I book 30-minute appointments but patients wait half an hour past their slot. I've lost 4 patients this quarter and I don't know why.

The situation

Dr. Kim runs a two-chair dental practice. She books every appointment at 30 minutes because that's what the practice management software defaults to. But cleanings actually run anywhere from 18 to 42 minutes depending on the patient — and when one appointment runs long, every subsequent appointment that day is delayed. By 3pm, the schedule is 45 minutes behind.

The analysis

It's not overbooking — it's treating a 40-minute new-patient visit the same as a 22-minute recall.

The problem is not that she's overbooked. It's that she's treating all appointments as identical when they're not. New patients routinely take 35–45 minutes. Routine recall patients average 22 minutes. When new patients and recall patients are intermixed in the same schedule column, a single long appointment cascades into a full-afternoon delay.

The Process Map models the schedule as a queue where each appointment's service time is drawn from one of two distributions (new patient: normal(40, 6); recall: normal(22, 4)) in proportions matching her actual booking mix (roughly 30% new, 70% recall). With a flat 30-minute booking policy, the simulation shows that by the 8th appointment, expected delay has accumulated to 22 minutes — matching the complaint exactly.

The fix is not longer slots across the board. It's type-based booking: new patients booked in dedicated slots at the start of each half-day (when delay hasn't accumulated), recall patients filling the remainder. With this policy, simulated end-of-day delay drops from 45 minutes to under 7 minutes.

The decision

Dr. Kim restructures her booking template: 2 new-patient slots per half-day at 8am and 1pm, recall patients filling the rest. She saves both visit-time distributions to her library and turns on Monitoring against her practice management system's daily export. Months later, Monitoring flags that new-patient visits have drifted longer — she's started taking more cosmetic consultations, which run closer to 55 minutes than 40. She re-fits and opens a third new-patient slot before delays creep back.