Towards efficient algorithms for planning surgeries in operation rooms

In this paper, the scheduling problem of elective patients in the Orthopedic Department of the “Lozano Blesa” Hospital in Zaragoza is considered. This problem takes into account two contradictory objectives: obtain a given occupation rate of the Operation Room (OR) and respect as much as possible the preference order of the patients in the waiting list. Three different mathematical models are discussed: 1) Quadratic Assignment Problem (QAP); 2) a Mixed Integer Linear Programing (MILP) model; and 3) Generalized Assignment Problem (GAP). These models solve combinatorial problems with a high computational cost; for this reason, heuristic methods have been used to solve large instances. In particular, 1) a meta-heuristic Genetic Algorithm (GA) for the QAP; 2) a heuristic Steepest Descent Multiplier Adjustment Method (SDMAM) for the GAP; and 3) a heuristic iterative method for MILP. Finally, the models and the heuristics are compared according to the occupation rate and the preference order criteria.