Given a command of garments to cut from a customer, we propose in this paper an algorithm permitting to choose the patterns to use in order to satisfy the various objectives and constraints related to this problem. Due to the complexity of this problem and the limitation of the time of resolution, the algorithm uses an heuristic technique based on a combination between a method of residues and the Simulated Annealing approach. It allows to reach the compromise between the quality of solution and the computing time. Examples using industrial data are proposed to illustrate the usefulness of the algorithm.