We study a single machine scheduling problem. The processor needs to go through a maintenance activity, which has to be completed prior to a given deadline. The objective function is minimum total weighted completion time. The problem is proved to be NP-hard, and an introduction of a pseudo-polynomial dynamic programming algorithm indicates that it is NP-hard in the ordinary sense. We also present an efficient heuristic, which is shown numerically to perform well. © 2008 Elsevier Ltd. All rights reserved.
Mosheiov, G., & Sarig, A. (2009). Scheduling a maintenance activity to minimize total weighted completion-time. Computers and Mathematics with Applications, 57(4), 619–623. https://doi.org/10.1016/j.camwa.2008.11.008