1. Outpatient Clinical Scheduling
Research Team
Mark Lawley, Principal Investigator
Kumar Muthuraman, University of Texas
Laura Sands, Purdue School of Nursing
DeDe Willis, MD, Indiana University School of Medicine
Ayten Turkcan, Research Scientist, Purdue
Po-Ching DeLaurentis, Research Assistant, Purdue
Rebeca Sandino, Research Assistant, Purdue
Ji Lin, Research Assistant, Purdue
Santanu Chakraborty, Research Assistant, Purdue
Joanne Daggy, Research Assistant, Purdue
Bo Zeng, Post-doc, Purdue
Funding: National Science Foundation, $460K, Regenstrief Foundation $395K

2. Partnering Clinics Wishard Health Services
Cottage Corner Health Center (low income)
North Arlington Health Center (low income)
Community Physicians of Indiana
Giest Family Medicine and Pediatrics (mid. class)

3. Project thrust Study and improve internal clinic operations
Develop new scheduling theory that accounts for environmental complexities
Sequential scheduling
Patient no-show
General service time distributions
Implement in real systems and validate impact

4. Outpatient Clinical Scheduling
In the US, almost 90% of patient care provided in the approx. 200,000 non-psychiatric outpatient clinics
Pressures for improving clinic operations
Aging population
Increased chronic disease
Hospitals to reduce LOS
Improved patient service
Access
Outcomes
Satisfaction
Revenue / Reimbursement
New modes of care

5. Why is out-patient scheduling complex?
Emphasis on patient satisfaction (low waiting time)
Emphasis on staff and physician utilization (low idle time)
High patient no-show, cancellation, walk-in
Tardy arrivals (patients and physicians)
Stochastic, patient dependent service times
Sequential schedule construction
On-call physicians
Physician constraints
Many others …

6. Patient no-show Ubiquitous problem in clinical operations
Can be 40-50% for some types of clinics
Approximately 20% for our partners
Can be modeled and used in scheduling
No show prob. can be estimated using
patient history, diagnosis, demographics, medications
lead time to appointment,
exogonous factors such as weather, public transp.
A patient’s no show probability should not be used to predict whether a given patient will arrive
The no show probability of a group of patients should be used to evaluate the no-show characteristics of a given schedule

7. Sequential Scheduling Process
Patient calls clinic for appointment with physician
Scheduler looks at the current schedule, negotiates with patient, adds the patient to a “slot” (we would add estimate no-show prob.)
Couple of days in advance, clinic might call to remind the patient
Patient is expected to, but might not, arrive at appointed time.
Schedules are built incrementally, patient by patient.
Information used is current schedule (plus no-show prob.)
No opportunity to “optimally” schedule final set of patients.
How can we create good sequential schedule that takes patient no-show into account?

8. Slot Model I slots in a consultation day
J patient types, pj probability of patient no-show
Xi denotes the number of patients arriving at beginning of slot i
Yi number of patients overflowing out of slot i
Li number of patients served in slot i, initially assumed Poisson
R(Sn) overflow probability matrix
Q(Sn) arrival probability matrix

9. Slot Model Objective max E[ r i Xi - c i Yi - C YI ]

10. Myopic scheduling algorithm

11. Unimodal Profit Function

12. Unimodal Schedule Evolution

13. Charles Joseph Minard (1781 – 1870), a French civil engineer noted for his inventions in the field of information graphics.

14. General Service Times
Overflow implies patient in service overflowing from one slot to next.
Must include time in service in previous slot
Distribution of Li takes more general form that requires numerical integration

15. Unimodularity continues to hold

16. Non-myopic approaches for sequential scheduling
Optimal Sequential Schedule: Dynamic Programming
Add simple forecasting to the previous assignment algorithm

17. Improvement over myopic up to 12% Small System with 4 slots and 2 patient types

18. Next Steps
Continue clinic process mapping, operational data collection, simulation – seeking opportunities to improve
Make suggestions to improve clinic operational efficiency, help implement
Continue no-show modeling efforts
Continue developing sequential patient scheduling theory and algorithms
Begin working with scheduling software vendors

19. Submitted and Working papers
Publications
Muthuraman, K., Lawley, M. A stochastic overbooking model for outpatient clinical scheduling with no-shows. To appear in IIE Transactions Special Issue on Healthcare
Submitted and Working papers
Chakraborty, S., Muthuraman, K., Lawley, M. Sequential clinical scheduling with general service times and no-show patients, Operations Research.
Zeng, B., Turkcan, A., Lin, J., Lawley, M., Clinic scheduling models with overbooking for patients with heterogeneous no-show probabilities, Annals of Operations Research.
Turkcan, A., Zeng, Muthuraman, K., Lawley, M., Sequential clinical scheduling with moment-based constraints, in preparation.
Daggy, J., Sands, L., Lawley, M., Willis, D. The impact of no-show probability estimation on clinic schedules, in preparation.
Lin, J., Muthuraman, K., Lawley, M. An Approximate Dynamic Programming Approach to Sequential Clinical Scheduling, in preparation. 19

20. Any doubts?