This paper describes an application of a Constructive Genetic Algorithm (CGA) to the Minimization Open Stack Problem (MOSP). The MOSP happens in a production system scenario, and consists of determining a sequence of cut patterns that minimizes the maximum number of opened stacks during the cutting process. The CGA has a number of new features compared to a traditional genetic algorithm, as a population of dynamic size composed of schemata and structures that is trained with respect to some problem specific heuristic. The application of CGA to MOSP uses a 2-Opt like heuristic to define the fitness functions and the mutation operator. Computational tests are presented using available instances taken from the literature.