The math, shown in full

Supervision comes in whole physicians

A room supervised at a ratio of 1:r uses 1/r of one physician’s capacity. A room run by an anesthesiologist working alone uses all of it. In every stretch of the day, the physicians needed is the total capacity rounded up:

physicians required = ⌈ Σ 1 / ratio of each live room ⌉

That rounding is the cliff. At 1:4, four rooms need one supervising physician; the fifth needs a second, who arrives with room for three more. Keelwright adds capacity in exact whole units (one physician = 2,520 units, divisible by every ratio from 1 to 10), so three rooms at 1:3 are exactly one physician, never 1.0000001.

Every room at a rooftop shares its physicians, whatever its type. So the planner’s cliff starts from the rooftop’s other rooms, counted at their busiest. Two endoscopy rooms at 1:4 already use half a physician, which brings the next general OR threshold forward.

physicians with n rooms of one type = ⌈ other rooms at their busiest + n × 1 / ratio ⌉6 general OR + 2 endoscopy at 1:4:  ⌈ 0.5 + 6 × 0.25 ⌉ = 2, with no room to sparethe 7th general OR room:            ⌈ 0.5 + 7 × 0.25 ⌉ = 3

That assumes the added rooms run while the other rooms are at their busiest. Where they don’t, the next threshold can come later than the chart shows, never sooner.

Every stretch of the day is costed separately

Rooms and people run different hours, so Keelwright never multiplies one daily room count by a rate. It cuts the day wherever any room or shift block starts or ends, and costs each slice on its own.

loaded hourly rate = annual pay ÷ paid hours per FTE × (1 + benefits load)cost of a shift block = assigned hours × loaded rate+ minutes past the assigned block × loaded rate × premium multiplier

Money is kept in whole cents per line and added up, so totals reproduce to the cent. On the home page, a late-hours premium applies to every staff-hour after a time you choose. In the planner, the premium applies to minutes someone works past their own assigned block, with a multiplier per role. It can be zero for salaried staff who aren’t paid extra.

Three ways to staff the same rooms

• Care team (MD + CRNA): ⌈rooms ÷ ratio⌉ supervising physicians plus one CRNA per room.
• MD-only: an anesthesiologist working alone in every room.
• Lowest-cost mix: for each slice, the cheapest combination of supervised rooms and rooms with a physician working alone. It is an arithmetic floor, not a staffing recommendation.

Past a cliff, the j rooms beyond the last full team can be covered by one more supervisor plus j CRNAs, or by j physicians working alone. Working alone costs less exactly when:

j × physician rate  <  physician rate + j × CRNA rate

With a physician costing exactly twice a CRNA, that’s only the first room past each cliff, with a tie at the second. With physicians costing less than twice a CRNA it can be more rooms. Keelwright compares the two in exact arithmetic and says which, in words.

A worked example you can check by hand

Rooms run 6:30a–2:30p (8 hours) at 1:4. Physician $250/h and CRNA $125/h, loaded.

4 rooms: 1 physician + 4 CRNAs = (250 + 500) × 8 =  $6,000 a day5 rooms: 2 physicians + 5 CRNAs = (500 + 625) × 8 =  $9,000 a daythe fifth room adds $3,000 a day; the fourth added $1,000.

Over 250 operating days, that’s $750,000 a year for the fifth room against $250,000 for the fourth. Covering the fifth room with an anesthesiologist working alone instead would cost $2,000 a day, $1,000 less than a new supervision team.

The planner

The planner adds what a real day has: several rooftops sharing one pool of people, rooms of different types and ratios, shift blocks that don’t line up with rooms, and people who were on call last night.

• Coverage gap: any stretch where the physicians present supply less capacity than the live rooms need, or a supervised room without its CRNA or resident. Gaps are reported as missing capacity (“2:30–3:00p needs 0.25 more physician”), never as blame.
• Unused supervision capacity: physician time present beyond what the rooms need, valued at the regular rate.
• Guaranteed floor: everyone in the pool, minus anyone on call who may have worked past midnight and is out until the post-call time you set.
• Optimizer: for each gap it considers extending an adjacent block (at the premium) or adding someone available from the pool (for at least the shortest added block you set). Lowest cost picks the cheapest; fullest coverage prefers adding people over keeping anyone past their block. Ending a room early is shown as a $0 alternative and never applied, because it’s a scheduling decision. The tool proposes; you decide.
• Call pay: per role, either included in base pay (or not paid by the group) or a stipend per call shift, by weekday or weekend, with optional call-back pay for hours worked and a minimum per call-back. Keelwright never fills in a dollar amount.

What’s not included

Sources

Keelwright assumes no payer, CMS or state rule. Every ratio, rate and salary is an input you set, and the samples are illustrative placeholders, not benchmarks. When a rule is confirmed for use here, its source will be cited on this page.

Glossary

Supervision

One physician responsible for several rooms, in the plain operational sense. Not a billing category.

Max supervision ratio (1:r)

The most rooms one supervising physician may cover. Your number.

Threshold (cliff)

The room that needs another supervising physician: rooms 5, 9, 13 at 1:4 when they’re the only rooms. The planner counts the rooftop’s other rooms too.

Time slice

A stretch of the day in which the live rooms, the people present and the premium don’t change.

Rooftop

Any location where your group staffs anesthesia.

Paid hours per FTE

The divisor that turns annual pay into an hourly cost. Use hours actually worked to fold paid time off into the rate.

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