We consider a system made of one resource. The execution of the tasks is non-preemptive on this resource. The tasks we consider are composed of a given number of subtasks, two consecutives subtasks being separated by an idle period. These idle periods may be used for executing other subtasks. We wish to insert a new task in a given schedule. The characteristics of this task are not known before it appears, and its execution must be completed before a given deadline. The criterion is the minimization of the increase of the sum of the delays of the tasks.