We present a novel approach for increasing the operating room efficiency by significantly reducing the turnover time in elective surgical case scheduling. Reduced turnover time typically leads to increased surgeon utilization and increased patient throughput. Our main contribution is an optimization model for generating operating room schedules in a surgery department, where the pre-procedure of a surgical case is allowed to overlap with the procedure and post-procedure activities of an ongoing surgical case assigned to the same operating room. In addition, we present a computational experiment, where we create and compare 1-day schedules for a surgery department consisting of three operating rooms. The results of the experiment clearly show the potential of the idea of allowing overlapping surgical activities. This feature allows for significantly improved schedules compared to when no overlaps are allowed. The experiment also verifies the correctness of the optimization model.