We consider in this work, a single machine problem with periodic maintenance activities. The objective is to minimize the weighted completion time of the jobs. The preemption of jobs is not allowed. Most of past studies considered such a scheduling problem but not for the same objective. We propose a MIP formulation to solve optimally this problem for small instances, then we present a new property which helps us solving the problem with an efﬁcient and effective heuristic designed to solve the big instances.
Mots clés : Single machine scheduling, Preventive Maintenance, Mathematical model