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

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)

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

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

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 …

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

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?

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

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

Myopic scheduling algorithm

Unimodal Profit Function

Unimodal Schedule Evolution

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

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

Unimodularity continues to hold

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

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

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

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

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