How Do I Lay Out Outpatient Appointments — Keeping Patient Wait and Doctor Idle Time Both Low?

Editor’s note

In plain speech this is called “the outpatient booking system”, “appointment-interval design” or “doctor calendar planning”. In the academic literature it has a single name: Outpatient Appointment Scheduling Problem (OAP). Inside it sit three linked sub-decisions — slot duration design, slot loading (overbooking) and intra-day assignment. If you walk into a vendor meeting without separating these three layers, you cannot test which decision layer the module being sold actually optimises — visualising a slot template is one thing, solving a stochastic OAP MIP for slot design is another.

Distinguish this from other healthcare OR problems. Operating-room scheduling (#008) is the inpatient surgery problem — operating room, surgical team, duration estimation. Patient flow + bed management (#038) decides which ward an admitted patient goes to, bed readiness, discharge timing. Outpatient appointment scheduling (#055) is wholly ambulatory — the patient arrives, is seen, leaves; never admitted. The decision is slot duration + overbooking rate + slot-loading priority. Software that conflates the three serves each with a half solution.

Most-skipped point in the sector: failure to model no-shows. In the Turkish outpatient sector the no-show rate fluctuates between 20% and 30% (industry-wide observation). Most clinics accept no-shows as “inevitable” and never overbook; the doctor then sits idle 1-2 hours a day, capacity is wasted. The academic overbooking model shows: with a calibrated no-show probability, certain slots receive two patients at once, mean wait time rises only slightly (3-6 minutes), and doctor idle time drops sharply (30-50%). The second skipped point: lab-result return windows. A patient is seen in the morning and told “come back this afternoon for the blood-test result”; by afternoon the queue is already deranged. If the slot template lacks a “lab-return window”, the second half-day always falls into queueing.

Step-by-step path — for the SMB

Stage 1 — Measure first, plan after. At least 6 months of appointment data: per patient, planned slot time vs actual room-entry time, actual consultation duration, no-show / cancel / late-arrival flag, patient type (new, follow-up, lab return), booking channel (web, call, the national central booking portal). Doctor inventory: weekly working window, leave calendar, specialty, panel-doctor or pooled. Demand pattern: weekday vs weekend, in-month peak days, seasonality (flu season, school start).

Stage 2 — Extract the knowledge capital. Actual consultation-time distribution per doctor and patient type (log-normal fit). No-show probability curve (by patient type and time of day — early morning slots may have high no-show; late afternoon slots may have low). Lab-return time distribution (blood test mean 60 minutes, imaging 90-180 minutes). Doctor idle-time and overtime curve by hour. Correlation between mean wait and patient-satisfaction score.

Stage 3 — Pilot. 8-12 weeks. For a subset (3-5 doctors, or 1 specialty, or 1 location) run the OAP optimisation recommendation alongside the current manual design. The decision stays with the clinic manager; the system only recommends. Success criterion fixed in advance: mean patient wait time -15% minimum, doctor idle time -25% minimum, patient-satisfaction score flat or up.

Stage 4 — Rollout. 9-15 months to full clinic + all specialties + multi-location + national central booking portal integration. SMS reminders and panel-doctor option. Quarterly committee: actual vs planned mean wait, no-show curve refresh, doctor productivity, patient-satisfaction score, capacity decisions (new doctor / specialty / time slot).

Risks — what can go wrong

1. Patient-satisfaction complaints. If the overbooking rate is set too aggressively, wait time goes above 30 minutes; complaints rise, second-visit rates drop. During the pilot, if wait time exceeds the contractual target, overbooking must be lowered; “productivity” cannot be optimised alone.
2. Insurance-contract duration constraint. Private-health-insurance contracts include quality targets such as mean wait < 20 minutes; missing this metric brings payment deductions. In the OAP model this metric must appear as a constraint, not a soft objective.
3. Shifting no-show model. Seasonal flu, pandemic, weather shift the no-show rate abruptly; a template optimised for a static no-show rate collapses in a crisis. Stochastic / scenario-based modelling and monthly recalibration are essential.
4. Lab-return window not modelled. If the slot template lacks a “lab-return window”, patients walk in spontaneously in the afternoon; the doctor always runs late after lunch. The slot template must include it.
5. Single-supplier booking-system lock-in. Without a contract clause exporting appointment history, no-show curve, slot rules and patient-satisfaction data in a standard format, leaving the system costs the clinic its operational memory. Data export must be a standard contract clause.

Solution method — a technical view

Objective function choice:

• Objective 1 — Minimise patient wait time: When the contractual quality target is the priority.
• Objective 2 — Minimise weighted doctor idle time + overtime spillover: Operational-efficiency oriented.
• Objective 3 — Minimise weighted wait + idle: Classical Bailey objective, balanced.
• Objective 4 — Maximise daily throughput: For capacity analysis / new-doctor decisions.
• Objective 5 — Maximise composite patient-satisfaction + productivity: Multi-objective, closest to reality.

Multi-objective: weighted sum or hierarchical (first wait-time constraint, then productivity).

Academic sources

Listed in the page frontmatter under sources.