Ambulatory surgery centers (ASC) are implementing new anesthetic techniques and recovery protocols to achieve earlier patient discharge after general anesthesia. If patients emerge from anesthesia more quickly, then the time from when surgery is finished (the anesthetic is discontinued) to the time the patient leaves the operating room (OR) may be decreased. The impact of shortening the time required for the patient to leave the OR on the costs of staffing an ASC is unknown. Patients whose anesthetic technique allows for minimal postanesthetic nursing care may also be able to bypass the phase I postanesthesia care unit (PACU) and transfer directly from the OR to the phase II PACU (step-down recovery room). The economic impact of increasing bypass rates has not been previously published.

There is a growing body of literature demonstrating the feasibility and safety of bypassing the phase I PACU-also known as "fast-tracking." A multidisciplinary educational program showing how to bypass the stage I PACU increased the bypass rate from a baseline rate of 0%-2% to 14%-42% ^{[1,2]}. Clinical trials have found that titration of anesthetics using the processed electroencephalogram Bispectral Index[trade mark sign] (BIS[trade mark sign]; Aspect Medical Systems, Natick, MA) can allow patients to be tracheally extubated more quickly after general anesthesia. Use of rapid recovery techniques (such as the BIS[trade mark sign] or lower solubility inhaled anesthetics) may also allow patients to recover sufficiently fast from general anesthesia to permit bypass of the phase I PACU ^{[3-5]}.

The conditions under which bypassing the phase I PACU can yield a reduction in PACU staffing are unknown ^{[6]}. We previously demonstrated that small changes in the times that patients remain in a PACU are unlikely to decrease labor costs at ASCs with full-time PACU nurses ^{[7]}. However, bypassing the phase I PACU after general anesthesia can produce large decreases in the average time that patients spend in the PACU.

Using computer simulation, we address two questions. First, what is the achievable decrease in an ASC's OR labor costs (nurses and technicians) if the time from which surgery ends (the anesthetic is discontinued) to the time the patient leaves the OR is decreased for all patients undergoing general anesthesia? We present the conditions under which decreases in labor costs are possible. Second, what is the impact on PACU nurse staffing if patients bypass the phase I PACU and proceed directly to the phase II PACU?

## Methods

### Overview of Computer Simulation to Analyze Management Problems

Simulation is a tool whereby a mathematical model is built to "act like" a system of interest (the OR suite or PACU) in certain important respects (employee staffing, patient entry and exit). Simulation is useful to address the research questions of this study because recruiting the thousands of patients required to perform the simulated randomized clinical trials to evaluate the effects of different rapid emergence and phase I PACU bypass rates on ASCs' labor costs would have been impractical (see Appendix 1 for calculations). Simulation is popular in the physical, engineering, and management sciences under such circumstances. Computer simulation can explore sensitivity effects (e.g., which variables have the biggest effect on results) and reproduce the amount of variability that occurs in the system being simulated (e.g., will any one patient bypass the phase I PACU? How many patients will be scheduled for surgery today?).

Computer simulation requires that we describe the logical operation of PACU staffing (e.g., ratios of nurses to patients, expected length of stays) and OR scheduling (e.g., number of cases each day). Simulation then allows us to experiment with the system (e.g., change the time it takes for a patient to emerge from anesthesia and exit the OR). In simulation, the behaviors of several factors (e.g., case duration) are represented by probability distributions. Simulation models use random numbers to generate uncertain events by making random draws from the probability distributions. Simulation does this repeatedly to represent the scheduling of thousands of patients in the OR and their admission to the PACU.

### Overview of Hourly Versus Salary Pay

To simulate labor costs of an ASC's OR suite, different methods of paying the staff had to be considered. Under the United States of America's Fair Labor Standards Act (FLSA), employees must be paid either on a "salary basis" (a set salary paid regardless of the number of hours worked) or an hourly wage ("regular rate") plus an overtime wage of 1.5 times the regular rate for work beyond 40 h a week.

We considered four different methods of paying ASC employees.

A. Hourly Employees Who Had no Minimum Number of Hours of Work Each Week. The first was hourly employees who had no minimum number of hours of work each week. The FLSA does not require a 40-h work week. Therefore, staff can be paid an hourly wage and have no minimum on the number of hours of work per week. This means that pay is based on the number of minutes worked (if the staff works 15 min less on a day, then the decrease in the ASC's labor costs equals the dollar cost of 15 min of staff time). In this setting, because the ASC has to pay the staff extra for working overtime, the ASC has a financial incentive to avoid paying overtime by scheduling employees to work <40 h a week.

In this compensation structure, the ASC minimizes labor costs by employing only part-time employees. In this study, we therefore assumed that all labor costs subject to this payment scheme are at the hourly wage or regular rate. We assumed that part-time employees are not paid for time that they are not caring for patients.

B. Full-Time Salaried Employees. The second method of paying ASC employees that we investigated included full-time salaried employees. The designation of professional status, which permits pay on a salary basis and exempts employees from the overtime requirements, can apply to registered nurses.

C. Full-Time Hourly (Not Salaried) Employees with no Minimum Number of Hours of Work Each Day. Next, we considered full-time hourly (not salaried) employees with no minimum number of hours of work each day. In this model, there is no overtime paid, but nurses occasionally work >8 h per day. For each day that an employee works >8 h, there will usually be another day within the pay period (e.g., 4 wk) when they can stop working sufficiently early without pay to ensure that the mean work week does not exceed 40 h.

D. Full-Time Hourly (Not Salaried) Employees with Frequent Overtime. Finally, we created a model using full-time hourly (not salaried) employees with frequent overtime. Some ASCs may have full-time hourly (not salaried) employees who work at least 8 h each day and have frequent overtime work paid at 1.5 times the regular rate. As there are progressively fewer cases throughout the day, such ASCs often minimize costs by scheduling such nurses to work fewer days with longer hours.

### PACU Definitions

For purposes of the study, we assumed phase I PACU to denote a nursing intensity (one nurse to two patients, i.e., 1:2), not a different geographic location ^{[8]}. That is, patients may be in the phase I physical area and be considered to be in phase II if their nursing care ratio is 1:3.

### Study 1.

What Is the Impact on the Quantity of PACU Nurse Staffing if Patients Bypass the Phase I PACU and Proceed Directly to the Phase II PACU? For this simulation study, we assumed that the ASC has part-time or full-time nurses in the PACU and that the OR suite is not scheduled routinely to have overtime (i.e., cases begin only if they can be completed before the time at which OR staff are scheduled to finish work). This study is appropriate for ASCs that do not frequently have overtime in the OR suite. Figure 1 summarizes the analysis for PACU with full-time nurses. The analysis included five variables:

1. Mean number of patients admitted to the PACU each day. We considered a mean daily load of 20, 30, 40, or 50 patients. All patients cared for in the PACU are included, including patients receiving only local anesthesia. The simulation varied the actual number of patients each day; the average over many days was the chosen mean. For example, in the simulation using a mean of 20 patients, on one day 18 hypothetical patients could have been admitted, and on another 23 patients. The likelihood of the computer selecting a particular number was governed by its assigned probability of occurring. This process was repeated for each of the thousands of days simulated.

2. Time after which no more patients are admitted to the PACU. Because patients treated at an ASC must be discharged home, a typical PACU admission deadline is 2:00 PM. We also considered 4:00 PM, because busy ASCs schedule surgical cases later into the afternoon.

3. The percentage of patients cared for in the PACU who bypass phase I was varied from 0% to 80%. The value of 0% implies that all patients cared for in the ASC are admitted to the phase I PACU. This scenario is common for practices limited to surgical specialties that typically require the use of general anesthesia (e.g., pediatric surgery). The value of 80% would be common at ASCs with practices with many cases performed with patients under local anesthesia or monitored anesthesia care (e.g., cataract extractions).

4. Patients who are admitted to the phase I PACU remain there for 0.5 or 1 h. We chose the value of 0.5 h because it is a minimum necessary to complete phase I PACU paperwork at many hospitals. Some other institutions' PACU protocols require that patients admitted to the phase I PACU remain there for at least 1 h. For simplicity, we did not consider random variability in this variable. Mean nursing hours for part-time nurses are insensitive to small, random variations in the times that patients remain in the PACU ^{[7]}. The number of full-time nurses required to care for the patients is insensitive to small variations in the times that patients remain in the PACU ^{[7]}.

5. Patients remain in the phase II PACU for either 1 or 2 h. This parameter was also not randomly varied for the reasons specified in the preceding paragraph.

The computer simulation methodology addressed the following six issues through assumptions that are explained.

1. Surgery start times. Surgery starts at 7:00 AM. At ASCs that start later in the morning, our results would be unchanged if other times (e.g., time at which no more patients are admitted to the PACU) are adjusted accordingly.

2. Rate and behavior of PACU admissions. The time between admissions of successive patients into the PACU varies randomly. To represent the impact of OR scheduling on PACU admissions, we considered the mean number of patients admitted into the PACU each hour versus the time of day to increase linearly, reach a peak, then decline linearly, as observed empirically and previously described ^{[7]}.

3. Peak PACU admissions time. The time of the peak rate of admission of patients into the PACU is 10:00 AM. Results are insensitive to this variable (i.e., it does not matter whether the time is 10:00, 9:00, or 11:00 AM) ^{[7]}.

4. Variability in PACU stay. Variability in times that ambulatory patients remain in the PACU has a negligible effect on the number of nurses required in a PACU (discussed above).

5. Nurse to patient ratios. No patient requires 1:1 care. One to one care implies that patients are unconscious on PACU admission, which would be rare in an ASC using rapid anesthetic recovery protocols. Nursing staffing ratio for patients in the phase I PACU is 1:2, per American Society of Post Anesthesia Nurses (ASPAN) guidelines ^{[9]}. Nursing staffing ratio for patients in the phase II PACU is 1:3, per ASPAN guidelines ^{[9]}. ASCs that choose to use lower cost nursing assistants to extend this ratio to 1:4 will achieve greater percent decreases in cost from bypassing the phase I PACU than predicted by our simulations.

6. Number of nurses employed. The ASC determines the number of full-time nurses to staff the PACU by scheduling the minimum number to handle the peak workload on 95% of days ^{[6]}. Full-time nurses are scheduled using overlapping shifts so that all nurses are present at the time of day of the expected peak in the number of patients in the PACU ^{[6]}. PACUs that satisfy ASPAN guidelines on <95% of days may achieve greater decreases in cost from bypassing the phase I PACU than predicted by our simulations. Part-time PACU nurses work whenever they are needed and are otherwise on call. PACU nurses are assigned to staff either the phase I or phase II PACU, but not both simultaneously.

We wrote the computer code such that the simulation effectively proceeded in the following manner.

1. A random number generator uses the technique described in Appendix 1 to calculate the time at which a patient is admitted to the phase I and II PACU.

2. A random number that is uniformly distributed between 0 and 1 is generated. If the random number is smaller than the specified proportion of patients who bypass phase I (Variable 3), then the patient enters the phase I PACU. Otherwise, the patient bypasses phase I and enters phase II.

3. Steps 1 and 2 are repeated for all patients admitted to the PACU throughout the day. The numbers of patients in the phase I and phase II PACU at each time of the day are used to calculate the number of full-time and part-time nurses needed in the phase I and phase II PACU throughout the day, as described in Appendix 1.

4. Final output of the simulations are the mean number of part-time nursing hours each day and 95% upper confidence interval for the number of full-time nurses to be scheduled each day.

### Study 2.

What Is the Achievable Decrease in an ASC's OR Staff Labor (Nurses and Technicians) if the Time from Which the Anesthetic Is Discontinued to the Time the Patient Leaves the OR Is Decreased for All Patients Undergoing General Anesthesia? For this simulation study, we assumed that the ASC employs full-time hourly employees who work at least 8 h each day and have frequent overtime to work in the OR suite. This study is therefore appropriate only for ASCs with frequent overtime. The computer simulation analysis included three variables that we varied.

1. Mean case duration for all cases performed in the ASC. Case duration refers to the time from when a patient enters an OR until they leave the OR. We considered 1.0, 1.5, and 2.0 h as typical mean case durations.

2. Ratio of costs for overtime versus regular wage. The FLSA requires that a value of 1.5:1 be used in the United States. We also evaluated overtime pay at the rate of 1:1 and 2:1.

3. Decreases in OR time per case that are achievable by an intervention to achieve faster emergence of patients from general anesthesia. We used the values of 3 and 6 min, which are characteristic of the magnitude of decreases in the time to extubation that may be possible after clinical interventions (e.g., using the BIS[trade mark sign] monitoring device) ^{[3,10]}.

This analysis assumed the following.

1. Case durations and turnover times follow a log-normal distribution, as considered in Appendix 1.

2. Cases are scheduled into an OR as long as the case will start during an 8-h day. This will lead to all rooms being used beyond 8 h.

3. Every patient in each simulated OR receives the intervention to achieve faster emergence (i.e., exit the OR sooner). Therefore, we are not necessarily simulating every OR in an OR suite, but only those ORs that meet this criterion.

4. The OR manager schedules the nursing staff to work the number of hours each day that will minimize labor costs. As explained previously, this implies that the average shift duration will exceed 8-h. This approach achieves cost-savings greater than or equal to that achieved by staggered 8-h and 10-h shifts, and as such, we may underestimate the decrease in labor costs that a PACU may achieve by faster emergence.

The simulation analysis (mathematical details in Appendix 1) proceeded as follows.

1. A case duration is generated. A turnover time is added. These steps are repeated until the total time is >or=to8 h. The total time and number of cases per OR is stored.

2. Step 1 is repeated 31,999 times. The cutoff time beyond which the ASC would not have regularly scheduled OR nurses and technicians is calculated. The criterion used to pick the cutoff time is the time that minimizes labor costs. The number of iterations ^{[11]} was sufficient for the width of the 95% confidence interval of the cutoff time to be <15 min.

3. Step 1 is repeated. The difference between the end of the day in each simulated OR and the cutoff time from Step 2 is calculated. To obtain the hours of overtime in the simulated OR that day, the difference is set equal to zero if it is less than zero. From this, we calculate the minimum of the number of hours of overtime in the OR that day and the (number of cases in the OR that day) x (decrease in time per case resulting from an intervention that allows faster emergence). This final value gives the decrease in overtime that day by having all patients emerge from anesthesia and leave the OR more quickly.

4. Step 3 is repeated 31,999 times. Mean values are calculated for the number of cases in each OR each day and the decrease in the hours of overtime achieved by the rapid emergence protocol, provided the protocol permits the patient to exit the OR sooner. The number of iterations was sufficient for the standard errors of these two means to be <0.2% and 1.0% of the means, respectively. The main output of the simulations is the decrease in the number of minutes of overtime per case.

### Study 3.

What Is the Impact on the Quantity of Full-Time PACU Nurse Staffing if Patients Bypass the Phase I PACU and Proceed Directly to the Phase II PACU and the OR Suite Is Scheduled in a Manner to Have Frequent Overtime?

As described in Study 2, for an ASC to schedule its ORs to achieve frequent overtime, a case is scheduled into an OR if it can start during an 8-h day. If the first case in an OR starts at 7 AM, then patients are starting to undergo surgery until 3 PM. Consequently, the last patient will be admitted into the PACU after 4 PM. Therefore, instead of using the rate and behavior of PACU admissions (Assumption 2) and the peak PACU admissions time (Assumption 3) from Study 1, we used the OR schedules generated by Study 2 to specify the times of admission of patients into the PACU. All other aspects of Study 3 were identical to Study 1. Study 3 applies only to ASCs with full-time hourly employees with frequent overtime.

When analyzing decreases in labor costs achievable by increasing the phase I PACU bypass rate, we excluded decreases in overtime payments for PACU nurses who are paid hourly and work full-time. By not including overtime, we may have underestimated the decreases in labor costs achievable by bypassing the phase I PACU.

## Results

Decreases in OR and PACU labor costs from faster emergence and PACU bypass vary depending on how the staff are compensated. The results of our computer simulation study vary depending on the particular method that an ASC uses to pay its staff.

### A. An ASC Employs Hourly Employees with no Minimum Number of Hours of Work Each Week (Part-Time)

If an ASC has hourly employees with no minimum number of hours of work each week (part-time), OR labor costs are strictly variable. Any time savings that result from a more rapid OR exit should translate into decreases in cost. Simply put, if a case is completed 3 min earlier (meaning the patient leaves the OR 3 min sooner), then the staff are paid for 3 fewer minutes of work.

The results of Study 1 (assuming staff work part-time) are presented in Table 1. The mean number of hours that part-time PACU nurses work each day depends on the times that patients spend in the phase I and phase II PACU, time that the last patient is admitted to the PACU, and the mean number of patients. For example, from the first row of Table 1, if an average of 20 patients are admitted each day to the phase I PACU, no more patients are admitted after 2:00 PM, length of stay in the phase I PACU is 30 min, and length of stay in the phase II PACU is 60 min, then our simulations suggest that an increase in the phase I PACU bypass rate from 0% to 40% would decrease part-time nursing hours by 2 h each day. As the bypass rate increases, the mean number of hours (part-time PACU nurses) needed for staffing decreases.

### B. An ASC Employs Full-Time Salaried Employees

An ASC with salaried employees can reduce OR staff if faster emergence permits fewer staff to be employed (i.e., an OR would need to be closed). This scenario is unlikely because the number of ORs used depends predominantly on how OR time is allocated to surgeons and how patients are scheduled into that OR time. Faster emergence of patients from general anesthesia will generally not decrease OR labor costs for salaried employees.

The results of Study 1 (assuming staff work full-time) are presented in Table 2. The number of full-time PACU nurses needed to work each day decreases as the bypass rate increases. For example, from the first row of Table 2, if an average of 20 patients are admitted each day to the phase I PACU, no more patients are admitted after 2:00 PM, length of stay in the phase I PACU is 30 min, and length of stay in the phase II PACU is 60 min, then simulations suggest that an increase in the phase I PACU bypass rate from 0% to 40% would permit one fewer PACU nurse to be employed. Increases in the phase I PACU bypass rate can produce greater decreases in labor costs in a PACU staffed with full-time nurses than part-time nurses Figure 2versus Figure 1).

### C. An ASC Employs Full-Time Hourly (Not Salaried) Employees with no Minimum Hours of Work Each Day

If an ASC has full-time hourly (not salaried) employees with no minimum number of hours of work each day, the results are the same as those for salaried employees (see preceding paragraph).

### D. An ASC Employs Full-Time Hourly (Not Salaried) Employees with Frequent Overtime

The decreases in overtime per case from a 3- or 6-min faster emergence are presented in Table 3. When staff are full-time hourly employees, minimizing overtime is important because the cost of overtime to an ASC is more than the hourly wage (regular rate). Management at an ASC with employees who work at least 8 h each day and have frequent overtime would be expected to schedule shifts >8 h to minimize labor costs. Therefore, a decrease in OR time of 6 min per case would cause a decrease in overtime of <6 min per case.

The results of Study 3 (assuming staff is full-time hourly with frequent overtime) are presented in Table 4. For example, if an ASC satisfies the conditions of the first row of Table 4, no increase in bypass rate is likely to change the number of staff needed in the PACU. However, if the average number of patients each day increases from 27 to 48 (moving from Row 1 to Row 3 of Table 4), then an increase in the phase I PACU bypass rate from 0% to 40% would permit one less PACU nurse to be employed.

### Example

Hypothetical Scenario to Show How to Use the Results. For example, a hypothetical ASC employs nurses who are paid a regular rate of $22 per hour. The FLSA specifies that the overtime rate equals 150% of the regular rate. There are an average of 2.5 nurses per OR in the OR suite. Average case duration for all cases done in the OR suite is 2 h.

The ASC introduces a clinical intervention or rapid emergence protocol (e.g., BIS[trade mark sign] monitoring) to decrease time to extubation and exit from the OR by 3 min and increase the frequency with which patients bypass the phase I PACU from 20% to 40% ^{[3,4,10]}.

In this example ASC, we assume that patients are all admitted to the PACU by 2:00 PM. An average of 30 patients are treated each day (t patients in each of six ORs). Patients stay an average of 1 h in the phase I and II PACUs. The 20% of patients who undergo monitored anesthesia care or regional anesthesia always bypass the phase I PACU. After introduction of the intervention to increase the frequency of PACU bypass, the percentage of patients bypassing the phase I PACU at the ASC = (20% of patients with monitored anesthesia care or regional anesthesia) + ([80% of patients who undergo general anesthesia] x [25% bypass rate with the intervention]) = 40%.

A. Example ASC: Part-Time Nurses Are Employed. If we assume that OR nurses are paid hourly and that they are not paid if there is no patient in their assigned OR, then the predicted decrease in OR labor costs = ($0.92 per minute) x (3 min) = $2.76 per case. OR labor costs = ($22 per hour) x (2.5 nurses per OR)/(60 min per hour) = $0.92 per minute.

The predicted decrease in PACU labor costs from increasing the bypass rate from 20% to 40% in this example is $2.20 per case. This is calculated by knowing how many hours PACU nurses are working, from the 10th row of Table 1. The (hourly rate for PACU nurses) x (decrease in mean number of hours worked by part-time PACU nurses)/(mean number of patients each day) = (cost per hour for each PACU nurse) x ([mean number of hours of PACU nurses before introduction of the rapid emergence protocol] - [mean number of hours of PACU nurses after introduction of the rapid emergence protocol])/(mean number of patients each day) = ($22 per hour) x ([26 h each day] - [23 h each day])/(30 patients each day) = $2.20 per case.

B. Example ASC: Salaried Nurses Are Employed. Assuming that salaried nurses are employed, the ASC is not expected to achieve a decrease in OR labor costs. If nurses are salaried, increasing the bypass rate from 20% to 40% should decrease PACU labor costs by $5.87 per case.

From the 10th row of Table 2, the predicted decrease in PACU labor is from 10 to 9 full time nurses. Decreased costs = (cost per day for each PACU nurse) x (decrease in number of scheduled full-time PACU nurses)/(mean number of patients receiving the rapid emergence protocols) = ($22 per hour) x (8 h each day) x (one less nurse)/(30 patients each day) = $5.87 per case.

C. Example ASC: Full-Time Nurses with no Minimum Number of Hours of Work Each Week Are Employed. If full-time nurses with no minimum number of hours of work each day are employed, the analysis is the same as for salaried nurses (above example).

D. Example ASC: Full-Time Nurses with Frequent Overtime Are Employed. Assuming a rapid emergence protocol that reduces case time by 3 min is established and that nursing staff are paid hourly and frequently work overtime, then the predicted decrease in labor costs = $1.52 per case. This result is calculated as follows. The costs of overtime = ($22 per hour) x (150% of regular rate) x (2.5 nurses per OR)/(60 min per hour) = $1.38 per minute. From the 8th row and 3rd column of Table 3, the predicted decrease in overtime for OR nurses = ($1.38 per minute) x (1.1 min) = $1.52 per case.

If nursing staff are full-time hourly with frequent overtime, then the predicted decreases in labor costs achieved by increasing the bypass rate from 20% to 40% equals $5.87 per case. The result is obtained from the 11th row of Table 4 and equals ($22 per hour) x (8 h each day) x ([six full-time nurses each day] - [five full-time nurses each day])/(30 patients each day) = $5.87 per case.

## Discussion

An ASC that wants to estimate the potential decrease in OR and PACU labor costs from rapid emergence protocols can substitute values appropriate for their institution into the Tables and follow the examples. We show how the decreases in labor costs can be expected to vary depending on how the ASC pays its staff: hourly employees with no minimum number of hours of work each week (or part-time employees), salaried employees, full-time hourly (not salaried) employees with no minimum number of hours of work each day, and full-time hourly (not salaried) employees with frequent overtime. Any dollar decreases in costs from less staff being required due to the rapid emergence intervention need to be evaluated against the cost of implementing the rapid emergence intervention.

### Impact of Nonmedical Factors on PACU Discharge

We did not include all possible confounding variables in the recovery process. For example, the potential decreases in PACU labor costs from bypassing the phase I PACU may be limited by a variety of system-based, nonmedical factors (e.g., waiting for test results or prescriptions, transport delay, or lack of physician release). Delays >30 minutes due to nonmedical reasons have been noted to occur in up to 54% of outpatients ^{[12]}. To achieve decreases in costs, managers must address the causes of unnecessarily delayed discharges. Furthermore, an ASC must develop PACU criteria permitting bypass of the phase I PACU and ensuring that patients who bypass the phase I PACU do not remain longer in the phase II PACU. These initiatives have some costs, and they were not included in our study.

### "Blended" or Dual Trained Staff

Our results are unchanged for ASCs with OR nurses who work outside ORs. At ASCs with part-time nurses, the costs of having nurses trained to work throughout the ASC (i.e., both in the OR and PACU) is the same as having two nurses working independently. At ASCs with salaried nurses or full-time nurses with no minimum number of hours of work each day, we found no expected decreases in labor costs from faster emergence in the OR suite. Finally, at ASCs with frequent overtime, the nurses from the OR would not work in the PACU because they are already accumulating overtime for working in the ORs.

### Sensitivity of PACU Results to Parameter Values

We used computer simulation to calculate PACU nursing labor for a wide range of conditions. By estimating PACU staffing changes, the simulations serve as a guideline for a more detailed analysis in clinical economic trials. The numbers of PACU nurses predicted by the simulation model are reasonable. For example, the University of Iowa's ASC cares for approximately 20 patients each day. The last patient is admitted each day by 4:00 PM. The 40% of patients who undergo monitored anesthesia care bypass the phase I PACU. Patients admitted to the phase I PACU have an average length of stay of 30 min. Patients are typically discharged home from the phase II in 1 h. The PACU employs five full-time nurses. As a measure of model validity, the value calculated by our computer model for this scenario was also five nurses (Table 2, Row 5).

An important difference between the results for part-time and full-time nurses is the expected reliability of predicted decreases in labor costs by the computer simulations. For example, consider a 20% or 30% increase in the phase I PACU bypass rate that may be achieved by introducing a rapid emergence protocol ^{[3,10]}. For part-time nurses, each such increase in the bypass rate causes a decrease in PACU nursing (moving within each row of Table 1 to the right shows a decrease in the number of nursing hours). In contrast, for full-time nurses, such an increase in the bypass rate does not always cause a decrease in full time nursing staff (Table 2). An ASC with full-time staff may want to evaluate expected decreases in PACU staffing for a range of bypass rates, in case the expected increase in the phase I bypass rate is less than expected. An ASC with full-time nurses is more likely to achieve decreases in labor costs as the number of patients in the ASC increases (Table 2).

## Conclusions

The focus of this work was twofold. First, we wanted to answer two current operational questions. The Tables are the concrete output of the simulations that should allow ASCs to estimate the decreases in labor costs from implementing currently touted rapid emergence and PACU bypass recovery protocols. Simulation modeling permitted us to deal with multiple uncertainties in OR and PACU staffing that would have required an impractical data collection period to study clinically (see Appendix 1). Second, we wanted to generate an appreciation of how computer simulation techniques can help an OR manager to estimate potential decreases in costs from implementing a process improvement.

Decreases in labor costs are possible from faster emergence and increased phase I PACU bypass rates. The range of decreases in cost depends on how the OR and PACU are scheduled, how nurses or technicians are paid, their salaries, and how many patients an ASC cares for in a day. Using the conditions described in our examples, the greatest decreases in labor costs ($7.39 per case) can occur at ASCs with full-time nurses with frequent overtime.

## Appendix 1

### Numerical Methods

Simulation modeling permitted us to deal with multiple uncertainties in OR and PACU staffing that would have required an impractical data collection period to study experimentally. In particular, Table 1 and Table 4 could have been developed experimentally at the same time as Table 2 and Table 3. To create Table 2 would have required more than (32 rows) x(7 bypass rates) x(>1000 PACU work days simulated)/(250 work days per year) = 896 yr of data collection. If we consider an ASC to have six ORs, then to create Table 3 would have required (18 scenarios) x ([32,000 OR days to calculate cutoff value] + [32,000 OR days to calculate final result])/([six ORs] x[250 work days per year]) = 768 yr of data collection.

For Study 1, the mean arrival rate of patients into the PACU was calculated ^{[13]} for each 1-min increment of the workday using Assumptions 1-3 and Variables 1 and 2. The times between admissions of patients into the PACU were described by a nonstationary Poisson process and were generated using the "thinning algorithm" ^{[13]}.

For Studies 1 and 3, the calculated number of full-time PACU nurses needed on a simulated day = the maximal value of (number of nurses needed in the phase I PACU at each 1-min increment of the workday) + (number of nurses needed in the phase II PACU at each 1-min increment of the workday). For Study 3, in an effort to minimize labor costs, an ASC would typically schedule these full-time PACU in two or three overlapping shifts with the overlap occurring at the time of the peak number of patients ^{[6]}. The number of hours of part-time PACU nurses for a simulated day = ([the sum of the number of nurses needed in the phase I PACU over all 1-min increments of the workday] + [the sum of the number of nurses needed in the phase II PACU over all 1-min increments of the work day])/(60 min per hour). Simulation runs were repeated until the width of the 95% confidence interval for the mean number of nursing hours each day was <1% of the mean and either the width of the confidence interval for the 95th percentile of the maximal numbers of nurses scheduled equaled zero nurses or the width of the confidence interval for the 95th percentile equaled one nurse and at least 1000 days had been simulated ^{[11,13]}.

For Studies 2 and 3, each case was assigned a random time duration from a statistical distribution. To choose a statistical distribution for case durations, we evaluated 300 sequential cases performed at the University of Iowa in June 1997. Although case durations themselves were not normally distributed, their logarithms were normally distributed (ExpertFit; Averill M. Law & Associates, Tucson, AZ, 1997), as confirmed by using the distribution function difference plot, density/histogram over plot, and Lilliefor's test (P = 0.67). Therefore, simulated case durations were generated using a log-normal distribution. First, a normally distributed random number was generated using the polar method ^{[13]}. We achieved large decreases in computational time by using this method rather than the Box and Muller algorithm ^{[13]}. Second, a log-normally distributed random number was generated from the normally distributed random number ^{[13]}. Random effects analysis of case durations at the University of Iowa showed that differences in mean surgical case durations among suites was not associated with differences in the standard deviation of the logarithm of surgical case durations among suites. Therefore, this step used a standard deviation of the logarithm of case duration 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 OR time available each day or 8 h. For example, if the case duration equaled 10 h, we assumed that the case would be scheduled in the OR suite by considering the case duration to equal 8 h. The same scheme was used for turnover times (patient out to patient in). Based on the same criteria as for case durations, turnover times followed a log-normal distribution. We used a mean +/- SD of 0.3 +/- 0.2 h, as is appropriate for the University of Iowa's ASC.

Computer code was written in Microsoft Excel Visual Basic.