APPOINTMENT SCHEDULING WITH OVERBOOKING TO MITIGATE PRODUCTIVITY LOSS FROM NO-SHOWS Linda R. LaGanga & Stephen R. Lawrence Mental Health Center of Denver Leeds School of Business, UCB 419 4141 East Dickenson Place University of Colorado at Boulder Denver, CO 80222 Boulder, CO 80309-0419 (303) 504-6665 (303) 492-4351 [email protected][email protected]ABSTRACT The challenge of balancing the interests of patients with those of healthcare providers is increased when patients fail to show up for scheduled appointments. Overbooking appointments mitigates the lost productivity caused by no-shows but increases patient wait time and provider overtime. In this paper, simulation analysis is used to develop and test the performance of scheduling rules that are designed specifically to accommodate excess overbooked appointments. Our analysis provides new insights into rules that perform well to increase provider productivity while balancing the increased waiting time and overtime costs of overbooked schedules. Keywords: Appointment Scheduling, No-shows, Overbooking, Service Operations, Simulation INTRODUCTION When patients fail to show up for their scheduled appointments, provider productivity and effective clinic capacity are reduced (Cayirli & Veral, 2003). To mitigate this loss, health care clinicians have experimented with a number of alternative appointment scheduling policies. Some clinics overbook appointments by double-booking patients into common appointment times and relying on no-shows to allow the schedule to catch up (Chung, 2002). Others have experimented with “wave scheduling” policies that build extra appointments into a schedule to boost provider productivity and that leave other appointment slots empty (Silver, 1975; Schroer 1
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APPOINTMENT SCHEDULING WITH OVERBOOKING TO MITIGATE PRODUCTIVITY LOSS FROM NO-SHOWS
Linda R. LaGanga & Stephen R. Lawrence
Mental Health Center of Denver Leeds School of Business, UCB 419 4141 East Dickenson Place University of Colorado at Boulder Denver, CO 80222 Boulder, CO 80309-0419 (303) 504-6665 (303) 492-4351 [email protected][email protected]
ABSTRACT
The challenge of balancing the interests of patients with those of healthcare providers is
increased when patients fail to show up for scheduled appointments. Overbooking appointments
mitigates the lost productivity caused by no-shows but increases patient wait time and provider
overtime. In this paper, simulation analysis is used to develop and test the performance of
scheduling rules that are designed specifically to accommodate excess overbooked appointments.
Our analysis provides new insights into rules that perform well to increase provider productivity
while balancing the increased waiting time and overtime costs of overbooked schedules.
Keywords: Appointment Scheduling, No-shows, Overbooking, Service Operations, Simulation
INTRODUCTION
When patients fail to show up for their scheduled appointments, provider productivity and
effective clinic capacity are reduced (Cayirli & Veral, 2003). To mitigate this loss, health care
clinicians have experimented with a number of alternative appointment scheduling policies.
Some clinics overbook appointments by double-booking patients into common appointment
times and relying on no-shows to allow the schedule to catch up (Chung, 2002). Others have
experimented with “wave scheduling” policies that build extra appointments into a schedule to
boost provider productivity and that leave other appointment slots empty (Silver, 1975; Schroer
Figure 6 about here. -------------------------------
Focusing on the scheduling rules on or near the efficient frontier in Figure 6 for the three
additional levels of service time variation tested, for cs = {0.25, 0.50, 0.75}, reveals that the
pattern of points on the efficient frontier remains unchanged with changes in service time
variation, and the magnitude of maximum patient wait time and provider overtime increase with
increased service time variability. Therefore, we conclude that service time variability has little
impact on the efficient frontier and is, therefore, immaterial in comparing the performance of
various scheduling rules; however, it does impact the magnitude of the performance components
─ maximum patient wait time and provider overtime ─ of the scheduling rules.
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SUMMARY AND RECOMMENDATIONS
The simplest practical overbooked schedule, the RNI rule, compresses all inter-appointment
times by the same factor S = show rate, and then places each resulting appointment time on the
nearest practical clock time. Our simulation results show that for the full range of show rates
tested, this schedule is always among the schedules that perform well and should be considered
for implementation because it is not dominated by other policies.
In contrast, we would not recommend scheduling policies with very tight uniform
compression at any show rate because they allow no catch-up time, and large accumulations of
patient wait time occur, even with stochastic no-shows. In particular, the RDI scheduling rule
results in high patient wait times for all show rates S; this would never be acceptable to patients
or their payers and advocates, especially with the existence of alternative schedules that result in
much less wait time. Similarly, schedules that use block scheduling of multiple patients at the
same time, especially in large block sizes, are not recommended unless 50.0≤S . Otherwise,
they result in large patient wait time. Breaking large blocks into smaller ones improves
performance.
From our experiments with S = 0.90, we found that patient wait time can be avoided
entirely by scheduling one extra appointment at the end of the clinic session, resulting in an
average of only 18 minutes of overtime. If less overtime is desired, this can be accomplished
with the wave schedule that compresses selected inter-appointment times from D = 20 minutes to
15 minutes to avoid a large accumulation of patient wait time anywhere in the schedule and
results in average maximum patient wait time of about 12 minutes. Hence, we recommend that
these schedules be considered if patients and providers can accept these relatively small impacts
for the benefit of adding capacity so that one extra patient per provider per clinic session (two
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per day if sessions run both morning and afternoon) can be offered access to services and
providers can be more productive.
For schedules under consideration, formal analysis of the benefits and costs can be
evaluated using a net utility U measure as proposed by LaGanga and Lawrence (2007):
( )U MS K N Wπ ω= − − − O (2)
where M is the marginal benefit of servicing an additional patient (other terms defined
previously).
CONCLUSIONS AND FUTURE RESEARCH
Health care providers need to manage their schedules to operate efficiently and to balance patient
needs with productivity concerns. Wave scheduling and block scheduling have been used and
recommended by providers to improve productivity and mitigate operating variation that is
detrimental to schedule performance. In this paper, we have examined the possibility of using
wave scheduling, double booking, block scheduling, and other scheduling rules to reduce lost
productivity caused by the prevalent problem of patient no-shows. We analyzed the operating
characteristics of overbooked schedules and demonstrated the challenges of developing
schedules for overbooked appointments. Scheduling complexity increases exponentially with
the number of overbooked appointments due to the new appointments that must be absorbed into
the schedule and to the increasing number of possible schedules that result. General discrete
scheduling rules were represented as practical clock-time schedules in planning models to
efficiently construct, evaluate, and improve potential schedules prior to conducting long
simulation runs that consume more resources.
Overbooking allows providers to increase their productivity and create additional
capacity to improve patients’ access to services. Our results demonstrate that, in overbooking to
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recover capacity that would be lost to no-shows, both overtime and patient wait time increase
with increased no-show rates and with increased service time variation. Although service time
variability does impact the magnitude of patient wait time and provider overtime, it has little
impact on the set of schedules that perform best. We showed that the selection of the best
schedule for a given show rate depends not only on the scheduling rule and the show rate itself
but also on the relative performance of alternative rules.
Our experiments and analysis show that a simple overbooking policy of compressing
inter-appointment times in proportion to show rates and rounding each calculated time to the
nearest practical clock time generally works at least as well as other scheduling policies,
including double booking, block booking, and wave scheduling. These other scheduling policies
provide overbooking alternatives that might be attractive to clinics that must minimize overtime
operation, but they result in increased wait time for patients. Also, they are more challenging to
design and implement than the simple compressed scheduling rule because the number and
pattern of the extra appointments that must be fit into the schedule varies with the no-show rate
of each clinic. This makes it more difficult for large organizations with multiple clinics to
consistently and effectively manage their scheduling operations across clinics.
There are many opportunities to extend this research by further developing the planning
models, performance measures, and their predictive capabilities under more generalized
conditions. For example, further experiments can be structured to focus on improving schedules
that performed well in this study. On the other hand, when schedule performance is poor, as is
likely for very low show rates because of high overbooking levels, insights about the
performance dynamics of scheduling systems could lead to the development of alternative health
care access systems. Another area of exploration is to vary the level of overbooking. Continued
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public interest in improving health care access and service delivery is likely to lead to further
exploration of the approaches developed in this paper.
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REFERENCES
Bailey, N. T. (1952). A study of queues and appointment systems in hospital out-patient departments, with special reference to waiting-times. Journal of the Royal Statistical Society, Series B, 14(2), 185-199.
Baum, N .H. (2001). Control your scheduling to ensure patient satisfaction. Urology Times, 29(3), 38-43. Barron, W. M. (1980). Failed appointments: Who misses them, why they are missed, and what can be done. Primary Care, 7(4), 563-574. Cayirli, T., & Veral, E. (2003). Outpatient scheduling in health care: A review of literature. Production and Operations Management, 12(4), 519-549. Chesanow, N. (1996). Can’t stay on schedule? Here’s a solution. Medical Economics, 73(21), 174-180. Chung, M. K. (2002). Tuning up your patient schedule. Family Practice Management, 9(1), 41-48. Fetter, R. B., & Thompson, J. D .(1966). Patients’ waiting time and doctors’ idle time in the outpatient setting. Health Services Research, 1(1), 66-90. Fries, B. E., & Marathe, V. P. (1981). Determination of optimal variable-sized multiple-block appointment systems. Operations Research, 29(2), 324-345. Ho, C., & Lau, H. (1992). Minimizing total cost in scheduling outpatient appointments. Management Science, 38(12), 1750-1763. LaGanga, L. R. (2006). An examination of clinical appointment scheduling with no-shows and overbooking. Doctoral dissertation, University of Colorado, Boulder, CO. LaGanga, L. R. & Lawrence, S. R. (2007). Clinic overbooking to improve patient access and increase provider productivity. Decision Sciences, 38(2). Rohleder, T. R., & Klassen, K .J. (2002). Rolling horizon appointment scheduling: A simulation study. Health Care Management Science, 5(3), 201-209. Schroer, B .J., & Smith, H .T. (1977). Effective patient scheduling. The Journal of Family Practice, 5(3), 407-411. Shonick, W., & Klein, B. W. (1977). An approach to reducing the adverse effects of broken appointments in primary care systems. Medical Care, 15(5), 419-429.
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Silver, M. (1975). Scheduling: Least developed art. Family Practice News, 5(23), 34. Vissers, J., & Wijngaard, J. (1979). The outpatient appointment system: Design of a simulation study. European Journal of Operational Research, 3(6), 459-463. Welch, J. D., & Bailey, N. T. (1952). Appointment systems in hospital outpatient departments. The Lancet, May 31, 1105-1108.
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TABLES
Table 1: Scheduling Rules. Scheduling Rule Name Abb. Description
1 Compressed Appointment Interval CAI The time interval between appointments is compressed from D to
T=DS.
2 Round to Nearest Interval RNI Compressed appointment times are rounded up or down to the nearest practical clock time.
3 Round Down Interval RDI Time intervals are compressed by rounding T down to the nearest multiple of 5 minutes that is less than D.
4 Multiple Appointments in First-block MAS Schedule all K–N overbooked appointments in the first (starting)
schedule block.
5 Multiple Appointments in Multiple-blocks MAM Schedule all K–N multiple appointments in multiple blocks
6 Multiple Appointments in Last-block MAL Schedule all K–N extra appointments in last normal schedule
block.
7 Multiple Appointments in Early-blocks MAE Spread the K–N extra appointments into slots earlier than the last
slot.
8 Multiple Appointments at Finish MAF Schedule all K–N extra appointments after the last block in clinic
session.
9 Multiple Appointments Distributed-evenly MAD Spread the K–N extra appointments evenly across the clinic
session.
10 Wave Schedule 1 WAV1 Schedule blocks of 3 in the first and last appointment slot, individual appointments in other slots.
Table 3: Appointment times adjusted for overbooking. Wait time and overtime are calculated for the case in which every scheduled patient shows up; S = 0.90; D = 20 minutes.
Baseline: Calculated Calculated CompressNo Overbooking T = S D Adjusted to 15 min
8:00 AM 8:00 AM 8:00 AM 8:00 AM8:20 AM 8:18 AM 8:20 AM 8:15 AM8:40 AM 8:36 AM 8:40 AM 8:30 AM9:00 AM 8:54 AM 8:50 AM 8:45 AM9:20 AM 9:12 AM 9:10 AM 9:00 AM9:40 AM 9:30 AM 9:30 AM 9:15 AM
10:00 AM 9:48 AM 9:50 AM 9:30 AM10:20 AM 10:06 AM 10:10 AM 9:45 AM10:40 AM 10:24 AM 10:20 AM 10:00 AM11:00 AM 10:42 AM 10:40 AM 10:15 AM11:20 AM 11:00 AM 11:00 AM 10:30 AM11:40 AM 11:18 AM 11:20 AM 10:45 AM
Table 5: Probabilities that patients show up for varying show rate S, K total appointments scheduled, and number of patients scheduled at the same appointment time (block size).
Probabilitythat all
K scheduledpatients Probability that more than one patient shows up when block size is: