Different stakeholders’ perspectives for a surgical case assignment problem: Deterministic and robust approaches

Adequate access to health care is one of the main strategic axes considered in the Portuguese National Health Plan. This plan seeks to ensure the best performance and adequacy of care maximizing the use of resources, quality, equity and access. This work results from a close collaboration with a large and publicly funded Portuguese hospital. The aim is to propose a systematic approach to help the surgical planner in the scheduling of elective surgeries, in order to optimize the use of the available surgical resources, and improve equity and access to operated and waiting patients. The decisions to be taken by this surgical case assignment problem are twofold: select patients to be scheduled in the planning horizon from a large waiting list for surgery; and assign a day, an operating room, and a time block to the selected patients. Three versions are modeled in (mixed) integer linear programming: from the administration’s intention up to the surgeons’ current practice, and a halfway reflecting a negotiation with the surgeons. A robust approach is proposed to tackle the uncertain surgeries’ duration without the need to assume a given distribution for these random parameters and allowing to control the level of conservatism in the solutions. Practical and real-sized problems from the hospital are solved providing very good optimization gaps within a short time limit, both for the deterministic and robust approaches. The schedules obtained are analyzed regarding quality and robustness, and are also compared with the surgical schedules performed by the hospital.