This presentation deals with a problem in which a set of inspection operations have to be scheduled to optimize the quality of products manufactured in a xed production schedule. The problem is formalized as a scheduling problem whose objective is to minimize a regular step cost function. A Mixed Integer Linear Programming model is presented, as well as a dedicated exact method for solving the case without release dates on a single machine. Experimental results are reported and discussed to compare the performances of a standard mathematical programming solver and our dedicated method.