% inpatient occupancy and afternoon discharges, so the ED's problem is a hospital-wide flow problem.

Push-back: Total room demand is 645 hours against 720 available, under 90%. Why would that cause walkouts?

Triage, providers and CT all run at 80% at the peak. Treatment rooms are the bottleneck: 30 rooms / 4.3 hours handle about 7.0 patients an hour, but 8 arrive, so rooms run at about 115%. Over the eight-hour peak, that leaves about 8.2 patients with no room, almost exactly the 8.3 walkouts a day in that block.

In 2024 the same 30 rooms at 3.32 hours each handled about 9.0 patients an hour against 7.5 arrivals, a peak utilization of 83%. Nothing in the ED shrank; boarding ate the room capacity. The daily average of 90% room utilization hides the problem because the overnight lull absorbs the slack.

What the interviewer is looking for

• Good: computes capacity for each step and identifies treatment rooms as the only step above 100%.
• Strong: compares with 2024 to show the same rooms went from 83% to 115% because room time rose, not because rooms were removed.
• Excellent: ties the unmet peak demand (about 8 patients) to the afternoon walkouts (about 8.3) and explains why the daily average hides the bottleneck.

Push-back: Providers are at 80%. Surely adding providers still shortens waits a bit?

Option 1 does nothing for walkouts. Rooms stay at 115% because providers were never the constraint; it costs $0.8 million a year for no recovered visits.

Option 2 gives 38 rooms / 4.3 hours = 8.8 patients an hour, so peak utilization falls to about 91%. Option 3 cuts average room time to 3.5 hours (0.8 x 3.0 + 0.2 x 5.5), so the existing 30 rooms handle about 8.6 patients an hour, and peak utilization falls to about 93%. Both clear the 95% bar.

Bringing walkouts from about 12.1 to 3.0 a day recovers about 9.1 visits a day, about 3,330 a year, worth about $2.0 million at $600 each. Option 3 nets about $1.1 million a year for $0.2 million up front and works in 4 months. Option 2 nets only about $0.4 million a year, needs $4.0 million up front (a payback of about 10 years) and takes 18 months.

What the interviewer is looking for

• Good: values the recovered visits at about $2.0 million a year and nets off each option's cost.
• Strong: recomputes utilization for each option and shows Option 1 recovers nothing because it adds capacity at a step that is not the bottleneck.
• Excellent: weighs time to impact and up-front cost too: Option 3 is 4 months and $0.2 million, Option 2 is 18 months and $4.0 million for less net value.

Push-back: Recovered patients are 20% admitted, and inpatient beds are already 96% full. Where do they go?

The director is right that the ED cannot deliver Option 3 alone, which is the main risk. The program only works if boarding falls far enough: to keep peak room utilization at 95%, average room time must be about 3.56 hours, which means boarding of about 2.3 hours. If the program only gets boarding to 3.0 hours, peak utilization stays near 99% and walkouts fall only partly.

I would still back it, because it is the only option aimed at the bottleneck and it is cheap to try, but I would manage it as a hospital-wide program, not an ED project.

• Ownership: the COO owns a hospital-wide target of under 2.5 hours average boarding, with inpatient unit leaders measured on noon discharges.
• Leading indicators, weekly: share of discharges before noon, average boarding hours, peak room utilization and walkouts by time block.
• Downstream capacity: earlier discharges free inpatient beds in the afternoon, which is what absorbs the extra admissions from recovered walkouts.
• Interim relief while the program ramps: move patients who are waiting only for results to chairs, freeing rooms for new arrivals.
• Decision gate: if boarding is not below 2.5 hours after 6 months, revisit Option 2, whose $4.0 million cost stays on the table as a fallback.

What the interviewer is looking for

• Good: names execution risk across departments and proposes clear ownership.
• Strong: computes the boarding target the program must hit (about 2.3 hours) and the downside if it lands at 3 hours.
• Excellent: sets a dated decision gate that keeps the room build as a fallback, and adds cheap interim relief so patients are not left waiting during the ramp.

Push-back: Why not do Options 1 and 3 together, just to be safe?

Fund the inpatient flow program, not more doctors or more rooms. Walkouts have quadrupled, from about 3 to 12 a day, while visits grew only 7%. The cause is admitted patients boarding in ED rooms for 6 hours instead of 1.5, because inpatient beds are 96% full and free up only in the afternoon. That pushes the 30 rooms to 115% of capacity at the noon to 8 p.m. peak, while providers sit at 80%.

Cutting boarding to 2 hours brings peak room use to about 93% and should recover about 9 visits a day, worth about $2.0 million a year, for $0.9 million a year and $0.2 million up front, within 4 months. More providers cost $0.8 million a year and recover nothing; 8 new rooms cost $4.0 million and take about 10 years to pay back.

The risk is delivery across departments: boarding has to fall to about 2.3 hours. We track it weekly and revisit the room build if it is not below 2.5 hours in 6 months.

What the interviewer is looking for

• Good: leads with one clear recommendation and names boarding as the cause.
• Strong: backs it with the bottleneck numbers (115% rooms vs 80% providers) and the net value of about $1.1 million a year.
• Excellent: explains why the two intuitive fixes fail and gives a measurable target with a decision gate.

Fund the inpatient flow program (Option 3): it is the only option aimed at the real bottleneck, and it is the fastest and cheapest.

Walkouts rose from about 3 to 12 a day while visits grew only 7%, because admitted patients now board in ED rooms for 6 hours instead of 1.5. Treatment rooms run at 115% of capacity at the noon to 8 p.m. peak; triage, providers and CT run at 80%.

Cutting boarding to 2 hours brings peak room utilization to about 93%, recovering about 9 visits a day worth about $2.0 million a year, a net gain of about $1.1 million a year for $0.2 million up front. Extra providers lose $0.8 million a year; 8 new rooms net only $0.4 million a year on a $4.0 million build.

Next steps: give the COO a hospital-wide target of under 2.5 hours average boarding, track noon discharges and walkouts weekly, and revisit the room build if the target is missed after 6 months.