Although the financially most important determinants of operating room (OR) efficiency are the OR allocations made months in advance,1–3 there are practical issues that must be addressed within the week of surgery. In this paper, we study 3 questions about OR scheduling offices.
Some anesthesiologists running scheduling offices are adept at sculpting the OR schedule to fill allocated hours (e.g., choosing cases for specific ORs to mitigate overutilized OR time).4 How this can be accomplished is unclear because most (>50%) cases are entered into the scheduling system more than 2 calendar weeks before the day of surgery.5 Understanding how this sculpting is done would be beneficial so that it can be accomplished in a systematic and consistent manner.
Recently, we showed that one possible explanation does not apply. Success in reducing overutilized OR time was not achieved by the coordination of case scheduling among facilities (e.g., when busy at one facility, overutilized OR time is reduced by moving the cases to another facility).6 Another possible explanation is that most ORs are full only a few workdays before the day of surgery, and it is only the most recently scheduled cases that result in the large observed differences in workloads among ORs.1,7 If this were true, scheduling offices could be achieving a high efficiency of use of OR time on the day of surgery (i.e., low mean overutilized OR time) in part by managing the scheduling of just those last cases of the day. Supporting this hypothesis, OR time, allocated appropriately on the basis of minimizing the inefficiency of use of OR time, was filled a median (among services) of only 2 workdays before the day of surgery.8,9 Whether this finding would relate to last scheduled cases in ORs was unknown, bringing us to the first question we studied:
Question 1: How many workdays before the day of surgery have changes to the schedule become sufficiently few that productive plans10–16 can be made for specific ORs to minimize expected hours of overutilized OR time (e.g., optimize staff assignments)?
A report we receive frequently from anesthesiologists providing leadership for scheduling offices is that a common decision they are asked to make is the OR into which to schedule a case of a service that has filled its allocated OR time and has another case to schedule. The optimal process to release allocated OR time on the basis of minimizing the inefficiency of use of OR time8–17 is sensitive to systematic underestimation or overestimation of case durations.1,18 However, we receive these qualitative reports even from hospitals at which such bias is absent and appropriate OR allocations have been implemented.19,20 This seems paradoxical because, if OR allocations are planned so that on fewer than one third of days there will be overutilized OR time, rarely should a service have another case to schedule once the service has filled its allocated OR time.1,8,9,15,19–21 One explanation for the reports is that OR allocations based on actual workloads of elective cases on the day of surgery do not reflect OR schedules 1 calendar week or 2 workdays before surgery. We showed previously that this explanation does not apply to services having their OR time released (i.e., the service with the most unscheduled OR time 1 week ahead usually also has substantial underutilized OR time on the day of surgery).8,9,a However, the explanation may apply to the service that has filled its allocated time and has another case to schedule (e.g., the additional case is balanced by a cancellation, resulting in little net additional OR time). Whether scheduling additional cases is an indicator of poor OR allocations (i.e., forecasts) brings us to the second question we studied:
Question 2: Do services that have filled their allocated OR time have few additional cases to schedule or do they have few net cases to schedule (i.e., many offsetting cancellations and additions)?
A final scenario relevant to OR scheduling relates to the use of OR allocations to predict case scheduling for a service on a date. Suppose on Thursday a service has a case to schedule into one of its allocated 2 ORs the following Monday. If the case would not result in overutilized OR time in either OR, the decision of whether the case would best be scheduled into the OR providing the earliest or the latest start time depends on the likelihood that the service will have a future change in the hours of cases scheduled in those ORs.17,22 Some schedulers and physicians consider this possibility on the basis of the characteristics of the service (e.g., “Vascular Surgery usually has a few cases they schedule the day before”). This decision model effectively assumes that the additional scheduling or cancellation of cases is independent of the cases scheduled so far. Yet, from studies of the variability among days in OR workload, days with fewer hours of elective cases had more scheduling of add-on cases and vice versa.23 Furthermore, the service with the largest current difference between allocated and scheduled time 5 workdays before surgery predicted the service with the most underutilized time on the day of surgery.8 This brings us to the third question we studied:
Question 3: Which better predicts net case scheduling 1 or 2 workdays before surgery: the combination of service and days ahead or the allocated, but currently unscheduled, OR time?
The Thomas Jefferson University IRB approved this retrospective study without a requirement for informed consent. Cases studied were those performed in the tertiary ORs, ambulatory surgery center, and endoscopy suites of Thomas Jefferson University Hospital. The sample size was n = 17 consecutive 4-week periods (Table 1).
The data used were extracted from the active and historical case scheduling transaction audit tables from the hospital’s anesthesia information management system (AIMS) and OR information system (Table 1). Scheduling information and changes were transmitted from the OR information system to the AIMS, allowing matching of the cases in the 2 systems. Each change to a scheduled case in the OR information system resulted in a new transaction in the AIMS, with the date and time of the previous scheduled date of surgery and the time it was posted captured in a corresponding audit table. These timestamps allowed reconstruction of the elective OR schedule for a specific day on all days preceding the day of surgery (Table 1). For example, if a case was scheduled originally on March 1, 2011, to be performed on March 30, but was cancelled on March 24, the case would have appeared on the tentative OR schedule for March 30 when viewed on March 23, but would not have appeared when viewed on March 25.
For all questions, the scheduled durations used were unbiased Bayesian estimates.24–26 For common procedures, these times are close to the mean of historical case durations. For uncommon procedures, they are close to the surgeons’ (schedulers’) estimates, except with outliers removed.25 The Bayesian method has been used for anesthesia decision support (e.g., time remaining in cases) at the studied hospital for several years.27 The OR location was determined automatically, as described previously (Table 1, step 8).28,29
The following scenario highlights the differences among the 3 questions:
- An otolaryngologist’s 3.5-hour case 1 was added on June 13 to the OR schedule for Friday June 30, 2011, to be performed in OR 1.
- The otolaryngologist’s 5.0-hour case 2 was added on Monday June 27 at 10:00 AM to the OR schedule for June 30 to follow in OR 1.
- On June 28 at 8:05 AM, the list of cases still to be performed on June 30 was moved to OR 2.
- On June 29 at 3:00 PM, the sequence of cases was switched by the otolaryngology nurse specialist so that the 5.0-hour case had the 8:00 AM scheduled start time, and the 3.5-hour case had a 1:30 PM scheduled start time.
- On June 30, the patient for the 5.0-hour case entered the OR, monitors were applied, and vital sign trending was started at 8:05 AM.28,29
Then, for question 1, the time difference studied was 48.0 hours, where 48.0 hours = (the date and time of the start of the case, 8:05 AM, June 30) – (the date and time of the room change, 8:05 AM, June 28). For questions 2 and 3, the time difference studied was 3 workdays, where 3 workdays = (the date of the start of the case, June 30) – (the date the case was scheduled, June 27). Importantly, for none of the questions was the change in case sequence considered (see Discussion section, second paragraph). Furthermore, the complexity of this scenario is realistic, with the many dates and times showing why there were so many steps involved in the data processing (Table 1).
For question 1, the timing of the last change to the schedule of cases that were performed in each OR for each date of surgery was determined (Table 1, step 20). For every case, the difference was taken between (the date and time when the patient entered the OR) and either the (date and time that the most recent change was made to the scheduled combination of OR and date of surgery) or, if no changes were made, (the date and time that the case was scheduled originally). For each combination of OR and date, the minimum difference was selected. For example, suppose that in OR 1 on January 20, 3 cases had been performed, entering the OR at 7:30 AM, 12:00 PM, and 4:00 PM, respectively. Each of these cases was elective, having been scheduled at 3:00 PM on January 5, January 10, and January 19, respectively. Then, the smallest difference in time would have been 23 hours, which would have been attributed to the combination of OR 1 on January 20.
For questions 1 and 2, results are reported as percentages, calculated using the method of batch means,30 as validated previously for OR management studies.18,31–33 Specifically, percentages were calculated as the ratio of sums within each 4-week period, and then the mean of the ratios was calculated among periods. Because percentages were reported to the nearest 0.1%, standard errors <0.1% were rounded up to 0.1% for reporting.
For questions 2 and 3, OR allocations were calculated for each combination of the day of the week and service.31,34 The services were mostly specialties (i.e., a group of individual surgeons sharing allocated OR time). For example, the 4 specialties that each accounted for at least 10% of the OR hours were orthopedics (20.6% ± 0.4%), general surgery (17.3% ± 0.3%), otolaryngology (16.0% ± 0.3%), and endoscopy (10.4% ± 0.2%). The relative cost of each hour of overutilized OR time to each hour of underutilized OR time was considered to equal 2.00.1,15,19 For purposes of optimizing OR allocations, recommendations are insensitive to the use of a ratio of 1.50 (“time and a half”) or 2.00 (“time and a half” + intangible costs).15 The ratio of 2.00 was used for simplicity of presentation. Using 2.00 is simple, because its use results in a 2:1 ratio (i.e., 66th percentile, because 2/(2 + 1) = 2/3 = 0.66).21 Conceptually, if it is twice as expensive to finish late than to finish early, two thirds of the days an OR should finish early and one third of the days it should finish late. The 66th percentiles were calculated using Cleveland’s method so that an assumption about the underlying statistical distribution of the data did not need to be made to estimate the percentiles.15,21,35 Whereas demographics (e.g., percentage add-on) were calculated using all n = 17 periods, for results from OR allocations, only the last 6 four-week periods were used for calculations of standard errors. Thus, the first 11 four-week periods were used to calculate the optimal OR allocations (i.e., “training”), and then the allocations were applied to the last 6 periods (i.e., “testing”).34,35 Excluding holidays, this resulted in 42 to 44 workdays used to calculate each of the 66th percentiles (i.e., 44 days = 11 periods × 4 weeks per period). Among the 81 combinations of service and day of the week, 27 had mean hours of elective cases <5.33 hours. The value of 5.33 hours is the breakeven point at which 2 services scheduling into the same shared OR time would result in the same inefficiency of use of OR time as each having its own 8 hours of allocated OR time.2,3,20,36 These 27 low workload service and day of the week combinations averaged 1.19 ± 0.34 hour of cases. These services were excluded from application to the subsequent n = 6 4-week periods. However, they were included in all other calculations.
For question 3, days of the same combination of service and 4-week period were compared (e.g., days with and without a cancellation within 2 workdays of surgery). The Wilcoxon signed rank test was used to calculate P values for the comparisons. The Hodges–Lehmann estimates for median differences were used for confidence intervals. Calculations were performed using exact methods (StatXact-9, Cytel Software Corporation, Cambridge, MA).
Cases were considered “add-on” if scheduled from 7:00:00 PM the working day before surgery through the day of surgery and “elective” otherwise. Excluding this period (i.e., add-on cases), all other 12-hour intervals from 7:00 PM to 6:59 AM the next working day accounted for just 0.2% ± 0.1% of OR date combinations. Consequently, quantification of the timing of decisions in the scheduling office can be by day (i.e., combining the 12-hour intervals starting at 7:00 AM and at 7:00 PM into single 1-day epochs).
The percentage of OR date combinations with at least 1 add-on case was 24.1% ± 0.3% (Fig. 1). This value using data from 2010 to 2011 was compared to results from a different academic (tertiary) hospital’s 1998 data.37 The earlier paper reported numbers of add-on cases per day per OR. Pooling among the hospital’s suites using fixed-effects meta-analysis,37,38 there were 0.247 ± 0.052 add-on cases per day per OR. Because most ORs had zero or 1 add-on case,37 the percentage of OR date combinations with at least 1 add-on case was slightly less than 24.7%. The concordance between the current result of 24.1% and the previous (slightly less than) 24.7%, despite over a decade difference in time, increased our confidence in the relevance of our new data and results to other hospitals.
The most recent addition of a case (actually performed) to an OR occurred 1 working day before surgery for 22.3% ± 0.4% of OR date combinations. Two working days ahead, the percentage was 5.2% ± 0.3%. Cumulatively, at least half (51.5% ± 0.5%) of ORs had their last case scheduled or changed within 2 working days of surgery (i.e., 51.5% @ 24.1% + 22.3% + 5.2%) (Fig. 1). Thus, our preliminary answer to question 1 was that managers should focus on the day of surgery starting 2 working days before the upcoming day of surgery.
These percentages of recent scheduling activity (e.g., 51.5%) seemed high to us in comparison with the ratio of the net number of elective cases added within 2 working days of surgery to total elective cases performed (3.9% ± 0.4%). However, this large difference did not represent an inconsistency in the data. The cancellation rate for the elective (scheduled) cases zero to 2 working days before surgery was 12.8% ± 0.3%. The scheduled cases added zero to 2 working days before surgery were 14.9% ± 0.3% of the total performed. Being “cancelled” should not be interpreted as not having been performed, nor should “additional” be interpreted as not having previously been scheduled, because movement of a case from one date to another “cancelled” from one date and “added” a case on another date. The total rate of substitution of one (or more) case for another (others) was 27.7% ± 0.4% of cases. Within the calendar week before the day of surgery, 43.1% ± 0.5% of cases had changed (i.e., change in date, complete cancellation, or newly scheduled). These findings suggest not only that planning for the day of surgery would be unproductive when done more than 2 working days before surgery, but that an active scheduling office has many opportunities to reduce overutilized OR time during those last 2 workdays.
Consideration of when the allocated OR time was fully filled also provided insight into case scheduling close to the day of surgery. When scheduled hours equaled or exceeded allocated hours, and the service scheduled an additional case, the median time ahead when each such case was scheduled was 2.2 ± 0.2 workdays (n = 6 four-week periods). This finding was compared with results from 1998 to 2001 at a different hospital.8,9 The median time ahead when each such case was scheduled was the same value, 2.2 ± 0.2 workdays ahead.9 The concordance increased our confidence in our answer to question 1, that starting 2 workdays ahead is the time when the day of surgery can most practically be considered in decision making.
Once allocated time for a service was full, the ratio of the net additional cases scheduled to the total number performed was 1.2% ± 0.6%. The percentage being small was expected, because allocated time is based on the predicted workload on the day of surgery. The percentage being slightly less than one third of the 3.9% above also was expected, because of the condition that allocated time be full. With the relative cost ratio used, that would occur for one third of service and day of the week combinations. However, among services on those days within a week of surgery when their allocated time was full, the ratio of the net number of additional cases scheduled each 12-hour interval divided by the total performed equaled 11.1% ± 1.7%. If 2 cases were scheduled and 2 were cancelled within the same 12 hours, none of those scheduled were counted toward the 11.1%, only unequal scheduling (e.g., 3 scheduled and 2 cancelled were treated as 1 case). Answering question 2, it is common for a scheduler to need to consider the releasing of allocated OR time even when the OR time has been allocated appropriately, because the goal of the statistical forecast is to predict the workload on the day of surgery.
Starting 2 working days before surgery, the difference between the hours of cases scheduled and the allocated OR time can be used to guide decision making.4,8,9,17,20,35 For each combination of service and final 6 four-week periods, n = 96 combinations had at least 3 days for which the scheduled hours did not exceed the allocated hours. The median was taken of the net increase in hours scheduled for each combination over the subsequent 2 working days. There were, logically, net increases in the hours of scheduled cases (P < 0.0001, median 4.2 hours, 95% confidence interval [CI], 3.3 –5.1 hours, n = 96 combinations). In contrast, when the scheduled hours 2 working days ahead exceeded the allocated hours, there was no significant net increase in hours of cases scheduled (P = 0.79, median 0.1 hour, 95% CI, −0.9 to 1.0 hours, n = 42 combinations). Taking the pairwise difference within combination of service and period, more hours of cases were scheduled when the time scheduled so far at 2 workdays ahead did not exceed that allocated (P < 0.0001, median 3.1 hour, 95% CI, 2.1–4.3 hours, n = 42 combinations). Therefore, answering question 3, additional hours of cases scheduled within the same number of workdays are heterogeneous within services based on the prior hours of cases scheduled.
The preceding answer to question 3 suggested an overall behavior consistent with efforts to fill, but not exceed, buckets. Whether this was due to surgeons’ and/or schedulers’ behavior could not be determined from the data. Regardless, the observation suggested that cancellations before the day of surgery may not reduce the net hours of cases performed. Combinations of service and the 6 four-week periods were studied that had both at least 3 days with no cancellations within 2 workdays of surgery and at least 3 days with at least 1 case cancelled. The median net additional hours of cases scheduled (including the cancellation) were compared pairwise for each of the combinations. Cancellation was associated with more net hours of cases scheduled (P < 0.0001, 1.6 hours, 95% CI, 1.3–2.2 hours, n = 170).b Thus, while cancellations on the day of surgery reduce hours of elective cases performed, this consequence does not apply to cancellations made before the day of surgery.
We used descriptive analytics to describe data from transaction audit tables created through the 1-way interface from an OR information system to an anesthesia information management system (Table 1). Because there are many results, with one finding leading to another, we presented interpretations in the Results section at the end of each paragraph. Three broad conclusions can be made.
First, making decisions to target specific ORs to reduce hours of overutilized OR time (e.g., through staff assignment) can be effective, but can take hours of planning.1,4,11–16 There are so many changes made to so many cases in so many ORs even 2 workdays ahead, that making plans more than 2 workdays ahead is unlikely to be productive. The finding of “2 workdays” may overestimate the appropriate period because we deliberately excluded case sequencing, even though such sequencing influences coordination among ORs and resulting overutilized OR time.4,7,11,39–42 Regardless, the fact that there are so many changes to the OR schedule within 2 workdays of surgery reveals why running the scheduling office effectively during that brief period can be fruitful at reducing overutilized OR time. The data suggest strongly that anesthesia groups should be engaged in the decision making during the last few workdays before the day of surgery. These results do not depend on how we calculated allocated OR times.
Second, the purpose of allocating OR time on the basis of minimizing the inefficiency of use of OR time is to plan staffing on the basis of the historical workload on the day of surgery.1–4,8,9,11,17,20,21,34,35 The allocations do predict the case scheduling before the day of surgery of services that do not fill their allocated OR time.8,9 That pattern does not apply to services that have filled their allocated time. By definition, these results do not apply if OR allocations are not evidence based, the reason for which principally is due to psychological biases.19
Third, when addressing a service that has filled its allocated time, case scheduling is fraught with ambiguity and constraints. Schedulers (and physician leadership) often rely on paper checklists rules of thumb (e.g., “joint replacement cases are scheduled far in advance”).20,43 These so-called “heuristics” are incomplete (e.g., neglect future cancellations) and thus do not predict the workload on the day of surgery. OR allocations are predictive. Just as we have learned for nearly every other major issue in OR management,1–4,8,9,11,15,16,17,19,20,35 the scheduling decisions close to the day of surgery are highly sensitive to the appropriate calculation and use of the statistical forecasts (i.e., the service-specific OR allocations).
The staffing (e.g., OR allocations) and staff scheduling (e.g., number of anesthesia teams assigned to the ORs used by the otolaryngology and neurological surgeons) considered in this paper was limited to that known months in advance, specifically 11 four-week periods.3 Recently, He et al. studied different statistical methods to use the incremental knowledge of cases scheduled to improve upon the staffing plan (i.e., the OR allocations) obtained by using only the data of service and day of the week.35 Deferring staffing decisions until the scheduled hours of cases were known significantly reduced labor costs.35 Our findings for question 1 show that such data are not available until at least 2 workdays before the day of surgery, and likely not until the evening ahead. Thus, a corollary is that, for labor contracts to be setup to facilitate the “flexing” of labor to reduce OR costs substantively, the “flex” needs to occur very close (e.g., 1 workday) to the day of surgery. These results can be helpful even for groups without such flexibility in staff scheduling, because leaders (e.g., of anesthesia groups) can explain to stakeholders why such flexing is not used. These results are not inconsistent with the finding of question 2 that once allocated time is full, net additional hours of cases are small, because the distribution of hours among ORs influences appropriate staff schedules.3,5
One limitation of our study is that the data are from 1 academic (tertiary) hospital. For this reason, in the Results, we made 2 comparisons to another such hospital in a different state with data from more than a decade earlier.8,9,37 The near-identical concordance was reassuring. Table 1 and the Methods section show the (many) steps to perform the study. We hope that future studies will be done by other such hospitals and that heterogeneity in findings will be learned.
A second limitation is that changes to the OR schedule within the last 2 workdays may be even larger at community hospitals with few hours of cases per OR per date. Such hospitals have more opportunities to move cases from one OR to another versus the academic (tertiary) hospital with long workdays studied in our Results.6,44 Such a hospital manually reviewed 2 workweeks of their case data to evaluate whether they could apply our Results from question 1. Among its 283 cases, 20% were add-on, matching our results. However, among its 118 OR date combinations, 48% included a case added (moved) to an OR after 7:00 PM of the working day before surgery versus our observed 24% (Fig. 1). Consequently, 70% had a change within 2 working days of surgery versus our observed 52% (Fig. 1). Thus, at some hospitals, the anesthesia department may be able to limit its engagement to the working day before surgery.
A third limitation of our study is that it used descriptive analytical methods to evaluate further2–4,6–9,16,17,19,20,34,35 how best to apply a predictive method (i.e., OR allocations) published more than 15 years ago.21 The current (just published) state of the art (basic science) in relevant stochastic optimization considers one OR at a time, not multiple ORs.45,46 Consequently, specific recommendations for scheduling offices are limited to the following heuristic. Subject to constraints such as surgeon availability, (1) release the allocated time of the service with the most unscheduled but allocated time; (2) put off every decision for as long as possible to have additional information; and (3) schedule each case into an OR resulting in no or little overutilized OR time but also the least amount of underutilized time (i.e., do not schedule cases into the most empty OR).1,4,8,9,17,20,37 As above, this approach relies, above all else, on the OR allocations being calculated appropriately, so as to minimize the inefficiency of use of OR time.
Dr. Franklin Dexter is the Statistical Editor and Section Editor for Economics, Education, and Policy for Anesthesia & Analgesia. This manuscript was handled by Dr. Steven L. Shafer, Editor-in- Chief, and Dr. Dexter was not involved in any way with the editorial process or decision.
Name: Franklin Dexter, MD, PhD.
Contribution: This author helped design the study, conduct the study, analyze the data, and write the manuscript.
Attestation: Franklin Dexter has approved the final manuscript.
Conflicts of Interest: The University of Iowa, Department of Anesthesia, Division of Management Consulting, performs some of the analyses described in this paper for hospitals, including for some of the hospitals in this paper. Franklin Dexter receives no funds personally from such activities. He has tenure and does not participate in any incentive programs. Income from the Division’s consulting work is used to fund research.
Name: Pengyi Shi, BS.
Contribution: This author helped design the study, and write the manuscript.
Attestation: Pengyi Shi approved the final manuscript.
Conflicts of Interest: This author has no conflict of interest to declare.
Name: Richard H. Epstein, MD, CPHIMS.
Contribution: This author helped design the study, conduct the study, and write the manuscript.
Attestation: Richard Epstein approved the final manuscript.
Conflicts of Interest: Richard Epstein is President of Medical Data Applications, Ltd., whose CalculatOR™ software includes some of the analyses described in this article. The University of Iowa pays licensing fees to use the software for hospital consultations performed by its Division of Management Consulting.
a OR time should be released whenever a service has filled its allocated time and has another case to schedule, any number of days before the day of surgery (i.e., a specific date for releasing allocated time is inconsistent with decision-making that minimizes the inefficiency of use of OR time).1,8,9,17,20
b Analyses were repeated using different statistical methods as sensitivity analyses. Each method gave similar results. First, when limiting analyses to combinations with at least 6 days for cancellation and not cancellation, the median difference was 1.4 hours (P < 0.0001, 95% CI 0.9 to 56 to 1.9 hours, N = 107 combinations). Second, when using the minimum sample of 6 days each and using means, followed by fixed-effects meta-analysis to pool among the 107 combinations, the mean difference was 1.4 hours (P < 0.0001, 95% CI 0.7 to 2.2 hours). Third, the analysis using means was repeated using restricted maximum likelihood estimation in a random-effects analysis, and the results were the same to the listed digits as that of the preceding fixed-effects analysis.
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