Operating room-to-downstream elective surgery planning under uncertainty

Motivated by our collaboration with a hospital, we introduce a new integrated elective surgery assignment, sequencing, and scheduling problem (ESASSP), involving multiple operating rooms (ORs) and downstream recovery units, as well as methodologies for solving it. Data from the collaborating hospital show significant variability and ambiguity in surgery duration and post-surgery length of stay (LOS) in recovery units. To address such ambiguity, we propose distributionally robust optimization (DRO) approaches for the ESASSP. Our DRO models find ESASSP decisions that minimize the fixed cost associated with performing or postponing surgeries plus the maximum expected operational costs related to overtime and idle time of ORs, delays in ORs, and congestion in recovery units. We evaluate the maximum expectation over all distributions residing in (moment and Wasserstein) ambiguity sets of distributions for surgery durations and LOS. We derive a novel characterization of LOS and introduce transformation techniques to derive equivalent solvable reformulations of the non-linear DRO models. Then, we propose a column-and-constraint-generation method to solve the reformulations. We present comprehensive results based on various ESASSP instances constructed using three datasets. Our results offer valuable insights into the ESASSP and demonstrate the practical impact of our proposed integrated approaches. Notably, implementing solutions from our models could significantly reduce congestion in the recovery units, surgery delays in ORs, overtime, idle time, and the associated costs compared with traditional non-integrated approaches.