At many surgical suites, the surgeons and patients can schedule their elective cases on whatever future workday they choose, which results in there being no limit on the number of cases performed each workday. In addition, labor contracts specify that hourly staff are paid to work a minimum number of hours each day (e.g., 8 h). Staff are then scheduled in the manner that satisfies the “marketing guarantee” to the surgeons, satisfies the labor contracts, and minimizes staffing costs. To do this, cases are scheduled in each operating room (OR) without planned delays between cases (1), and overtime is essentially mandatory (2). We refer to this system as the mission statement, or business model, of the surgical suite.
Statistical methods to minimize staffing costs (i.e., maximize labor productivity) have been developed for such surgical suites (2–4). Using data from the surgical suite’s OR information systems, the statistical methods determine how many staffed ORs should be available each day for each surgical service and how long shifts should be scheduled to last (2,3).
Although the statistically derived staffing solutions may be optimal, it is unknown whether staffing costs using these methods can be significantly less than those already implemented by practicing anesthesia group managers, based on their experience and the data. We suspect, for example, that the manager of an office-based surgical suite with one OR would do just as well as a statistical analysis at determining whether to staff the one OR for 8, 10, or 12 h. We also suspect that a statistically derived staffing solution can provide for decreased staffing costs at a 60-OR surgical suite than an empiric solution determined by a manager based just on data and experience. We did not know at how large of a surgical suite statistical algorithms can be expected to identify staffing solutions of a decreased cost than those obtained based on a manager’s experience alone.
The CalculatOR (Medical Data Applications, Ltd., Jenkintown, PA) software combines the previously published algorithms (2–4) giving the smallest possible staffing cost and highest labor productivity with graphical and inferential statistical tests (5) of the assumptions of the statistical methods to ensure that they give the correct answer. In this study, we used CalculatOR to assess weekday anesthesia group staffing at nine independently managed surgical suites that follow the above mentioned mission statement. What these surgical suites had in common was that the hospital managements were sufficiently concerned about costs that they hired us to review nurse anesthetist staffing. This suggests that the anesthesia group managers were under pressure to decrease costs. We used staffing and OR data from these surgical suites to test whether the statistical method can identify staffing solutions whereby all the cases are covered but for which nurse anesthetist staffing costs are less than those obtained using the staffing plans developed and implemented by the anesthesia groups’ managers.
Two years of historical data were analyzed from the surgical suites. The start and end times and surgical groups for all OR cases performed during the workdays were exported from the surgical suites’ information systems into CalculatOR. Surgical groups comprised one or more surgeons who shared allocated OR time (e.g., a burn team). Total hours of elective cases (from time of patient entrance into an OR until his or her exit from the OR) and turnover times were then calculated (6) for each service on each day (2) of the week.
A first-shift staffing solution for a surgical group on a day of the week is a combination of the number of ORs allocated to the surgical group and for each of these ORs how long the staff are scheduled to work: 8, 10, or 13 h (3). For example, a first-shift staffing solution for a cardiac surgery group on Mondays might be two ORs, one with staff scheduled to work 8 h and the other for 13 h. The “best” staffing solution for a surgical group minimizes the sum of under-utilized hours (staffed first-shift hours during which no cases are performed) and the relative cost of overtime multiplied by the sum of over-utilized hours (OR hours after the scheduled end of the first shift) (2). An overtime ratio of 1.75 was used, because the anesthesia groups’ managers considered the federally mandated overtime rate of 1.5 times the regular hourly wage to underestimate the true cost of overtime. The additional factor of 0.25 was used to account for the fact that frequent, mandatory overtime can lead to employee dissatisfaction, resignation, and recruitment costs (4).
We found the smallest cost first-shift staffing solution by considering all possible staffing solutions (3), starting with 0 h and progressively increasing the staffed hours until additional increases in the staffed hours caused the sum of under-utilized hours and over-utilized hours times the overtime rate to increase. If providing 0 h to a service resulted in less cost than providing the minimum of one OR for 8 h, then no OR was assigned to that surgical group for that day and all such groups were combined into an “other” service. The solution for the “other” service was then calculated. At least one OR was allocated for “other” services for at least 8 h each day of the week. In addition, we created a phantom “urgent” service to incorporate all urgent and emergent cases performed, at least in part, during the first shift. If on a day of the week a surgical suite had too few urgent case hours to warrant allocation of an OR but the surgical suite was a designated trauma center, then one OR was allocated.
CalculatOR implemented the second-shift analyses exactly as previously (4) described. We applied it to the maximum number of ORs with a case in it between 3:30 pm and 11:00 pm to determine the number of anesthetists who should be scheduled to work second shift to minimize staffing costs (4). When there was no difference in costs between two choices (e.g., zero second-shift anesthetists and more overtime costs versus one second-shift anesthetist with more scheduled hours), the choice with the fewer number of second-shift anesthetists was used (see Discussion).
The total cost for the statistically-derived first- and second-shift staffing solutions for each surgical suite was determined by applying the best staffing solution for each surgical group, and summing daily costs in contiguous 4-wk (6) periods. Cost for a 4-wk period was calculated by multiplying the regular hourly wage by the sum of first- and second-shift scheduled hours for the 4-wk period and 1.75 times the number of hours of overtime during the 4-wk period (4). Student’s t-test was used to calculate confidence intervals for the difference in cost among 4-wk periods (6) between using just 8-h shifts versus 8-, 10-, and 13-h shifts. Comparison was also made using Student’s t-tests between the cost of the anesthesia groups’ managers’ OR staffing to the cost of the statistically-derived first- and second-shift staffing solutions with 8-h shifts. Staffing for breaks and anesthesia service outside of the surgical suites was excluded. In that the data were available previously to the managers, our analysis focused on the value of the statistical analysis of the data, not the data itself.
Data were not available for which OR in each surgical suite the anesthesia group managers had assigned each second-shift anesthetist each day. We therefore deliberately designed the cost accounting methodology to underestimate the true difference between the cost of the OR manager’s current staffing to the cost of the statistically-derived first- and second-shift staffing solutions. In particular, we assigned second-shift anesthetists in the manner which minimized total costs, and thus minimized the potential incremental benefit of the statistically-derived staffing solutions.
The first-shift staffing solution and the cost accounting methodologies assumed that there were no systematic differences among weeks in the expected workload of the surgical suite. We confirmed this assumption of no trend or autocorrelation for all surgical suites by applying the runs test to the total cost over each consecutive 4-wk period (5).
The statistical methods identified staffing solutions with significantly smaller staffing costs than those currently being used at eight of the nine surgical suites (Table 1). For seven of the nine surgical suites, the statistical method identified anesthesia staffing plans with costs which were at least 10% less than the costs of the plans used by the managers. The surgical suite at which the manager’s staffing achieved costs which were as small as possible was the smallest surgical suite, with only two ORs.
Table 2 provides an example of how the statistical method identified a staffing solution with less cost than the manager’s staffing solution at a seven-OR, community, multiple specialty surgical suite. Table 1 shows that there was variation among surgical suites in the ways in which the statistical methods identified staffing solutions with smaller costs than the plans used by the managers. At four of the nine suites, the number of staffed ORs per day was more than 10% higher than optimal to minimize costs; however, at two suites, too few ORs were being staffed to minimize costs. For seven of the suites, decreased costs could be achieved by varying the number of staffed rooms by more than 10% among days. Whereas all managers used the same staffing plan for Monday through Friday, the statistical method considered each day of the week separately. For five of the suites, second-shift staffing (expressed as a percentage of total staffed hours) could be reduced by more than 10%. The statistical methods relied on overtime instead of assigned second shifts. Cases would also be scheduled sequentially into ORs.
Rather than having first-shift staff work 8-h shifts each day, overlapping 8-, 10-, and 13-h shifts could be used (Table 3). This would result in fewer first-case of the day starts for the surgeons and longer hours for the OR staff, but potentially fewer staffing costs. Nevertheless, the incremental decrease in staffing costs achievable by using overlapping 8-, 10-, and 13-h shifts was much smaller financially than the decrease between using statistically-based staffing versus that developed by the anesthesia group managers.
The surgical suite originally with 12 staffed ORs had both the largest average decrease in the number of first-case of the day starts and the largest difference between current costs and those of a staffing solution identified by the statistical method. Organizational barriers may prevent the relatively large (theoretical) decreases in the number of first-case of the day starts recommended by CalculatOR. We investigated how much of the cost difference was accounted for by the decrease in the number of first-case of the day starts. We increased the overtime ratio in increments of 0.25 until we achieved 12 ORs. The overtime ratios which achieved 12 staffed ORs were, for Monday to Friday, 4.75, 3.5, 6.0, 6.0, and 3.5. The implication of staffing 12 ORs on Wednesdays and Thursdays was that if offered a paid 8-h day off in the future for working 11/2 h of unplanned overtime, the anesthetists would prefer to not work the overtime. We repeated the analysis in Table 1 for this surgical suite using the revised ratios for each day of the week to assign ORs, but continued to cost account for overtime using a ratio of 1.75 (see Methods). With staffing 12 ORs each day at this surgical suite, the percentage difference between current costs and those identified by the statistical method decreased from 45% to 22%, which is in line with the percentage decreases from the other surgical suites. The increase in total staffed hours that were overtime decreased from 12% to 4%, because of the increase in the number of first-case of the day starts. There remained the 27% decrease in total staffed hours that are second shift.
At surgical suites where the surgeons and patients can schedule their elective cases on whatever future workday they choose, there is no limit on the number of elective cases performed each workday. If, in addition, hourly staff are paid to work a minimum number of hours each day, then either frequent overtime, overlapping 8-, 10-, and 13-hour shifts, or second-shift staff will be required. For seven of the nine surgical suites, the least expensive approach was to use overtime, despite valuing overtime at 1.75 times the regular hourly rate. At such surgical suites, to minimize costs, only as many anesthetists should be assigned to work second shift as are needed to provide coverage for urgent cases. Only if there are no queued urgent cases should the second-shift anesthetists be used for relief purposes. Instead, relief should be handled by having some first-shift anesthetists assigned to work late each day and relieve others when their own cases finish. Statistical methods are available to assist the OR and anesthesia managers in choosing which rooms to relieve first to minimize costs (7).
Anesthetists at a surgical suite may consider mandatory overtime to be markedly undesirable. Then, a ratio larger than 1.75 can be used (e.g., 2.0), which will result in providing surgical groups with more first-case of the day starts, surgeons less likely to need to follow one another, and thus cases finishing earlier in the day. Likewise, if overtime costs are large because the surgeons are scheduling many hours of cases each day, the appropriate staffing solution may be not to use longer (10- or 13-hour) shifts but to open more ORs (Table 3). Overlapping 8-, 10-, and 13-hour shifts may be useful when the number of ORs needed to be staffed each day to minimize costs exceeds the physical number of ORs, as in the five-OR surgical suite in this study (Tables 1, 3). The methods described in this study may have value in providing quantitative, statistically reliable, analysis to hospital administrators in deciding whether to build more ORs.
Eight of nine management teams had developed and implemented weekday OR staffing plans that were more expensive than a solution identified by statistical analysis of data from their OR information systems. For seven of the nine surgical suites, the statistically-identified staffing solutions would have satisfied the surgical suites’ scheduling “mission statement” while saving more than 10% per year. For six of the nine surgical suites, the difference in staffing costs exceeded US$100,000 per year. Since this study was completed, the surgical suite with only two ORs was closed because its relatively high labor costs could not be reduced by altering staffing.
We calculated decreases in staffing costs (i.e., increase in labor productivity) using nurse anesthetists’ staffing and pay. In that the identical methodology applies to OR nurses, the true differences in staffing costs may be more than those given in Table 1. However, we did not have staffing data on OR nurses to perform the analysis statistically. The productivity of anesthesiologists differs, because it depends heavily on the number of nurse anesthetists or residents supervised simultaneously (8). We were unable to evaluate scientifically anesthesiologists’ productivity as part of this study because of a lack of sufficiently accurate data on concurrency of care.
We limited consideration to surgical suites at which the surgeons and patients can schedule their elective cases on whatever future workday they choose and the staff labor contracts specify that hourly staff are paid to work a minimum number of hours each day. For such surgical suites, the statistical method does what an anesthesia group manager does: adjusts staffing on a long-term (monthly) basis to minimize staffing costs while satisfying both the “marketing guarantee” to the surgeons and labor contracts. The difference between the statistical methods and current practice is simply that the computer considers millions of different staffing solutions to find the best one to minimize staffing costs while covering the surgeons’ cases. However, anesthesia group managers at surgical suites with a different mission statement from the perspective of elective case scheduling will probably find the changes in staffing recommended by the statistical method to be too onerous for implementation, because the statistical method is predicated on the assumption of performing all of the surgeons’ cases every workday. Different statistical methods are available for surgical suites that care for all elective cases within a “reasonable” (not decided by the surgeon) number of days (1,6,9) and/or have a limited number of hours of OR time for elective cases (10,11).
In summary, we found that statistical methods can identify for some surgical suites staffing solutions whereby all the cases are covered but for which costs are significantly less than those obtained using the staffing plans developed by the managers based on their experience and the data.
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