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We considered elective case scheduling at hospitals and surgical centers at which surgeons and patients choose the day of surgery, cases are not turned away, and anesthesia and nursing staffing are adjusted to maximize the efficiency of use of operating room (OR) time. We investigated scheduling a new case into an OR by using two patient-scheduling rules: Earliest Start Time or Latest Start Time. By using several scenarios, we showed that the use of Earliest Start Time is rational economically at such facilities. Specifically, it maximizes OR efficiency when a service has nearly filled its regularly scheduled hours of OR time. However, Latest Start Time will perform better at balancing workload among services’ OR time. We then used historical case duration data from two facilities in computer simulations to investigate the effect of errors in predicting case durations on the performance of these two heuristics. The achievable incremental reduction in overtime by having perfect information on case duration versus using historical case durations was only a few minutes per OR. The differences between Earliest Start Time and Latest Start Time were also only a few minutes per OR. We conclude that for facilities at which the goals are, in order of importance, safety, patient and surgeon access to OR time, and then efficiency, few restrictions need to be placed on patient scheduling to achieve an efficient use of OR time.