The purpose of this paper is to propose and compare several optimization methods for elective surgery planning when operating room (OR) capacity is shared by elective and emergency surgery. The planning problem is considered as a stochastic optimization problem in order to minimize expected overtime costs and patients' related costs. An "almost" exact method combining Monte Carlo simulation and mixed integer programming is presented, and its convergence properties are investigated. Several heuristic and meta-heuristic methods are then proposed. Numerical experimentations are conducted to compare the performance of different optimization methods.