A branch-and-price-and-cut algorithm for operating room scheduling under human resource constraints

In this paper, we address an integrated operating room planning and scheduling problem that includes, with fine detail, constraints commonly encountered in practice (i.e., sequence, capacity and due date constraints) and for human resources other than surgeons, i.e., nurses. A new model of the sequence-dependent operating room cleaning times that arise because of surgeries with different infection levels is considered. To solve this difficult integrated planning and scheduling problem, we devise a branch-and-price-and-cut algorithm based on the time-indexed formulation of the problem. The basic column generation scheme relies on a label-correcting algorithm that we purposely developed for solving the pricing problems that are modeled as single operating room scheduling problems with time-dependent costs and sequence-dependent cleaning times. The pricing problems are strongly NP-Hard. The efficiency of the label-correcting algorithm is ensured by dominance rules among labels and by two algorithms for computing the upper and lower bound of labels. An effective cutting procedure, inspired by Benders' decomposition and based on duality theory for linear programming, is developed for tightening the linear relaxation of the problem. With instances from the literature and that we generated, we conduct a numerical study to demonstrate the computational effectiveness of the solution method.