This paper uses a genetic algorithm to solve the order-acceptance problem with tardiness penalties. We compare the performance of a myopic heuristic and a genetic algorithm, both of which do job acceptance and sequencing, using an upper bound based on an assignment relaxation. We conduct a pilot study, in which we determine the best settings for diversity operators (clone removal, mutation, immigration, population size) in connection with different types of local search. Using a probabilistic local search provides results that are almost as good as exhaustive local search, with much shorter processing times. Our main computational study shows that the genetic algorithm always dominates the myopic heuristic in terms of objective function, at the cost of increased processing time. We expect that our results will provide insights for the future application of genetic algorithms to scheduling problems.