Scheduling a delay between different surgeons' cases in the same operating room on the same day using upper prediction bounds for case durations

At some surgical suites, elective cases are only scheduled if they can be completed during regularly scheduled hours. At such a surgical suite, a surgeon may be scheduled to perform one or more cases in an operating room (OR), to be followed by another surgeon who will perform one or more cases. Scheduling a delay between the two surgeons' cases will improve the likelihood that the second surgeon's case(s) will start on time. We show that the mathematics of calculating a scheduled delay between the different surgeons' casts in the same OR on the same day is that of calculating an upper prediction bound for the duration of the second surgeon's case(s). We test an analytical expression for the upper prediction bound for the last one case of the day in an OR, and a Monte Carlo simulation method for the last two cases. We show that these 90% upper prediction bounds are at least as long as the actual durations for 90% +/- 0.2% of single cases and 92% +/- 0.6% of pairs of cases. We conclude that our methodology can be used to calculate an appropriate, and reasonably accurate, scheduled delay between two surgeons' cases in the same OR on the same day.