Insertion of a Random Bitask in a Schedule: a Real-Time Approach

We consider a set of tasks defined by their duration and their due-date. They are performed by a single resource and scheduled in order to minimize the sum of the delays. This schedule is given. A task appears in the system at time 0. It is made of two subtasks separated by a fixed period. The duration of the two subtasks and of the period are known only when the task appears. It is also the case for the due date that cannot be violated. The goal is to insert this random task in the schedule while increasing as less as possible the criterion of the initial schedule, that is the sum of the delays. The main difficulty is to insert the task in real-time, which implies that the proposed method should manage to make most of the computation off-line