Semi-cyclic rostering of ranked surgeons — A real-life case with stability and flexibility measures

We consider the rostering problem for surgeons in residency at the Clinic of Surgery at St. Olav’s Hospital, Trondheim University Hospital, in Trondheim, Norway. Each surgeon in residency has a rank depending on experience. An exact number of surgeons of each rank must work emergency shifts in a cyclic structure. Each surgeon is affiliated to a section, which has a minimum staffing level. Section shifts can be planned in an acyclic structure, thus establishing a semi-cyclic structure in the full roster. The addition of more typical rostering constraints establishes the novel Semi-Cyclic Ranked Physician Rostering Problem. In manually created rosters, the staffing at sections varies greatly, leading to frequent understaffing. With the addition of absence among staff when rosters are executed, this is problematic for the Clinic of Surgery. We present a two-step matheuristic based on mixed integer linear programming to solve the problem for five real-life instances. Comparing our results with a manually created roster demonstrates superior results in terms of staff availability at sections, greatly improving roster resilience to absence. We also introduce shadow shifts designed to increase the flexibility of rosters to cover for absence at emergency night shifts.