A stochastic model for operating room planning under uncertainty and equipment capacity constraints

In the present economic context, the operating theater is considered as a critical activity in health care management. This paper describes a model for operating room (OR) planning under constraint of a unique equipment. At first level we schedule elective surgeries under the uncertainty of using a unique equipment. At the second level we consider emergency surgeries, and at the third level a coefficient factor for surgeons is introduced in using this unique equipment. The planning problem consists in scheduling a unique equipment and assigning elective cases to different periods over a planning horizon to minimize the sum of elective patient related costs and overtime costs of ORs. The most important factor that we have focused on this paper is equipment resource constraint. A new mathematical programming model is first proposed and at the second and third level, a new stochastic mathematical programming model is proposed. Then sample average approximation is presented to approximate the problem with sample size N and then Lingo is used as an exact approach. Because of NP-hardness, exact method does not work for large size problems, so a Metaheuristic approach (differential evolution) is proposed for large size problems. Numerical results show that important gains (approximately 3.5 % in overall cost) can be realized by this stochastic OR planning model.