I NTRODUCTION

In this chapter, we applied stepwise regression and best subset to identify the most influential factors that impact the OR utilization. Simulation models were built to validate the results and provided us with more insights into OR utilization management. Based on the

results, to increase OR utilization, the OR management should focus on the scheduling of cases, including the scheduling of add-on cases and management of cancellations. The prediction of the duration of surgery lists is also important in the determination of the utilization as both under- or over-predicted case duration make the actual OR utilization deviate from it scheduled value. For individual case duration prediction, the OR management can refer to the mean case duration of historical cases to assign scheduled case duration as previous indicated this approach provides a simple but useful estimate (Dexter et al.1999, Alvarez et al. 2010).

To manage the OR utilization, it is more important to control the uncertainties brought into the system by the variability of case durations. As illustrated by the simulation study, given the same mean case duration, a higher variability of case duration brings into the system more uncertainty in the patients’ wait time and reduced the optimum utilization and the efficiency of use of OR time. After a certain point, an increase in the OR utilization results in a decrease in the OR cost efficiency; thus 100% utilization should not be the goal of management but how to balance between the under- and over-utilized OR time, which requires an approach that would provide the OR managers with accurate estimates of the probability of under- and over utilization, which is the topic of our next chapter.

CHAPTER 3 PROBABILITIES OF UNDER- AND OVER-RUN OF SURGERY LISTS CONSISTING OF MULTIPLE CASES

3.1 Introduction and Literature Review

Operating room (OR) is one of the most expensive units for any hospitals (Macario et al.

1995, Denton et al. 2007). In order to control the costs, it is important for the OR management to ensure that the allocated OR time is utilized as much as possible with little over-utilized OR time, i.e. maximizing the efficiency of use of OR time (Strum et al. 1997, Dexter et al. 2001, Dexter and Traub 2002, McIntosh et al. 2006). When the duration of surgery lists is longer than the allocated OR time, over-utilized OR time is observed. On the other hand, when the duration is shorter than the allocated OR time, under-utilized OR time is seen and some OR capacity is wasted. In previous chapter, we concluded that the scheduling and the accuracy of case duration prediction are the most important factors that affect OR utilization. And the simulation results suggested that scheduling case use the mean case duration of historical cases and having scheduled OR utilization approximately equal the allocated OR time would generate the optimum OR utilization and efficiency of use of OR time. The simulation also show the importance of control the case duration variability as the higher the variability, the lower the OR utilization and efficiency. Thus, it is important for the OR management to have a reliable tool to evaluate and manage the variability of case duration. When surgeons are allowed to schedule elective cases on any workdays they choose, the maximum efficiency of use of OR time can be achieved by predicting the future OR workload (Dexter et al. 1999) and determining the optimum OR allocation (Dexter et al. 2001, McIntosh et al. 2006). If the costs of over-utilized OR time is 1.75 times the costs of under-utilized OR time, then 2/3 of the ORs’ should be closed within the allocated OR time (McIntosh et al. 2006). In most U.S. OR suites, the decisions on OR allocation can be made every 2-3 months. For these system, the case duration prediction accuracy is less a problem as the decisions on OR allocation take into consideration of the case

duration prediction inaccuracy as they use the actual workload for calculation (Dexter et al.

2001, McIntosh et al. 2006). With more than two historical cases of the same combination of surgeon and procedure(s), the reduction in over-utilized OR time is negligible from a more accurate prediction in case duration model instead of the mean case duration of historical cases. People work late because of the workload rather than underestimation in case durations (Dexter et al. 2004).

However, the OR allocation optimization approach does not apply any more to European OR theaters. In these facilities, the demand for surgery is so high that patients have to enter waiting list and might need to wait months before their surgeries are scheduled. In addition, the allocated OR time is static. The ORs in Europe do not usually change the OR allocation (Pandit and Tavare 2011). The way to maximize the efficiency of use of OR time is to avoid both under- and over-utilized OR time through scheduling versus OR allocation decisions. A method to accurately estimate the duration of surgery lists is needed for this type of system.

Much research has been done in predicting the case duration of single cases (Zhou and Dexter 1998, Strum et al. 2000, Strum et al. 2003, Ejkemans et al. 2010, Li et al. 2010).

However, even with very complicated models, the improvements in case duration accuracy were not enough to significantly reduce the tardiness of case starts (Zhou et al. 1999, Wachtel and Dexter 2009) or were better than simpler methods (Strum et al. 2000, Macario and Dexter 1999). More accurate models only improved the prediction on the central tendency (Zhou and Dexter 1999). As there is high variability associated with case duration (Macario 2009), such improvements only would have limited impacts in practice. Especially when there are multiple cases along with turnover times, the cumulative effects of the high variability make it even more difficult to predict the duration of surgery lists accurately.

The expected duration of surgery lists can be derived using the mean case duration of historical cases. However, the high variability of case durations makes the expected close time of OR not a reliable estimate. It is not uncommon to see the surgery lists under- or over-run by

more than an hour. To have a good efficiency of use of OR time, it is more practical for OR managers to estimate how reliable that the surgery lists can be done within a pre-defined range with some tolerances in both under-utilized and over-utilized OR time. For example, the allocated OR time is 8 hrs, and the OR manager wants to know what the probability is that the scheduled surgery list can be finished between 7 hrs and 8.5 hrs. If the probability is high, such as 85%, then the list can be finalized as it will not generate huge amount of under- or over-utilized OR time. Otherwise, the OR manager can rearrange the cases on the surgery list until an acceptable probability is obtained. This problem has been barely studied in OR setting.

Dexter et al. (Dexter et al. 1999) built an optimization model and concluded that using mean case duration of historical cases to schedule the surgery lists actually generates the optimum efficiency of use of OR time. But their problem is different from ours as it assumed that surgeons had open access to OR and the allocated OR time had been optimized to maximize the efficiency of use of OR time which is not applicable to European systems. Alvarez et al.

(Alvarez et al. 2010) explored if the second tertile cut-off point was better than sum of mean case duration in predicting over-utilization. They reached the same conclusion as Dexter et al.

(Dexter et al. 1999). However, they only studied the cardiovascular surgeries, and the results could not be generalized to other specialties. In 2011, Pandit and Tavare (Pandit and Tavare 2011) proposed a scheduling algorithm with the concept of planning surgery lists based on the probability that the duration of surgery lists would not exceed the defined limits for under- and over-utilization. In their work, the duration of surgery lists was assumed to followed t-distributions with a mean equaling the sum of mean case durations of each case on the surgery list plus the turnover times and a standard deviation equaling the pooled standard deviation from cases scheduled. They proved that this approach was much better than the ad-hoc scheduling approach in their facility. Although their approach generated promising results, the assumption that the duration of surgery lists followed t-distributions is not a good representation of the duration of surgery lists as indicated by previous research that individual surgery case

duration followed normal distributions (Strum et al. 2000, Strum et al. 2003). The sum of log-normally distributed case durations does not follow a Gaussian distribution. The probabilities calculated from t-distribution would deviate significantly from the true values.

In this study, we proposed a new way to approximate the real distribution of the duration of surgery lists. First, we tested the hypothesis that the individual case duration was log-normally distributed. Then, the new distribution was introduced to approximate the true distribution of duration of surgery lists. We checked the accuracy of the proposed method by testing the distribution percentiles generated from the proposed distribution against real data from one-year surgery lists with multiple cases (Zhou and Dexter 1998, Dexter et al. 2001, Dexter and Ledolter 2005). If the percentiles were accurate, then the proposed distribution should be close to the real distribution. We compared the results from the proposed distribution with the results generated by t-distribution (Pandit and Tavare 2011). After this, we identified the optimum number of previous cases for the combinations of surgeon and procedure(s) to derive reliable parameters of case duration distribution to facilitate the implementation of the proposed method in practice.