A note on scheduling on a single processor with variable speed

Alidaee and Ahmadian considered a single machine scheduling problem with varying processing times, and presented a polynomial algorithm that minimizes the sum of absolute deviations of jobs' completion times from a common due date. In this short note we remark that it is possible to eliminate one of the algorithm steps, therefore obtaining a more efficient procedure. We also show that the approach used can easily be generalized to the problem with different weights for earliness and tardiness