Clinic capacity maths: worked out examples

The interviewer shares Exhibit 1: the current schedule and proposed extra hours. It supplies the staffing, appointment and attendance inputs for your first calculation.

Assume appointments are comparable, every available slot can initially be booked and no other required resource limits delivery. The available-time share and resulting slot counts are planning averages across comparable weeks; appointment time can be scheduled across those weeks.

The manager wants to know how many extra completed appointments the proposal creates.

Booking fill is initially 100%. Calculate the expected increase in completed visits before reading the solution; later information will change the booking assumption.

Two clinicians provide 2 × 35 = 70 scheduled hours weekly. At 80% productive time, that becomes 56 appointment hours.

Thirty minutes is 0.5 hours, so 56 ÷ 0.5 = 112 available slots. With every slot booked and 90% attendance, expected completed visits are 112 × 90% = 100.8 per week.

The fractional result represents an average across comparable weeks. It is not a proposal to schedule part of a patient. Individual weeks contain whole visits and will vary.

Do not apply attendance to the hours and again to the slots. That would count the same missed visit twice. And if the prompt supplied observed completed visits instead of scheduled capacity, you would need to understand what adjustments were already included before applying them again.

The proposed increase adds 2 × 4 = 8 scheduled hours per week. After the same productivity adjustment, there are 6.4 appointment hours, creating 12.8 additional slots.

At 90% attendance, the added expected completed volume is:

12.8 × 90% = 11.52 visits per week.

You can check through the full new schedule. Two clinicians working 39 scheduled hours each produce 2 × 39 × 80% ÷ 0.5 = 124.8 slots. Expected completions are 124.8 × 90% = 112.32, compared with 100.8 previously. The difference is again 11.52.

An upper bound is also useful: eight hours can create at most 16 half-hour visits before either adjustment. An answer above 16 needs correction.

To judge the effect on the queue, ask for new demand and the existing waiting list. The manager adds two figures: patients need 110 completed appointments each week, including any required repeats, and the backlog is equivalent to 100 completed visits. Hold those figures constant for this planning calculation.

Current expected capacity is 100.8, so the backlog grows by 9.2 visits per week. The new expected capacity is 112.32, leaving only 2.32 visits weekly to reduce the existing backlog after serving new demand.

Clearing 100 visits at that net rate takes 100 ÷ 2.32 = about 43 weeks on this average-flow model.

Dividing the backlog by the 11.52 additional visits would give about nine weeks, but it would ignore the ongoing shortfall that the extra capacity must cover first.

The shift stops average queue growth, yet clears the backlog slowly. Keep available capacity, ongoing demand and the existing waiting list separate, including attendance and rebooking in the service model.

Suppose an operational improvement raises attendance to 95% while clinical appointment requirements remain unchanged.

With the original 112 slots, completions rise to 106.4 weekly. That helps, but still falls short of 110 demand by 3.6 visits.

With the added hours and 124.8 slots, 95% attendance gives 118.56 completed visits, leaving 8.56 weekly for backlog reduction. The same 100-visit backlog would take about 12 weeks to clear on average.

The calculated comparison below brings together the original attendance assumption and the hypothetical 95% attendance case. It shows the effect of each lever separately and in combination:

The 95% attendance is a scenario to validate, not a guaranteed outcome. The table tells you what improvement would be valuable enough to investigate.

For a separate booking check, return to 90% attendance and keep the extra hours. The earlier calculation assumed every slot was booked. If booking fill is only 90% across the new schedule, completed visits become 124.8 × 90% fill × 90% attendance = 101.088 weekly. That does not meet the 110 weekly demand.

To serve 110 at 90% attendance, the new schedule needs a booking-fill rate of 110 ÷ (124.8 × 90%) = about 98%. Enough aggregate demand does not guarantee that patients can attend the offered slots or that every appointment type has the right staff and facilities.

Check demand for the specific added sessions before treating nominal slots as delivered activity. Timing and type of need determine whether patients can use them.

For the recommendation below, return to the extra-hours case with 100% booking fill and 90% attendance. The other scenarios identify what needs testing before committing.

A useful answer is:

“The extra hours add about 11.5 expected completed visits weekly. That covers the current average shortfall but leaves only 2.3 visits a week to clear the backlog, so recovery would take roughly 43 weeks. I would check whether the new sessions can be filled and assess attendance improvements alongside the extra hours.”

Try the specialty-clinic capacity drill next. Keep scheduled capacity, completed activity and net backlog reduction separate throughout the explanation.