A note on single-machine group scheduling problems with position-based learning effect

In many situations, the skills of workers continuously improve when repeating the same or similar tasks. This phenomenon is known as the “learning effect” in the literature. However, most studies considering the learning effect ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as “group technology” in the literature. In this paper, we propose a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. We then show that the makespan and the total completion time problems remain polynomially solvable under the proposed model.