A robust approach for the single machine scheduling problem

This paper describes a robust approach for the single machine scheduling problem 1|ri|Lmax. The method is said robust since it characterizes a large set of optimal solutions allowing to switch from one solution to another, without any performance loss, in order to face the potential disruptions which occur during the schedule execution. It is based on a dominance theorem that characterizes a set of dominant sequences, using the interval structure defined by the relative order of the release and the due dates of the jobs. The performance of a set of dominant sequences can be determined in polynomial time by computing the most favorable and the most unfavorable sequences associated with each job, with regard to the lateness criterion. A branch and bound procedure is proposed which modifies the interval structure of the problem in order to tighten the dominant set of sequences so that only the optimal sequences are conserved.