A note on scheduling a rate modifying activity to minimize total late work

We study a single machine scheduling problem with a rate modifying activity. In most cases, performing such an activity (e.g., a maintenance procedure) improves the system performance, as reflected by shorter processing times of the jobs processed after it. The scheduling measure assumed is total late work: each job is considered as a collection of unit-time jobs, and the late work is defined as the number of tardy units. The problem is NP-hard, and we introduce and test numerically a pseudo-polynomial dynamic programming algorithm. Our results indicate that the algorithm solves large problem instances efficiently.