The problem of programming operations in a manufacturing production plant with eligibility of workers according to their qualification for the different tasks is considered.  A mathematical model corresponding to an integer linear programming problem with binary encoding is formulated.  To solve it, a genetic algorithm with a randomly generated population, crossover points, mutation probability and stopping criteria set by the user is proposed.  The algorithm is implemented in a software application and tested with data from a manufacturer of wooden barrels.  The results show attraction towards the best value of the objective function, and allow us to detect that the factors that most favor it are the stopping criterion and the probability of mutation.