Abstract.  Conventionally, job processing times are assumed to be constant from the first job to be processed until the last job to be completed. However, recent empirical studies in several industries have verified that unit costs decline as firms produce more of a product and gain knowledge or experience. This phenomenon is known as the learning effect. This paper focuses on a bi-criterion single-machine scheduling problem with a learning effect. The objective is to find a sequence that minimizes a linear combination of the total completion time and the maximum tardiness. A branch-and-bound and a heuristic algorithm are proposed to search for optimal and near-optimal solutions, respectively. Computational results are also provided for the problem.