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Department of Anesthesia, University of Iowa, Iowa City, Iowa
Address correspondence and reprint requests to Franklin Dexter, Department of Anesthesia, University of Iowa, Iowa City, IA 52242. Address e-mail to franklin-dexter{at}uiowa.edu
| Abstract |
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Implications: Operating room utilization can be maximized by allocating block time for the elective cases based on expected total hours of elective cases, scheduling patients into the first available date provided open block time is available within 4 wk, and otherwise scheduling patients in "overflow" time outside of the block time.
| Introduction |
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Utilization equals the time an OR is used (occupancy plus setup and cleanup) divided by the length of time an OR is available and staffed. For example, if patient care in an OR starts at 7:00 AM and finishes at 1:00 PM, and if the regularly scheduled period of elective cases extends from 7:00 AM to 3:00 PM, then there are 2 h of unused OR time. OR utilization equals 75% (6 h used/8 h staffed). In a previous study in which we used computer simulation to model how the OR suite functions, we evaluated the impact of different interventions that might be implemented to increase OR utilization (3). Using OR suite data from the University of Iowa, we found that large increases in OR utilization are unlikely to occur even by (i) improving scheduling accuracy such that all errors in predicting durations of cases are eliminated, (ii) eliminating variability in turnover times, or (iii) eliminating day to day variation in number of hours of add-on cases. Instead, the computer analysis of OR utilization suggested that the most effective strategy to maximize OR time utilization is to select the days on which to perform elective cases so as to best match the OR caseload with the days on which full-time OR personnel are scheduled to work (4).
One common method to match elective cases and staff availability is to allocate "block time" (i.e., OR time) to surgeons. OR utilization is then maximized by filling block time with as many hours of cases as possible. The key to maximizing OR utilization is to determine (i) the appropriate amount of block time to allocate to each surgeon and (ii) how to choose which day to schedule a patient for surgery. In this study, we used computer simulation and survey data collected from patients to develop an OR scheduling strategy designed to maximize OR utilization.
| Methods |
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To perform simulation, the behavior of several parameters (e.g., case duration) was represented by probability distributions. The simulation model used random numbers drawn from these probability distributions to generate uncertain events. This was done repeatedly to represent the scheduling of many patients into OR block time.
With the aid of computer programming, we constructed simulated OR suites and scheduling systems. Using these computer-based, hypothetical OR suites, we tested different OR scheduling strategies to develop an OR scheduling strategy aimed at maximizing OR utilization. Computer simulation was particularly useful for this study because some proposed OR scheduling strategies resulted in poor OR utilizations, posing an economic danger to a real OR suite had we tested these algorithms in clinical practice. Simulation also provided a mechanism to deal with multiple uncertainties that would have required an impractical data collection period to study experimentally. By using a computer to simulate OR suites, we were able to analyze data that otherwise would have required recruiting enough OR suites to collect 100,000 yr of OR scheduling data.
Summary of Computer Simulation Modeling Performed
We wrote the computer program so that each computer simulation allocated a certain amount of block time, scheduled elective cases into the block time, and then evaluated unused OR time in each block to compute OR utilization.
We performed each simulation with a different combination of values for the five input parameters: (i) scheduling algorithm to determine the day on which a patient will have surgery; (ii) average case duration (in hours) for all cases performed by a surgeon; (iii) average length of time (in days) patients wait for their surgery once the decision to have surgery has been made; (iv) number of hours in each block; and (v) number of blocks allocated to the surgeon each week.
The end point or output of this computer modeling was the average OR utilization, defined as the percentage of block time that was used by elective cases and turnover times. This percent utilization equals the adjusted percent service utilization as defined in the Association of Anesthesia Clinical Directors' glossary (http://aacdhq.org/glossary.htm) (5).
Programming
In real clinical settings, OR scheduling involves allocating block time to a surgeon, then scheduling patients into the block time. This scheduling was represented in our computer simulations (Appendix 1) (Figs. 1 and 2), as follows:
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Computer code was written in Microsoft Excel Visual Basic (Redmond, WA).
Assumptions of the Simulations
The computer simulation methodology made three assumptions.
1. The number of work days between patients' requests to be scheduled for surgery was assumed to follow an exponential distribution (6). This assumption implies that patients do not delay their requests to be scheduled for surgery depending on how many other patients have been scheduled for surgery. Likewise, the time from when the preceding patient was scheduled until the current patient is scheduled is independent of the time until the next patient is scheduled.
2. Each case was assigned a random time duration generated from a log-normal statistical distribution (Appendix 1). In the simulations, mean case durations (with resulting 25th, 75th percentiles) for all cases performed by a surgeon were set to equal either 1 h (0.5, 1.3), 2 h (0.9, 2.5), or 3 h (1.4, 3.8).
3. Turnover time in the ORs ("patient out" to "patient in") equaled 0.5 h. This value equals the mean turnover time for all elective cases performed between July 1, 1994 and June 30, 1997 at the University of Iowa's OR suites. The rationale for using a constant turnover time is explained in Appendix 1.
Algorithms Used to Decide into Which Block to Schedule Each Case
The rules by which cases were scheduled into blocks are "on-line bin-packing algorithms," a term from operations research literature. "On-line" refers to giving a patient a surgical date as soon as the patient requests to be scheduled for surgery. A patient is assigned a surgical date (e.g., by the particular OR suite's scheduling system) without consideration of requests by other subsequent patients. This practice is in contrast to the use of waiting lists (see Discussion), whereby a patient may wait weeks to months to be told the day on which they can have surgery. Patients are "packed" into "bins," where the bins are the surgeon's blocks.
Each case was scheduled into a block (i.e., assigned a surgical date) subject to rules specified by the algorithm being used in the simulation. We evaluated four standard algorithms (7).
All four of the algorithms that we considered effectively assume that if a surgeon plans to be away on a day with allocated block time, the surgeon would rescind that date before the day of surgery. Otherwise, the surgeon would be unable to schedule patients into future dates.
Patient Survey of Acceptable Waiting Times for Surgery
From the results of the simulations, we learned that OR utilization depends greatly on (i.e., is very sensitive to) the average length of time patients have to wait for surgery once the patient requests to be scheduled for surgery. The longer patients wait to have surgery, the greater the percentage of OR block time used, because more surgical dates (blocks) can be evaluated for a good match between a case's duration and the remaining OR time in the block.
To develop an OR scheduling strategy to maximize OR utilization, we needed to use in the computer simulations lengths of time that patients consider reasonable to wait to have surgery. Thus, we undertook a survey study to determine patients' perceptions of acceptable waiting times for elective surgery.
Description of Patient Survey Study
After approval of our human subjects committee, we surveyed patients to quantify their views of acceptable waiting times. The primary end point of our survey was the median longest amount of time that patients considered acceptable to wait for surgery and its corresponding 95% lower distribution-free confidence bound (8).
All patients reporting for outpatient surgery at the reception desk of the University of Iowa's anesthesia evaluation facility over 10 consecutive work days in January 1998 were eligible for inclusion in the survey. Parents of pediatric patients completed the questionnaire. Prison inmates, nonEnglish-speaking patients, and developmentally delayed patients were excluded. Patients seen at this facility were going to undergo surgery at either an ambulatory surgery center or a tertiary OR suite (including cardiac surgery). Subjects were asked to "put an `X' over the longest/most time you would have wanted to wait for surgery." A time line was given below the statement. As secondary analyses, we chose post hoc to use Spearman rank correlation coefficients to assess the ability of demographic parameters to predict the longest acceptable waiting times.
Description of Percent Changes in OR Utilization
To compare the impact of different OR scheduling strategies on OR utilization, we defined a change in OR utilization of 1%3% to be small, 4%7% to be moderate, and >8% to be large. These values were selected because, at the University of Iowa, a change in the system of scheduling patients that could close one, two, or three ORs would increase OR utilization by 3%, 7%, or 10%, respectively ([100%] x [1, 2, or 3 ORs]/[30 ORs regularly scheduled each work day]).
Sequence of Studies
The goal of this study was to develop an OR scheduling strategy to maximize OR utilization. To develop the strategy, we addressed the following questions.
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2 wk, OR utilization is likely to be similar whether two 4-h blocks or one 8-h block is used. | Discussion |
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1. If the length of time patients have to wait to have surgery is small (e.g., <1 wk), a surgeon's block time use cannot be near 100%. It is unrealistic for OR suites to aim to have OR utilization rates consistently >90% unless the average patient waiting time is at least 2 wk. As waiting time increases, more surgical dates (blocks) can be evaluated for a good match between a case's duration and the open times in the blocks. In some communities, competition among surgeons and hospitals may not allow the average length of time that patients have to wait for surgery to be as long as 2 wk. An OR suite then cannot expect block time utilization from elective cases to exceed 90%, assuming that enough block time is allocated for a surgeon to complete all of the elective cases in the block time.
2. The maximal possible OR utilization for a particular surgeon can be much <100%, depending on his or her practice profile (e.g., the average length of time patients wait before having their surgery).
3. Objectives in scheduling an OR suite may be to allocate just enough block time for each surgeon to complete the elective cases in the block time while maximizing OR utilization. In this setting, determining an appropriate amount of block time and selecting a method to schedule cases into a surgeon's blocks must be done simultaneously. This "method" to schedule cases means specification of three parameters: an algorithm to choose on what day to schedule each case, the average length of time patients must wait before having their surgery, and the number of hours of time in each block.
4. Among patients undergoing outpatient (ambulatory or same day admit) surgery, the median longest amount of time that patients consider acceptable to wait for surgery is 2 wk.
5. The average lengths of time patients have to wait for surgery can be controlled by setting a corresponding maximum patient waiting time.
Importance of Maximizing OR Utilization to Anesthesia Practices
Even if anesthesiologists are paid on a fee-for-service basis, maximizing OR utilization is important because it minimizes "down time." Alternatively, if anesthesiologists and/or nurse anesthetists are employed based on working a set shift (regardless of whether a case is to be performed), increasing OR utilization may decrease the staffing costs by matching workload with staffing. To estimate the cost-savings from increased OR utilization, we estimated the labor cost of OR time to equal $190 per hour (salaries for two full-time OR nurses, one full-time anesthesiologist, and one ancillary full-time personnel [representing housekeeping, sterilization, and other staff] = 2 x [$25 per hour] x [125% to include benefits] + 1 x [$180,000 per year] x [120% to include benefits]/[2000 clinical hours a year] + 1 x [$15 per hour] x [130% to include benefits] = $190 per hour). We found that increasing the average length of time that patients wait for surgery from 1 to 2 wk (for a surgeon with a mean case duration of 3 h who has one 8-h block each week) increased utilization of a surgeon's block time by 27% (from 47% to 74%). This predicted increase in OR utilization would decrease labor costs by $154 per case ([$190 per hour] x [3-h mean case time] x 27%). To interpret a $154 saving per case, we considered that, at Duke University, the mean cost per case for all anesthesia drugs and supplies equaled $70 (9). Clearly, changes in OR utilization are likely to have a greater impact on perioperative costs than reducing anesthesia drug and supply costs (1).
To Maximize OR Utilization, Control of Choosing the Surgical Date Must Be Moved from the Surgeon and Patient to the OR Suite
Simulation provided a mechanism to deal with multiple uncertainties that would have required an impractical data collection period to study experimentally. By using computer simulation, we were able to manipulate the allocation of block time and the average length of time patients wait to have surgery. However, a scheduling system to maximize OR utilization must specify how the patient is scheduled into a surgeon's block time. The process of implementing a scheduling system that specifies how surgeons schedules cases into their block time raises important issues that need to be addressed. For example, balancing a surgeon's convenience versus the cost of unused OR block time may be a complex organizational problem. OR managers also need to determine whether 4 wk is an appropriate maximum patient waiting time and whether all surgeons should have the same mean waiting time for their elective cases to be completed.
Scheduling Add-On Cases
Add-on elective cases increase OR utilization by decreasing unused OR block time. If the parameters assumed for our simulations were applied to an OR suite, we would expect actual measured OR utilization for the block time allocated for elective cases to be higher than predicted because of add-on elective cases. The total hours of urgent cases during some period (e.g., 4 wk) will be statistically independent of the total hours of elective cases during the period. Therefore, OR time must be forecasted and allocated independently for elective and urgent cases. Urgent cases will therefore not affect the proposed OR scheduling strategy for elective cases. The principles for allocating block time for urgent cases may be simpler than those for elective cases. To illustrate this concept, we consider a hypothetical OR suite that allocates one block during each work day for urgent cases. Because patients requiring urgent surgery have a short waiting time, we expect block time allocated for urgent cases to have a relatively low OR utilization (e.g., 40%). Consequently, if the urgent case block time has a relatively high utilization on one day, utilization would not be more likely to be high in the block the following day. Urgent case block time use would not be expected to be auto-correlated. The common practice in OR management of measuring OR utilization and adjusting block time accordingly is reasonable when OR utilization is low. The practice becomes unreasonable (Fig. 5) as allocations are decreased in an effort to increase OR utilization.
Scheduling Strategy for a Group of Surgeons, Providing for Decreased Mean Waiting Time
To maximize OR utilization, the allocation of block time and the selection of a method to schedule cases into the allocated time must be done simultaneously. The bin-packing algorithms that we considered assume that a case can be scheduled in any block with sufficient open OR time. Even an algorithm as simple as "schedule the patient into the first available date with sufficient open OR time" (Next Fit) is generally not suitable for a group of surgeons. This algorithm would be appropriate only if the surgical group does not specify at the time that the patient is scheduled for surgery which surgeon in the group will operate. Some patients may forego being scheduled for a specific surgeon to have an average waiting time <2 wk. For illustration, we considered all patients to undergo a specified procedure, such as breast biopsy or coronary artery bypass grafting. Each patient would be scheduled to have surgery on the first available date within the block time allocated to the group of surgeons for all patients undergoing the procedure. The patient's surgeon would be the surgeon in the group who was previously scheduled to care for patients in the block. The total hours of elective cases performed by the surgical group each week on the patients undergoing the procedure may be sufficient to fill four blocks a week. The surgical group could then use a maximum patient waiting time of 2 wk and achieve an OR utilization as high as a single surgeon filling two blocks a week would achieve with a maximum waiting time of 4 wk. The surgical group may have a sufficient workload to fill five blocks a week with patients undergoing the procedure. The group could then use a maximum patient waiting time of 1 wk to achieve OR utilization higher than a single surgeon filling one block a week would achieve with a maximum waiting time of 4 wk.
Length of Time Patients Wait to Have Surgery: An International Perspective
Half the patients we surveyed considered a wait of 2 wk to be the longest time that they considered acceptable to wait for elective surgery. Although we did not ask our study patients what type of surgery they were undergoing, outpatient surgery at the University of Iowa includes many patients undergoing joint replacement. The longest acceptable waiting time of 2 wk measured in our study was shorter than the acceptable value of 13 wk elicited from patients who underwent knee replacement in Canada (10). This difference may reflect differing patient expectations for medical service in Iowa versus Canada. The patients we surveyed had already been scheduled for surgery and, as such, had already committed themselves to proceed with surgery. Our results probably apply to the true wishes of the Iowa population when faced with the prospect of elective surgery, because 99.4% of patients for whom a surgical procedure is recommended choose to undergo surgery (11). The survey consent form stated that the patient would not realize a benefit from completing the questionnaire. We suspect that our patients would have been willing to wait longer than the average of 2 wk, provided that they expected to realize some benefit from an increase in waiting time. Patients in Iowa are very concerned about continuity of care and would be willing to wait longer for treatment, provided that they would be seen by the same permanently assigned surgeon (12). Patients with breast cancer in Ontario are willing to wait an average of 7 wk for radiation therapy, provided that they can undergo treatment close to home (13). Of patients in Ontario, 57% are willing to wait an additional 5 mo for joint replacement surgery, provided that they will realize a 1% decrease in the risk of postoperative mortality (14). The acceptable lengths of time patients have to wait for surgery is being addressed in other countries. For example, Sweden's Patient Guarantee specifies that patients should get an appointment with a specialist within 4 wk and undergo surgery within 3 mo after an opinion has been given by the surgeon (15). The United Kingdom's National Health Service's Patient Charter specifies that patients should undergo surgery within 18 mo (17,19). The Danish Medical Association's resolution on a set of minimal rights for patients states that patients should see a surgeon (examination in the secondary health service) within 4 wk and undergo surgery (treatment) within 2 mo (20). The OR manager must balance patients' desires not to wait for surgery versus the fact that OR utilization will increase as waiting time increases. Our simulations predict that an increase in the mean time patients wait to have surgery from 1 to 2 wk causes a median 13% increase in OR utilization, whereas an increase from 2 to 3 wk causes a median 5% increase. Therefore, we believe that a mean waiting time of 2 wk is a reasonable goal. This recommendation may be a longer patient wait than is typical in the United States (21,22). Two articles have addressed whether the United States should consider increasing waiting periods to decrease the cost of healthcare (22,23). Our simulations suggest that this strategy is reasonable for perioperative care. Bell et al. (22) surveyed hospitals in the United States and Canada and found a strong correlation (r = 0.44) between median charges and waiting times for total knee replacements. This result suggests that increased waiting times are associated with lower perioperative costs.
How Does OR Use Change as the Maximal Waiting Time Increases from Four Weeks to One Year?
Given the markedly longer patient waiting times in countries other than the United States, a relevant question is: how does OR utilization change as the maximum waiting time increases from 4 wk to 1 yr? Using simulation as described in Question 8, we found that, for a maximum patient waiting time of 4 wk, the predicted OR utilization equaled 91%. An increase in the maximum patient waiting time to 8 wk caused predicted OR utilization to increase to 94%. Further, increasing the maximum patient waiting time to 1 yr increased OR utilization to 96%. We would expect countries with longer maximal waiting times to have higher OR utilization, assuming that the unique characteristics of OR suites in different countries could be controlled.
Use of Waiting Lists
Surgeons in some countries schedule elective cases into their block time by using waiting lists (24,25). Waiting lists differ from waiting times in that patients' requests for surgery are considered simultaneously. Patients are then given the days that they will have surgery. By reviewing all pending cases before scheduling a new case, waiting lists allow for better placement of cases into blocks to match scheduled OR time. However, to achieve the benefit of increased OR utilization, patients must agree to the date of their surgery when it is presented to them. In contrast, the on-line bin-packing algorithms, which we considered in this study, permit patients to be told on which day they will have surgery as soon as the patient requests to be scheduled for surgery.
Coordinating a Surgeon's Clinic and OR Days
Patients' requests to be scheduled for surgery may be received at regular intervals (e.g., every Monday) corresponding to a surgeon's clinic days. A surgeon's patients may agree to be scheduled for surgery during the clinic visit. It can then be important to coordinate the day(s) of the week of the surgeon's clinic with the day(s) of the week of the surgeon's OR block time. Coordination of the days of the week can affect the average length of time that patients wait to have surgery, OR block time utilization, and the percentage of the surgeon's total hours of elective cases that the surgeon can complete within the block time.
| Conclusions |
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| Appendix 1 |
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Surgical Case Duration.
Surgical case duration was described using a log normal distribution, with the result right truncated. We chose this distribution based on the durations of 300 consecutive surgical cases performed at the University of Iowa in June 1997. The cases represented a mixture of both ambulatory surgery and tertiary medicine. Case durations were log-normal (ExpertFit; Averill M. Law & Associates, Tucson, AZ, 1997), as confirmed by using the distribution function difference plot, density/histogram overplot, and Lilliefor's test (P = 0.67). To generate case durations, a normally distributed random number was first generated using the polar method (26). We achieved large decreases in computational time by using this method rather than the Box and Muller algorithm (26).
Second, a log-normally distributed random number was generated from the normally distributed random number (26). Differences in mean surgical case durations among OR suites at the University of Iowa are not associated with differences in the standard deviations of the logarithm of surgical case durations. Therefore, we used a standard deviation of the logarithms of case durations in hours equal to 0.725, as obtained at the University of Iowa. Third, the resulting value was truncated at the number of hours of block time allocated to the surgeon each day. For example, if the case duration equaled 13 h and 8-h blocks were used in the OR suite, we assumed that the case would be scheduled in the OR suite by considering the case duration to equal 8 h.
Turnover Times.
We used a constant turnover time for two reasons: (i) The standard deviation of turnover times is negligible relative to the standard deviation of case durations. Therefore, for OR suites at which turnover time and case duration are independent, using a constant turnover time did not affect our results. (ii) For some OR suites, turnover time and case duration are correlated. For example, short cases, such as successive myringotomy tube placements, characteristically have short turnover times. Therefore, the difference between actual turnover times and our constant turnover time of 0.5 h can be considered to be incorporated into the case durations.
Details of the Computer Simulations.
The first step of each simulation was to calculate the maximum mean number of patients who could be requesting to be scheduled for surgery each week for the surgeon to complete all of the elective cases within the specified number of hours of block time each week while satisfying the specified mean patient waiting time and permitting all patients to have surgery within 4 times the mean patient waiting time. For simulations using an exponential distribution of patients' requests to be scheduled for surgery, we varied the mean number of patients requesting to be scheduled for surgery each week by varying the exponential distribution's only parameterthe mean time between patient requests. For simulations using a constant time between patient requests, we varied the constant time between requests. We found, to the nearest 0.002 days, using a trial and error approach (27), the minimum time between successive patients' requests to be scheduled for surgery for which the 95% two-sided confidence interval (26) for the calculated mean patient waiting time contained the desired mean patient waiting time. This trial and error approach was inefficient computationally. However, we did not have success with the Golden Section Search (27) method because there was not always a monotonic relationship between the time between patient requests and the mean patient waiting time. For each simulated trial testing a mean time between patient requests, the same seed was used for random number generation. The confidence interval for the observed mean patient waiting time was calculated using the replication/deletion approach for means (26), with each successive simulation having a duration equal to 100 surgical blocks completed. Once the time between successive patients' requests to be scheduled for surgery was known, the final simulation was run using Programming Steps 27 (Methods). The end points that were calculated included the (i) percent OR utilization, (ii) percent empty blocks, and (iii) percentage of block time that was unused while weighting by the probability that each block's unused time was of a sufficiently long duration to permit another case to have been performed in it. The latter was calculated using the distribution function for the log-normal distribution while incorporating the right truncation (26). Confidence intervals for these three end points were calculated using the replication/deletion approach for means (26), with each successive simulation having a duration equal to 100 surgical blocks completed. Simulations were continued until the width of the 95% confidence interval for each of these three end points was <0.4%.
| Appendix 2 |
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| References |
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F. Dexter, A. Macario, and R. D. Traub Enterprise-Wide Patient Scheduling Information Systems to Coordinate Surgical Clinic and Operating Room Scheduling Can Impair Operating Room Efficiency Anesth. Analg., September 1, 2000; 91(3): 617 - 626. [Full Text] [PDF] |
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F. Dexter and R. D. Traub Sequencing Cases in the Operating Room: Predicting Whether One Surgical Case will Last Longer than Another Anesth. Analg., April 1, 2000; 90(4): 975 - 979. [Abstract] [Full Text] [PDF] |
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F. Dexter, A. Macario, and L. O’Neill Scheduling Surgical Cases into Overflow Block Time-- Computer Simulation of the Effects of Scheduling Strategies on Operating Room Labor Costs Anesth. Analg., April 1, 2000; 90(4): 980 - 988. [Abstract] [Full Text] [PDF] |
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W. J. Mazzei Maximizing Operating Room Utilization: A Landmark Study Anesth. Analg., July 1, 1999; 89(1): 1 - 1. [Full Text] [PDF] |
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