Scheduling with a position-weighted learning effect and job release dates

This article addresses how to minimize total completion time on a single machine with a position-weighted learning effect. Under non-zero job release dates, a lower bound on the objective function, a number of dominance properties, and an initial solution (i.e. an NEH-based heuristic) are derived, which are used to expedite the elimination process of a branch-and-bound solution procedure. The performance of the branch-and-bound algorithm and the heuristic algorithm are evaluated on a set of randomly generated problem instances.