Abstract
This work analyzes strategies for better allocation of surgeon resources in an elective surgical practice. Among the metrics considered to evaluate the assignment of tasks are OR-to-Clinic ratio per provider, OR-to-Clinic ratio per day, patient access to clinic, and patient access to surgery. In addition, a simulation model is used to evaluate the clinical and surgical capacity of the calendar to identify potential inefficiencies and propose strategic changes to the calendar.
Introduction
The challenge of optimal assignment of human resources is one that is universal across all industries where human capital is a primary resource. In the health care industry this is especially true as people are involved in all aspects of patient care. From the person coordinating appointments, to the medical assistant checking vital signs, the doctor evaluating the patient, the nurse caring for hospital patients; the management decisions related to these resources are critical to a well-running integrated practice. Too few or too many of any of these resources can have negative impacts that could include: wasted resources, long waiting times, and poor quality of care. Health Care organizations are constantly challenged with these questions of resource assignment and how to best deliver quality care in the most efficient/cost effective way possible.
This paper addresses resource assignment in a specialty surgical practice with specific focus on how surgeons are assigned. In a specialty surgical practice, a surgeon can be assigned in one of two ways: clinic or surgery. Clinic time will result in new surgical procedures to be performed; while time assigned to surgery will reduce the number of procedures in the surgeon’s queue, see Figure 1.
Figure 1.
General patient flow for an elective surgical practice.
It is important to maintain a proper balance of clinic and surgery. At a high level, too many patients entering the practice through clinic could result in very long queues for surgery. On the other hand, too much time assigned to surgery results in poor clinic access and under-utilization of operating room (OR) resources. These concepts are true of any surgical practice.
Capacity planning in health care industry is a complex problem which has been analyzed in the literature. For example, queue theory is used in1 to determine the number of clinic appointments needed per day by a specialty clinic. The authors in2 study the planning of operating rooms, they formulate an optimization problem to built a master surgical schedule. In contrast with previous works, this paper focuses on the strategic assignment of both clinic and OR. The surgeon assignment is done in a way to maintain appropriate OR-to-Clinic ratios for the overall practice as well as for each day in the planning horizon. The work presented in3 considers a one-surgeon practice, our work considers time-allocation of multiple surgeons and its effects on patient access. As in 4,5 we use simulation to evaluate the performance of the calendar. The reader is referred to 6,7,8 for a literature review on capacity planning problems in health care.
Materials and Method
This section discusses, in detail, an approach for addressing the surgeon time-allocation problem in an elective surgical practice at Mayo Clinic.
Assignment of Clinical Resources: Individual Calendar Pattern
Individual calendar patterns are the foundation for how surgeon resources are allocated between OR and Clinic. Mayo Clinic uses a 12-week planning horizon to assign clinical resources, surgeon calendars are updated on a rolling monthly basis. This means that calendars are available for clinical and/or surgical services twelve weeks into the future. Surgeons are assigned using a calendar where the days of the week are either blue or orange – in an alternating pattern. There are an equal number of blue and orange days each calendar year. A “blue” surgeon operates on blue days and is in clinic on orange days. This calendar structure creates a natural every-other-day clinic/surgery pattern for surgeons. Table 1 illustrates a two-week pattern for a surgeon. It can be observed that the resulting pattern for surgeon 1 defines a 1:1 OR-to-Clinic ratio.
Table 1.
Two-week calendar pattern – Surgeon with 100% practice time (clinic and surgery).
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Another scenario will illustrate a common calendar pattern for surgeons where non-practice time (A) is included, see Table 2. This time is generally related to research, education, or administration. The goal of the calendar patterns is to maintain a balanced practice for each surgeon where the number of new cases closely matches surgical capacity. For this to occur, the number of clinic days should be in the proper ratio to OR days. Therefore, non-practice time is added into the calendar pattern so that the resulting OR-to-Clinic ratio of the surgeon calendar is adequate. The placement of this time is based on the following criteria:
External requirements, such as, meetings/lab time on specific days
Surgeon clinic/OR flow
General practice clinic/OR flow.
Table 2.
Two-week calendar pattern – Surgeon with 80% practice time.
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Table 2 shows a calendar pattern of a surgeon with 20% non-practice time. The allocation of non-practice days into the calendar of surgeon 4 defines a 5:3 OR-to-Clinic ratio which is appropriate for surgeon 4 based on historical practice data.
Assignment of Clinical Resources: Aggregate Calendar Pattern
The aggregate calendar pattern is the combination of all of the individual calendar patterns together. When we combine the eight individual calendar patterns, the resulting aggregate calendar pattern should be appropriate for the whole practice. This means that the OR-to-Clinic ratio is appropriate for each surgeon and also for each day of the two-week pattern. For this eight-surgeon practice the aggregate calendar with non-practice time is shown in Table 3. Of the 14 non-practice (A) days assigned, 10 displace clinic days and 4 displace OR days. This results in an aggregate calendar that has: 1) an OR-to-Clinic ratio of 6:5 (36 OR and 30 Clinic days); 2) an even distribution of (A) days - one surgeon on (A) time on seven of the ten days; 3) a well-balanced daily OR-to-Clinic ratio.
Table 3.
Aggregate Practice Calendar.
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Assignment of Clinical Resources: Aggregate Calendar Pattern with Discretionary Time
The calendar in Table 3 would repeat every two weeks if no other non-practice time were added. However, in reality there is additional discretionary time (D) that is available to all surgeons. This (D) time is made up primarily of trip time and paid time off. In this practice of eight surgeons there are approximately 500 days per year of (D) time – an average of about 10 days per week. This discretionary time, especially if the OR-to-Clinic ratio is changed significantly, can have a major impact on the surgeon and/or aggregate calendar. One of the policies in place to govern (D) time ensures a minimum of 4 surgeons assigned to either OR or Clinic each day. This is to ensure a minimum level of access for both Clinic and OR.
For the two-week period illustrated in Table 4, the addition of 19 discretionary days has a disruptive effect. As compared to Table 3: 1) Surgeon 1 has a ratio less than 1; 2) Surgeon 2 no longer has OR time; 3) the overall ratio has dropped below 1 (23:24); 4) three days (M, Th, and F) have an imbalance of OR and Clinic. These disruptions can have some of the following consequences:
Patient access – too few clinic/OR days will result in poor clinic/OR access.
Day-to-day variation – imbalance of surgeons assigned to clinic and OR (see Th and F) will cause variation in access and case volumes. Thursday will have high surgical volumes and low clinic access; Friday the exact opposite would occur.
Capacity utilization – The overall ratio below 1 could result in any of the following: low utilization of clinics, reduced OR throughput, or OR overtime.
Table 4.
Aggregate calendar with discretionary days added
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The management team recognizes that there is a need to monitor and adjust the practice calendar in order to minimize the impact of calendar disruptions. The next section discusses the process to strategically adjust the calendar to maintain a proper balance between OR and Clinic time.
Aggregate Calendar Planning and Maintenance Process
The management team meets each month to review and finalize the aggregate calendar. At the time of the meeting the calendar is finalized (patients can be scheduled) twelve weeks into the future. At the meeting, the calendar for weeks 13-16 is reviewed and finalized. Major changes can be made to the 13-16 week calendar and minor changes for weeks 1-12. An example of a major change is to switch a surgeon from Clinic to OR. Minor adjustments include additional resources assigned to a surgeon. This process is illustrated in Figure 2.
Figure 2.
Calendar finalization process
At the management team meeting the aggregate calendar with discretionary days is reviewed along with the following practice data:
OR access - number of days to the next available day a case can be listed by surgeon and division
OR cases listed - total number of surgical cases listed in the 1-12 week period by surgeon and by division
OR-to-Clinic ratio per day
Number of surgeons assigned to clinic each day
Number of surgeons assigned to OR each day.
This data provides insight into the current state of the practice. Table 5 has an example of the data that would be used at this point in the process.
Table 5.
Assignment allocation and practice data for surgeon 2 (13-16 week period).
| Clinic Assignment | OR Assignment | OR-to-Clinic Ratio | Cases Listed | Next Available OR |
|---|---|---|---|---|
| 8 days | 6 days | 0.75 | 25 | 14 days |
In Table 5, the cases listed and next available OR indicate that the OR schedule for surgeon 2 is currently busy with 25 cases listed and a 14 day wait for the next available OR. In addition, the OR-to-Clinic ratio is less than 1 for weeks 13-16 which is likely to further increase the queue for next available OR. This data suggests that major changes should be made to the schedule for surgeon 2; for example, a switch of one clinic to OR would increase OR capacity and bring the OR-to-Clinic ratio to 1. This analysis is done for each surgeon to identify opportunities.
The total number of surgeons assigned to clinic and OR on each day is also reviewed. As shown in Table 4, there can be imbalances in the number of surgeons assigned to clinic and OR on given days. In these instances, major changes are considered. The team looks for changes that can both positively impact the daily balance and improve the surgeon calendar(s). For example, in Table 4 for Surgeon 6 a major change from clinic to OR can be made on the second Friday. This change will balance the number of surgeons assigned to clinic and OR on that day. Also, it will change the surgeon 6 OR-to-Clinic ratio to be greater than 1. Any change to any calendar is allowed using this process as long as non-practice (A) time, approved discretionary (D) time, and more importantly, patient care are not impacted.
Performance of Calendars
This calendar management process has made a positive impact on the overall practice: OR capacity has been added with limited impact to clinic access (Figure 3). Anecdotally, we have seen reduced variation in the number of cases per day and per week, and the hospital census has become less variable. Table 6 shows the number of OR and Clinic days for the practice. The left columns reflect the calendar data before the above-described process was completed. For the same time period, the right columns reflect calendar data post-management process. Over this 9-month period, 24 additional days of OR capacity were added.
Figure 3.
Third next available clinic.
Table 6.
Clinic and OR days.
| before changes | with changes | |||||
|---|---|---|---|---|---|---|
| Surgeon | OR | Clinic | %OR | OR | C | %OR |
| 1 | 60 | 54 | 53% | 61 | 53 | 54% |
| 2 | 36 | 41 | 47% | 41 | 37 | 53% |
| 3 | 41 | 38 | 52% | 44 | 34 | 56% |
| 4 | 59 | 58 | 50% | 61 | 55 | 53% |
| 5 | 61 | 44 | 58% | 66 | 39 | 63% |
| 6 | 80 | 83 | 49% | 85 | 78 | 52% |
| 7 | 30 | 20 | 60% | 30 | 20 | 60% |
| 8 | 75 | 74 | 50% | 78 | 71 | 52% |
| Totals | 442 | 412 | 52% | 466 | 387 | 55% |
One of the counter-measures to the additional OR capacity is clinic access. The “third next available” metric9 is used to track the number of days from a given day to the third open clinic consult slot on the aggregate calendar. Figure 3 shows this metric for the same time period as Table 6. The average for this metric was 2 days which is considered acceptable clinic consult access.
In the process, there are a number of factors that are not considered that could yield more prospective and precise schedule changes. Patient arrival data, including variation of demand, is an important input to identify bottlenecks and periods of high variation. The performance of the schedule has many downstream impacts, for example, hospital census and staffing levels. The manual management process as described above can be automated to incorporate this additional data and metrics. The next section of this paper describes this more automated approach using simulation.
Data-Driven Analysis of Calendars
A model is used to evaluate various metrics into the decision making process of the calendar. The simple patient flow in Figure 1 is expanded to include metrics and downstream impact, for example, patient arrival and census. To this end, historical billing data of clinic appointments and surgeries performed by the practice were used to model patient flow, see Figure 4.
Figure 4.
Patient flow model - Simulation.
Four years of clinic appointment and surgical billing data were used to determine the surgical yield of the practice. The surgical and clinical data was linked by patient, then it was assumed that a clinic appointment within two weeks of the surgery date was the one which yielded surgery, more details can be found in 10. The estimated surgical yield of the practice is 68%. The proportion of inpatients, 70%, was estimated with billing data of surgeries performed in 2015. Patient arrivals were modeled with historical billing data on high-yield (HY) clinic appointments of 2015 since nearly 80% of patients of this practice are residents of other countries or other states of the US10. HY visits comprise clinic consultations of new patients (60 minutes visits) and comprehensive consultations (45 to 50 minutes visits) of established patients; these visits capture patients work-up/itineraries since early/mid week appointments are preferred to avoid weekend stays before surgery. Patients requiring short clinic visits (15 minutes) are not considered in the model In what follows, we provide more details of the parameters used in the simulation.
Patient demand (random) – Daily patient arrivals were modeled as homogeneous Poisson processes11 with intensity parameters estimated from (HY) visits performed by the practice per day. The estimated patient arrival rates for the practice are shown in Table 7. The arrival rate per day shows that high-request days are Tuesday, Wednesday, and Thursday. The arrival rate of Fridays are low to accommodate travel patterns of national/international patients.
Clinical capacity (deterministic) – Clinical capacity of a surgeon is defined as the historical maximum number of HY visits seen per day; the parameters are listed in Table 8. The clinical capacity of the calendar depends on the combination of surgeons assigned to Clinic. For example, the calendar in Table 4 has a clinic capacity of 19 and 13 consultations on Thursdays which are high patient arrival days.
OR capacity (random)– Historical data on surgeries performed in 2015 was used to estimate the number of cases that a surgeon can perform on an OR day. As illustrated in Figure 5, there exists a difference among surgeons, which implies that the surgical capacity on a given day depends on the combination of surgeons assigned to the OR.
Census (random) – The length of hospital stay (LOS) of an individual post-surgery was estimated with admission\discharge data of 2014 and 2015. The staffing level for postoperative care for this practice is generally constant, therefore, staffing levels effects were ignored12. The average length of stay is 5.04 days; the discrete LOS probability distribution is shown in Figure 6.
Table 7.
Poisson process daily arrival rates.
| Arrival rate | M | T | W | Th | F |
|---|---|---|---|---|---|
| λd [patients/day] | 10.04 | 16.96 | 12.07 | 15.68 | 7.92 |
Table 8.
Daily clinical capacity per surgeon. Number of appointment slots available per day.
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Figure 6.
LOS descriptive box-plot and probability distribution.
The simulation models the interaction between clinic and OR calendar days considering patient arrivals. For each calendar day the number of patients requesting a clinic visit is generated with its corresponding weekday-arrival rate parameter, and OR capacity is sampled from the distributions of the surgeons assigned in OR. It is assumed that patients prefer to have their clinic appointment close to their arrival date, then the following metrics are estimated: 1) access to clinic - the number of days patients need to wait for a clinic consultation; 2) patient seen – number of patient seen in clinic; 3) new surgical cases – surgical yield of each patient seen in clinic is 68%; 4) under\over-utilization – unfilled or fully utilized daily clinic capacity. The OR capacity and the number of patient seen in clinic are used to estimate: 5) access to OR - number of days a new surgical case needs to wait to access OR; 6) number of surgeries performed; 7) census – admission rate is 70% and length of stay is sampled from the LOS distribution.
Results
The simulation model was used to evaluate the performance of the aggregate calendar for the period of October 2015, November 2015, December 2015, and January 2016. The simulation was conducted after the placement of discretionary (D) days and changes to OR-to-Clinic ratio were made. Figure 9 shows the number of patients seen in clinic and their access to clinic. The left figure in Figure 9 shows the simulated patient seen in clinic, the dotted red line is the clinical capacity of the calendar and the percentile lines corresponds to the number of patient seen in clinic with probability 0.50, 0.75, and 0.90. It can be observed that the current clinical capacity is conservative resulting in unused appointments on several days. Most of the days with this clinic time waste have 3 to 4 surgeons assigned in clinic. The figure on the right shows the average time to access clinic (blue line) and worst-case time observed in the simulation (red line); the results show that third available clinic access of the calendar is at most three days.
Figure 9.
Left figure: Simulated patient seen in clinic. Right figure: access to clinic.
The simulation results suggest that a clinical capacity level equal to the 75-percentile of patients seen in clinic could be an adequate level for the practice without compromising clinical access. To validate this, we compared the suggested clinical capacity level (75-percentile of Figure 9) with the historical number of clinic consultations of the period analyzed. Figure 10 shows that the suggested clinic capacity is an appropriate level for most of the days of the period. In December, the simulation model suggests a conservative clinical capacity level, this might be caused by demand seasonality. More historical data is needed to incorporate demand trends and improve the model.
Figure 10.
Comparison of suggested clinical capacity and current capacity. Purple line is the actual number of patient seen.
Figure 11 shows the number of surgical cases that can be performed and the number of patients in post-operative care per calendar day. The OR capacity experiences periods of high variation, for example, January has sudden variations from week to week caused by the discretionary time allocated in that month. The variations in OR capacity have an impact in the census, for example, the number of patients in post-operative care decreases during the last week of December, and it has a sudden increase in January. Census projections could help planning the allocation of post-operative staff for different risk-levels, for example, the orange line could be used for worst-case scenario planning.
Figure 11.
Left figure: Estimated number of OR cases performed. Right figure: Estimated census.
The demand for surgery is modeled with the projected number of patients seen in clinic multiplied with the probability 0.68 that a patient will require surgical treatment. Figure 12 shows the estimated number of days for OR access. The average time during the months of October and November is below two weeks. Discretionary days distributed in December have a negative impact on access to surgery, for example, patients seen after January 15 are likely to not be able to access an OR in January. Therefore, major changes are needed in January to increase the surgical capacity of the practice, in particular, within the first two weeks of the month.
Figure 12.
Access to OR. Blue line is the average scenario, and red dotted line is the worst case.
Discussion and conclusions
Balancing OR and Clinic days in the calendar has made a positive impact on the overall practice. Strategic changes were made to increase the operating room capacity of the practice with limited impact on clinic access. A simulation-based tool was implemented to address some areas of the planning process where improvements could be made. Calendar inefficiencies which may be difficult to identify in a manual process are highlighted by the simulation tool since useful performance metrics such as access to clinic, access to surgery, OR and clinical capacity, and census could be estimated. Most importantly, the simulation tool would help illustrate to the management team the impacts of any changes to the calendar and performed what if scenarios analysis before calendar finalization.
Further improvements are needed to improve the predictive measures of the simulation. The access to OR analysis was done only considering patients accessing OR through clinic, data on transferred patients to the practice will be incorporated to obtain a better model of patient flow. The simulation model currently handles demand seasonality by scaling the arrival rates, more HY visit data is needed for a statistical model of seasonality of patent arrival. Finally, an optimization model will be incorporated to determine the best possible allocation of resources.
Figure 5.
Distribution of number of cases on a given OR day by surgeons.
Figure 8.
Simulation flow – blue font represents deterministic variables. Random variables are represented with green font.
Acknowledgement
This work is funded in part by the Mayo Clinic Robert D. and Patricia E. Kern Center for the Science of Health Care Delivery.
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