Comparing Policies for Case Scheduling Within 1 Day of Surgery by Markov Chain Models

In previous studies, hospitals' operating room (OR) schedules were influenced markedly by decisions made within a few days of surgery. At an academic hospital, 46% of ORs had their last case scheduled or changed within 1 working day of surgery, and a private hospital had 64%. Many of these changes were for patients who were admitted before surgery (i.e., inpatient cases). In this study, we investigate the impact on OR productivity of how cases are scheduled within 1 working day before the day of surgery.

We consider the case-scheduling choice between 2 ORs. We compare 3 scheduling policies: Best Fit Descending, Worst Fit Descending, and Worst Fit Ascending. "Descending" strategies consider new cases from longest to shortest, whereas "Ascending" considers new cases from shortest to longest. Best Fit schedules each new case into the OR with sufficient but the least remaining underutilized OR time for the case. Worst Fit does the same but with the most remaining time. For our application, Best Fit chooses a later start time, whereas Worst Fit chooses an earlier start time. In our computational model, cases are of 2 possible durations, brief or long. Case cancellation is incorporated explicitly, and the number of new cases to schedule depends on the current number of scheduled cases in each OR, both new from previous studies. The number of cases in each OR is modeled as a Markov chain, evolving between 2 periods, corresponding to 1 day and 0 days before the day of surgery. For each scheduling policy, we evaluate the mean overutilized OR time and productivity. Our sensitivity analyses cover many cancellation rates, arrival settings, case durations, and initial conditions (i.e., how cases are scheduled into the 2 ORs preceding 1 workday before the day of surgery).

Best Fit Descending and Worst Fit Descending achieved almost the same overutilized time and productivity. Worst Fit Ascending caused greater overutilized time (as much as 6.6 minutes more per OR) and thus lesser productivity (as much as 1.6% less) compared with Best Fit Descending or Worst Fit Descending. When the staff were scheduled for less time than the optimal allocated OR time, there were nearly the same differences between the staff productivity resulting from the use of Worst Fit Ascending rather than Worst Fit Descending or Best Fit Descending.

Scheduling office decision making within 1 day before surgery should be based on statistical forecasts of expected total OR workload (i.e., forecasts that include the addition of non-elective cases and the subtraction of cases that cancel). As long as a case is not scheduled into overutilized time when less overutilized time could be achieved in another OR, and cases are considered in descending sequence of scheduled durations, the differences in overutilized time and productivity among the scheduling policies are small. Cognitive bias in staff scheduling causes a significant reduction in productivity, but the differences among scheduling policies are nearly the same as when there is no bias.