Improving operating room schedules

Operating rooms (ORs) in US hospitals are costly to staff, generate about 70 % of a hospital's revenues, and operate at a staffed-capacity utilization of 60-70 %. Many hospitals allocate blocks of OR time to individual or groups of surgeons as guaranteed allocation, who book surgeries one at a time in their blocks. The booking procedure frequently results in unused time between surgeries. Realizing that this presents an opportunity to improve OR utilization, hospitals manually reschedule surgery start times one or two days before each day of surgical operations. The purpose of rescheduling is to decrease OR staffing costs, which are determined by the number of concurrently staffed ORs. We formulate the rescheduling problem as a variant of the bin-packing problem with interrelated items, which are the surgeries performed by the same surgeon. We develop a lower bound (LB) construction algorithm and prove that the LB is at least (2/3) of the optimal staffing cost. A key feature of our approach is that we allow hospitals to have two shift lengths. Our analytical results form the basis of a branch-and-bound algorithm, which we test on data obtained from three hospitals. Experiments show that rescheduling saves significant staffing costs.