Which Patient to Which Ward and Bed, and When to Trigger Discharge?

Editor’s note

This problem is known in everyday hospital language as “bed occupancy”, “ward placement”, or “discharge triggering”. In academic literature it carries two coupled names: Patient Flow for the patient-movement chain and Bed Allocation for the assignment decision. Hulshof et al. (2012) structurally survey OR/MS planning in healthcare, separating offline decisions (weekly / monthly capacity plan) from online decisions (intraday assignment). If both layers are not considered together, the capacity plan looks balanced on paper while the intraday assignment turns into a crisis every morning.

This problem differs from operating-room scheduling (Problem 8). #008 is about which surgical case at what time goes to which OR (case sequencing, room utilisation, team rotation). #038 is about which patient is admitted to which ward and bed and when discharge is triggered (flow chain, capacity balance, off-service placement). The two problems feed each other: when an OR-exit patient waits for a ward bed, #008 hits OR-exit blockage; when wards cannot trigger discharges, #038 hits a capacity crisis.

The most-skipped point in the sector: discharge forecasting. Most hospitals decide on discharge during morning rounds, with paperwork finished by midday or afternoon. The morning wave of ER admissions, however, lands between 06:00 and 10:00 — beds are not ready in that window. Hulshof et al. (2012) explicitly separate online (intraday) and offline (weekly) decisions; if discharge forecasting is run 24-48 hours ahead (using length of stay, diagnosis, lab trend, clinical state), morning bed readiness becomes operationally achievable. The second most-skipped point: the cost of off-service placement. When an internal-medicine patient is placed in a cardiology bed, the nursing team’s specialty does not match and length of stay grows by 0.5-2 days; this cost must be represented as a penalty weight in the MIP objective (Bachouch et al. 2012).

Step-by-step — for the SMB

Stage 1 — Measure first, then plan. At least 12 months of admission data: per admission, admission time, discharge time, source (ER / elective / referral), assigned ward, primary clinical diagnosis, actual off-service flag. ER triage data: arrival time, triage level, admission decision time, transfer-to-ward time (ED boarding). Ward inventory: per ward bed count, room type, isolation capacity, nurse-to-patient ratio. Clinical compatibility matrix: which diagnosis is primary, acceptable, or unsuitable in each ward.

Stage 2 — Extract the planning knowledge. Length-of-stay distribution per patient type / ward. Which diagnoses typically admit to which ward. Which wards feed each other (intensive-care step-down chain). Seasonal and weekly demand patterns (ER hourly distribution, Monday elective peak).

Stage 3 — Pilot. 12-16 weeks. For a sub-set (e.g. an internal-medicine block of 3-5 wards) run the bed-assignment MIP recommendation in parallel with manual placement. The decision still rests with the bed coordinator; the MIP gives advice. Success criteria set up front: ED boarding -10% minimum, off-service placement -15%.

Stage 4 — Roll out. Over 9-18 months extend to all wards plus intensive-care step-down plus elective reservations. ER-triage-triggered real-time assignment. Quarterly hospital committee: length-of-stay drift, off-service rate, ED boarding report, bed-utilisation balance.

Risks — what can go wrong

1. Discharge forecast is mis-calibrated. Without a mechanical forecast generated before morning rounds, bed readiness turns into a daily crisis. The forecast model must run 24-48 hours ahead (using admission day, lab trend, clinical state).
2. No pandemic / seasonal-surge plan. Anomalies like a winter flu wave or pandemic break the bed-pool balance; for these scenarios a surge-bed trigger rule and a simulation-based capacity plan are essential.
3. Off-service placement quietly loads cost. Placing an internal patient in a surgical bed clears a slot in the short term but adds 1-2 days of stay; the objective must carry a calibrated penalty weight.
4. Single-supplier lock-in. If the contract does not include ‘annual export of admission history, discharge-forecast data, off-service records in a standard format’, exiting the system means losing the hospital’s operational memory.

Solution method — technical view

Objective function options:

• Objective 1 — Minimum ED boarding time: Prevents ER congestion.
• Objective 2 — Minimum weighted off-service penalty: Preserves clinical compatibility.
• Objective 3 — Bed-utilisation balance: Even occupancy across wards.
• Objective 4 — Minimum elective cancellations: Protects trust of scheduled patients.

Multi-objective: weighted sum or hierarchical (first clinical compatibility, then ED boarding, then balance).

Academic sources

Listed in the page frontmatter under sources.