An analysis of sequencing surgeries with durations that follow the lognormal, gamma, or normal distribution

The smallest-variance-first-rule (SV) is generally accepted as the optimal policy for sequencing two surgeries, although it has been proven formally only for several restricted cases. We extend prior work, studying three distributions as models of surgery duration (the lognormal, gamma, and normal) and including overtime in a total-cost objective function comprising surgeon-and patient-waiting-, operating-room-idle-, and staff overtimes. We specify expected waiting and idle time as functions of the parameters of surgery duration to identify the best rule to sequence two surgeries. We compare the relative values of expected waiting and idle times numerically with that of expected overtime. Results recommend that the SV rule be used to minimize total expected cost of waiting, idle and overtime. We find that gamma and normal distributions with the same mean and variance as the lognormal give nearly the same expected waiting and idle times, observing that the lognormal in combination with either the gamma or normal gives a similar result. We extend to the three-surgery case, showing that sequencing the first surgery is most important. We demonstrate how our results can be applied by using them as a basis for a heuristic that assigns surgeries to multiple operating rooms and then sequences them.