Many hospitals in the United States of America (USA) are losing money (1). Some are trying to lose less money by doing more cases. In this study, we focus on how to increase the hospital contribution margin (i.e., revenue minus variable costs) so that hospitals can better cover their large fixed costs.
Our analysis specifically applies to surgical suites that limit the hours that operating room (OR) staff (e.g., nurses, anesthesiologists, and nurse anesthetists) are available to care for patients undergoing elective surgery. This means that staffing costs are fixed. For example, the analysis applies to surgical suites in which elective cases are scheduled only if they can reasonably be expected to be completed before the end of the regularly scheduled day (e.g., 7 am to 3 pm) (2). Our analysis does not apply to surgical suites where surgeons can add on elective cases, at their discretion, which would be expected to finish after the end of the regularly scheduled day.
Hospitals that limit the hours for elective cases to the regularly scheduled day can aim to maximize utilization of the surgical suites. Keeping adjusted utilization relatively high (e.g., 90%) maximizes revenue (i.e., total hours of elective cases) without increasing costs. “Utilization,” in this context of OR staffing, is expressed as a ratio. The numerator equals total hours of elective surgical cases including turnover times. The denominator equals the available, staffed OR hours for elective cases (3–5). Every use of the word “utilization” in this paper is “adjusted utilization” as defined by the Association of Anesthesia Clinical Directors glossary (5). As such, a utilization of 90% corresponds to patients being in an OR for 75 to 80% of the staffed OR hours.
Some hospitals in the USA may sign contracts at discounted rates to increase surgical clinic volume, increase OR utilization, and increase revenue. The rationale for this strategy is that if current OR utilization is 90%, the surgical suite is still 10% empty. The number of hours of cases can be increased by 11%, where 11% equals 100%/90% − 100%. If the surgical suite were able to schedule the additional cases so that they would be expected to be completed before the end of regularly scheduled hours, staffing costs would not be increased (2,6).
To obtain the new cases, a reduction (e.g., 15%) in the average fee-for-service payment may be required. The goal of this study was to test whether increasing eligible patient volume while being reimbursed less for each additional patient can reliably achieve an increase in revenue when initial OR utilization is 90%. We determined, using computer simulation (3,7,8), the revenue impact of using a 15% reduced fee-for-service contract to increase the volume of referred patients by 11% at a surgical suite with a 90% utilization. We evaluated whether the revenue would likely increase by the full 9%, where 9% = (11% increase in volume × [100% full fee − 15% discount]). We hypothesized that efforts by some hospitals to increase OR utilization by signing deeply discounted contracts can adversely affect profitability by paradoxically decreasing revenue. We also performed a series of studies (sensitivity analyses) to determine why our findings occur and under what conditions they hold.
We designed a mathematical model that was built to “act like” a surgical suite with respect to surgical case scheduling. Simulated cases were scheduled into OR block time. After simulating the creation and scheduling of thousands of cases, OR utilization was calculated. The revenue that a hospital would achieve if a 15% reduced fee-for-service discount were applied was then calculated, with revenue considered to be proportional to OR time used (i.e., the more the utilization, the more the revenue). Mathematical details of the computer simulations are given in Appendix 1.
The baseline computer simulations had the following assumptions and parameters.
The number of workdays between successive patients’ requests to be scheduled for surgery was assumed to be exponentially distributed (7). This implies that the timing of when a patient makes his or her request to be scheduled for surgery is not affected by how many days the patient expects to wait to have surgery. The exponential distribution is characterized by the mean number of patients who request each week that the surgeon care for them in the OR. The value of this parameter was chosen using the method described in the Appendix.
Each case was assigned a scheduled time duration generated randomly (8) from a log-normal distribution (3) with mean ± sd = 3.79 ± 2.36 h or 1.63 ± 0.92 h. These distributions describe the scheduled durations of all the elective cases performed at the University of IA’s hospital surgical suite (n = 25,634) and ambulatory surgery center (n = 12,235), respectively, between June 1, 1994 and June 30, 1997. At the hospital surgical suite, cases are a mixture of inpatient, tertiary procedures and outpatient procedures. The corresponding 10th and 90th percentiles for these two probability distributions are 1.5 and 6.7 h for the longer (tertiary) surgical cases and 0.7 and 2.8 h for the shorter (ambulatory) cases.
Scheduled turnover times (“patient out” to “patient in”) in the turnover times equaled 30 min for the hospital surgical suite and 15 min for the ambulatory surgery center. We used constant times because at surgical suites turnover times are usually scheduled as being constant durations.
The surgical suite allocated to the surgeon (3) one 8-h block of OR time each week.
Each patient requested to be scheduled for surgery on the first available date with sufficient open block time for the case.
Patients balked (i.e., left the queue for surgery) if they would have to wait more than 8 wk for surgery. This means that they would either receive care at a different surgical suite or not receive care.
Increasing the number of cases does not increase costs.
We also modified the above baseline case by considering six separate scenarios.
Sensitivity Analysis #1.
We modified Assumption #5 by specifying that each case was scheduled into the block that permitted the case to be completed as early in the day as possible. This method was designed to simulate a surgeon requesting the first block with a “first case of the day” start. If a “first case of the day” start was not available, the computer considered the surgeon to request the block permitting surgery as early in the day as possible. If blocks had the same amount of open time, the case was scheduled into the block permitting surgery on the earliest possible date.
Sensitivity Analysis #2.
We modified Assumption #6 by specifying that patients would choose to not be scheduled for surgery if they would have to wait longer than 4 wk for surgery.
Sensitivity Analysis #3.
We modified Assumption #4 by specifying that the surgeon has been allocated two 8-h blocks per week, instead of one.
Sensitivity Analysis #4.
We modified Assumptions #2 and #3 by assigning cases scheduled time durations generated randomly (8) from a log-normal distribution (9) with a mean ± sd of 0.25 ± 0.25 h. By doing so, we investigated the impact of having a very short duration, as applies for many surgical clinic appointments (9). For these short visits, we used a scheduled turnover time of 0 min. We performed this sensitivity analysis to investigate the differences between hospital surgical suites, ambulatory surgical suites, and hospital clinics. In particular, we hypothesized that the two differ because of the “bin packing” nature of OR scheduling for hospital surgical suites with limited hours for elective cases. This means that when case durations are relatively long compared with the limited hours, only a small discrete number of items (cases) can be packed (i.e., scheduled). By simulating the surgical clinic with its very short case durations, we considered a scenario without a bin packing component.
Sensitivity Analysis #5.
We performed this sensitivity analysis to examine further why hospital surgical suites may differ from ambulatory surgery suites in the relationship between patient volume and utilization. At a hospital surgical suite with a median of two cases per OR per day, random variation in the timing of patients’ requests to be scheduled for surgery may have a large effect on utilization. If the queue is brief, and one patient happens to be ready to be scheduled for surgery just late of the cutoff the working day before surgery, utilization decreases significantly because each patient contributes a lot to utilization on any one day. In contrast, for an ambulatory surgery suite with several patients per OR per day, random variation in the timing of patients’ requests to be scheduled for surgery may be less important. To test whether this effect has a substantive impact on differences between hospital and ambulatory surgery suites, we repeated the simulations after increasing the number of patients requesting to be scheduled for surgery 10-fold.
Sensitivity Analysis #6.
An increase in utilization can require an increase in variable costs (e.g., an increased used of disposable supplies). Equivalently, to attract new patients, the hospital may provide additional services to surgeons whose use will be related to patient volume (e.g., free parking and food). We evaluated this using a mathematical derivation in Appendix 2.
Sensitivity Analysis #7.
To test our hypothesis that results would be substantively different for surgical suites with a relatively low utilization, we repeated the baseline case with an initial lower utilization of 80%.
The computer simulations predict that, for a surgical suite with a 90% (adjusted) utilization, increasing the volume of referred patients by the amount expected to fill the surgical suite (100%/90%) would increase utilization by <1% for a hospital surgical suite (with longer duration cases) and 4% for an ambulatory surgery suite (with short cases) (Fig. 1). The remaining patients would balk at the long waits, and either receive surgical care at a different surgical suite or not receive surgical care.
With a 15% reduction in payment for the new patients, the simulations predict there to be no increased revenue for the hospital surgical suite because of increasing case volume, and perhaps even a decrease in revenue and contribution margin. This occurs because the additional patients simply displace other more lucrative patients from OR time. There can still be a small financial benefit for an ambulatory surgery center, the difference being that its cases are shorter than those of the hospital surgical suite.
Sensitivity analyses #1 to #3 show that the results hold qualitatively as parameter values are changed (Table 1). For a hospital surgical suite with a relatively long average case duration, an increase in patient volume designed to “fill” the surgical suite may not increase revenue.
We performed, in sensitivity analysis #4 and #5, two simulations to test whether results were accounted for by the “bin packing” nature of OR scheduling for surgical suites with limited hours for elective cases. Increasing patient volume by 11% increased utilization by 7% for a clinic with very short cases. The results were less sensitive to increases in patient volume, in that utilization of the hospital surgical suite increased to only 94% from 90% when the number of patients requesting to be scheduled for surgery was increased 10-fold.
For sensitivity analysis #6, we found that if the fraction of total cost that is variable is greater than zero, then the increases in contribution margin achieved by increasing patient volume will be even less than shown in Figure 1 (see mathematical proof in Appendix 2).
We confirmed, in sensitivity analysis #7, that results would be substantively different for surgical suites with an initial lower utilization than 90%. Increasing patient volume for the hospital surgical suite from 80% to the level expected to fill the surgical suite (i.e., by 100%/80%), resulted in an increase in utilization of 6%. With a 15% reduction in payment for the new patients, revenue would increase by 5%. If nonlabor variable costs were incurred in adding new cases (e.g., more sutures), then the increase in contribution margin would be less.
Hospitals may try to attract new surgical volume by offering discounted rates and/or by providing additional (costly) services to surgeons. For hospitals with a relatively high adjusted OR utilization (e.g., 90%), the computer simulations predict that increasing patient referrals by the amount expected to “fill” the OR (e.g., by 11% = 100%/90%), would actually increase utilization by <1% for a hospital surgical suite (with long cases) and 4% for an ambulatory surgery suite (with short cases). The increase in patient volume would simply result in longer patient waiting times for surgery and more patients leaving the surgical queue. The net effect of increasing patient volume will most likely be a decrease in contribution margin. This occurs because the additional patients may displace other more lucrative patients from the OR time.
At ambulatory surgical suites with shorter cases, a small increase in utilization and revenue may be achievable. For health care systems with both a hospital surgical suite and an ambulatory surgical suite, the impact on revenue would be in between these two results. However, if negotiating discounted rates for some patients were to influence future negotiations with previously nondiscounted contractors who subsequently demand similar discounts, contribution margins and profitability may decline.
Our results apply to surgical suites at which OR time is allocated to surgeons based on OR utilization and elective cases are scheduled provided they can be completed during regularly scheduled hours. Our analysis applies also to surgical suites that schedule elective cases provided they can almost be completed during regularly scheduled hours. The reason that our results also apply to the latter surgical suites is that at such surgical suites with a high OR utilization, the use of some flexibility (e.g., 15 minutes) in scheduling cases is no different than extending the duration of the regularly scheduled day by that duration (i.e., by the 15 minutes) (2). However, our analysis does not apply to surgical suites where the mission statement from the perspective of case scheduling includes caring for all of the surgeons’ patients on whatever day the surgeon may choose (3,10–13).
Explanation for Our Findings
We performed simulations of clinic scheduling to understand why it differs fundamentally from OR scheduling. Even for the surgical clinic where appointments are of shorter duration than cases in the surgical suites, increasing volume by 11% does not increase utilization to 100%. Patients’ requests to be scheduled arrive randomly rather than constantly. When there is an open appointment, there may not be a patient request to fill the slot. The smaller increase in utilization for the hospital (long case durations) rather than the ambulatory surgery center (shorter case durations) or clinic results from the combined effect of there being both fewer patients (so that random variation in timing of patients’ requests has a larger proportional effect) and poorer “packing” of the case durations into an 8-hour workday.
We showed that it was the “bin packing” nature of the OR scheduling problem that was most important in resulting in the finding that an 11% increase in the number of patients requesting to be scheduled for surgery hardly increased utilization for the hospital surgical suite. This means that there was a large impact of the phenomenon that for the hospital surgical suite only a small discrete number of cases could be scheduled (i.e., “packed”) into each OR each day. On average, if an 8-hour block had a 90% utilization, then 0.8 hr remained. To put a case into 0.8 hr, first there was a 0.5 hr turnover. Therefore, there needed to be a case with a 0.3 hr scheduled duration. This was less than the first percentile for scheduled durations. Results may therefore differ quantitatively, but not qualitatively (3), for surgical suites with blocks longer than 8-hours.
Predicting Impact of Individual Contracts
When OR utilization is high (i.e., 90%), the increase in revenue achieved by increasing caseload is sensitive to how the surgeon chooses the day of surgery, the number of weeks that patients are willing to wait for surgery, the statistical distribution of case duration, and how many days per week the surgeon cares for patients at the surgical suite (3). As described in Appendix 1, the computer simulations used these parameters to predict the effect of increasing patient volume on OR utilization. Few of these parameters will likely be known with sufficient precision for a financially useful prediction when a hospital considers a new contract (for details see sections 3 and 7 of reference (3)). An OR manager may want to know something like: “At what [high] utilization can no additional patients be accommodated at our surgical suite without increasing staffed OR time?” The imprecision of parameter values means that this question cannot be answered reliably for any one surgeon or surgical group with a high utilization unless the OR manager can wait and collect many years of data (3).
The imprecision of parameter values means that when utilization is large, the financial impact of a contract that will increase caseload but decrease payment per hour of OR time will be difficult to predict accurately using existing statistical methods. A statistically practical solution for the OR manager at such a surgical suite is to change the strategy in scheduling elective cases from allocating OR time based on a surgeon’s utilization of his or her OR time to allocating OR time based on his or her contribution margin (14). However, this may alienate some surgeons, and may conflict with educational missions, charitable initiatives, and public relations. The OR manager could also change the strategy in scheduling elective cases to performing all of the surgeons’ elective cases (3,10–13). Unfortunately, this strategy can decrease workplace satisfaction of the nursing staff and anesthesia providers.
Validity of Simulation Results
We simulated 11 different scenarios. We used computer simulation in this study, because it was impractical to study experimentally the effects of discounted contracts on OR utilization and hospital revenue. Several hundred years of data collection (3) would have been required for each of 11 different surgical suites.
Our simulations were designed intentionally to overestimate the potential increase in utilization and revenue from increasing caseload because we neglected other important factors. For example, we did not model the impact of surgeons taking their cases elsewhere because the surgical suite was “inadequately staffed.” No cases were cancelled in the simulations once the case was booked. No surgeon moved his or her surgical day because of a vacation, conference, or illness. Every patient chose to have surgery on the day recommended by the surgeon. To the extent that all of these assumptions are unlikely to hold “in the real world,” when we say that for a hospital surgical suite once utilization is 90% an increase in caseload will not increase utilization further, this result is reliable.
Implications for Academic Medical Centers
Many academic medical centers in the USA follow the scheduling strategy that we studied, of limited hours for elective cases. Some of these hospitals try to increase OR utilization by signing deeply discounted contracts, with the intention of increasing revenue so as to cover their large fixed costs. Our simulations provide insight into why this practice can adversely affect profitability of the hospital.
We think that our simulations may also be of assistance to OR managers pressured by hospital administrators and other parties to increase already high OR utilizations. We showed that it will generally be difficult to increase utilization beyond 90% at hospital surgical suites, although a precise quantification for each surgeon or surgical group is unrealistic statistically (3). Our results show that scheduling the hospital surgical suite is inherently different than other aspects of hospital scheduling, because of the bin packing nature of OR scheduling.
Appendix 1. Computer Simulation Methodology
For the computer to generate simulated surgical cases, the mean number of cases to be scheduled for surgery each week (assumption #1) had to be known. However, the analyses started with the mean number of cases per week that achieved a 90% utilization. We identified this parameter value by first performing simulations using an arbitrary value for the mean number of cases per week. Once the mean utilization had been calculated, a new mean number of cases per week was chosen. The process was continued using trial and error until the mean number of cases per week was known, to within 0.1 patients per week, which resulted in the mean utilization equaling 90%. That mean number of cases per week was then used in the analyses. In particular, the value was increased by 11%, simulations were performed, and mean utilization was recalculated.
We wrote the computer code in Excel Visual Basic 6.0 (Microsoft, Redmond, WA) to perform the simulations in the following sequence.
Step #1. The computer used a random number generator (8) to generate the length of time (e.g., 0.5 days) until the next patient requests to be scheduled for surgery.
Step #2. The computer used a random number generator to generate the duration of the new case. Surgical case duration was described using a log normal distribution, with the result right truncated (3,8).
Step #3. If the width of the 95% two-sided confidence interval for mean percent utilization was <0.05%, the simulation was halted. The confidence interval was calculated using the replication/deletion approach for means (8), using a batch size of 100 blocks to eliminate auto-correlation between successive blocks (3) and an arcsine transformation because utilization was a percentage (15).
Step #4. Using the time remaining in each future block, the duration of the case from step #2, and the turnover time from assumption #3, the computer determined the available surgical date.
Step #5. The probability that the patient would balk when offered that date was calculated as a linearly increasing function (7) between a probability of zero for a 0 day wait and a probability of one for the maximum wait from assumption #6. A uniformly distributed random number was generated and compared to the probability that the patient would balk. The patient was then either scheduled for surgery or considered to no longer desire surgery at the surgical suite.
Step #6. The simulation returned to step #1.
If a surgical suite schedules cases using the mean of the durations of historical cases of the same procedure type, then utilization calculated using scheduled durations equals utilization calculated using actual durations (2,6,10).
Appendix 2. Effect of Variable Costs on Increase in Contribution Margin
The variable costs considered are those that vary in direct proportion to workload (e.g., disposable supplies or medical records work), not OR labor. We define CMold as old contribution margin ($), CMnew as new contribution margin ($), Uold as old utilization (proportion), Unew as new utilization (proportion), Krevenue as revenue if utilization was 100% without discounts ($), Kdiscount as discount (proportion), Pdiscount as patients discounted (proportion), and Kvariable as variable costs if utilization was 100% ($).
Then,MATHMATHThus,MATHIf an increase in utilization would cause an increase in variable costs (e.g., from supplies), then Kvariable > 0. Because Unew ≥ Uold, then the increase in contribution margin achieved by increasing volume would be less than if costs were fixed (i.e., if Kvariable = 0).
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