Dr. Atkin asks five questions that we address individually. Each of the questions adds insight to our original results.
1. “The duration of each simulated add-on case was … not … subjected to a second simulation designed to cause [the] duration to vary around the result of the first selection [i.e. , its mean value]… . Omitting the case duration variance as applied to the simulations could have an important impact on the results.”
We performed the analysis recommended by Dr. Atkin and found that Best-fit Descending with fuzzy constraints remained the best algorithm for maximizing operating room (OR) use. Calculated OR uses were within 0.3 and 0.4% of our original values for the ambulatory surgery center and tertiary surgical suite, respectively. Our methods were to repeat the calculation of OR use for the 10 algorithms, while no longer considering each case’s scheduled duration to equal its actual duration. We did this 1by considering the actual case duration to equal the scheduled duration multiplied by a normally distributed random number with a mean 2of 1.0 and a standard deviation 3of 0.25. This statistical technique was described and analyzed by Kennedy. 4
2. “Were the open times taken from daily, projected next-day schedules, available at the official cutoff time on the scheduling day?”
Yes, this was how we obtained the open times.
3. “In calculating use, did the authors account for overtime caused by the use of ‘fuzzy constraints’ by including additional time in the denominator?”
“The OR utilization [was] calculated using the total hours of regularly scheduled and add-on elective cases, including turnover times.” So, to compensate for the use of fuzzy constraints, rather than adding additional time to the denominator, we subtracted the additional time from the numerator. No “credit” was given for having completed a case outside of regularly scheduled hours.
4. “Long turnover times were truncated at 1 h. Did the authors test the effect of a different maximum?”
We cannot perform the recommended analysis accurately because it is not possible to differentiate retrospectively between turnover times and scheduled delays between cases. We recently discussed this issue extensively. 1
5. “The authors have not provided evidence …that their results are applicable to real problems… .”
When interpreting the applicability of an economic analysis, the relevant question is: To what variables are the results sensitive? If the results depend largely on a variable that varies in the “real world” at a surgical suite, the results will not apply to that surgical suite, and vice versa . Quoting from our Discussion, “Our results are relevant economically to surgical suites that schedule add-on elective cases into open OR time provided the cases are scheduled to be completed during regularly scheduled hours.” Our results are not applicable to surgical suites that do not do this. In addition, “our results are subject to the condition that the surgical suite usually has sufficient additional time in each OR to schedule either zero or one add-on elective case. If only zero or one add-on elective case could be scheduled for each OR, then Best-fit Descending with fuzzy constraints …[will] produce … maximal OR utilization.” This is a mathematical fact—there is no uncertainty in this statement. Our results are not applicable to surgical suites that have many brief add-on elective cases, such that this condition does not apply.