A note on parallel-machine scheduling with controllable processing times and job-dependent learning effects

This note studies a unrelated parallel-machine scheduling problem with controllable processing times and job-dependent learning effects, where the objective function is to minimize the weighted sum of total completion time, total load, and total compression cost. We show that the problem can be solved in O(nm+2) time, where m and n are the numbers of machines and jobs. We also show how to apply the technique to several single-machine scheduling problems with total criteria.