Six-bed short-stay unit and the 4-hour target
You are the operations manager of a district emergency department (ED) that sees 180 presentations per day. About 30% are admitted, and the ED currently meets the 4-hour target for 76% of patients. The executive team proposes a six-bed short-stay unit (SSU), open 10:00–22:00, staffed by 1.0 FTE doctor and 2.0 FTE nurses redeployed from the ED. The business case assumes 40% of admitted patients are SSU-eligible, with an average SSU stay of 18 hours. Capital cost is $600,000; annual staffing cost is $1.1 million. The hospital has six physical beds available but no extra medical staff. The ED's 4-hour target is 90%, and the board meets on Thursday.
1. Calculate the daily number of admitted patients, the number eligible for the SSU, and the maximum daily throughput of six SSU beds at an 18-hour average stay. What does this imply?
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Admissions: 180 × 0.30 = 54 per day. SSU-eligible: 54 × 0.40 = 21.6 per day, say 21–22. Bed capacity: six beds × 24 hours ÷ 18-hour average stay = 8 patients per day.
Implication: the unit can handle only about 8 of the 21–22 eligible patients per day-about 37%. It cannot deliver the assumed 40% diversion. The 10:00–22:00 opening does not fix this: beds remain occupied for 18 hours, so throughput is limited by length of stay. At best, eight diversions per day is 8/54 = 14.8% of admissions, before accounting for the doctor redeployed out of the ED. The claimed 90% target is not supported by the arithmetic.
2. The proposal claims the SSU will lift the 4-hour target to 90%. Identify three assumptions and the data you would request.
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Assumptions to test:
- Eligibility and length of stay: 40% eligible and 18 hours are optimistic; if the average stay is 24 hours, capacity falls to six per day.
- Staffing neutrality: redeploying 1.0 doctor and 2.0 nurses from the ED may reduce ED capacity, offsetting any SSU benefit.
- Flow effect: the SSU must free ED beds and clinician time; if admitted patients board in the ED until an SSU bed is free, the target may not improve.
Data needed: arrivals and admissions by hour; ED boarding time; SSU exclusion criteria; actual length-of-stay distribution; discharge timing; staffing rosters; readmission and cost per patient; baseline breach reasons. Ask for a sensitivity analysis, not a single point estimate.
3. Recommend a decision for the board, with at least one condition.
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Recommend a conditional pilot, not a full rollout. Start with three beds or a 12-hour operation and a narrower eligibility rule-for example, expected stay under 12 hours-with the doctor funded additionally rather than redeployed. Predefine measures: ED 4-hour breach rate, boarding time, SSU occupancy, unplanned readmissions and staff hours. Set a decision rule: continue only if the SSU achieves at least eight diversions per day without reducing ED staffing and improves the 4-hour target by a pre-specified margin. The board should reject the 90% claim as unsupported. The binding constraint is bed-hours, not physical beds.