New single machine and job-shop scheduling problems with availability constraints

In this paper we deal with variants of traditional cases of unavailability constraints in scheduling problems. In the literature, two main approaches are usually found. In the first one, operations can be interrupted by unavailability periods and in the second one, operations cannot be interrupted. The context we consider is more general; some operations can be interrupted, the others cannot. Moreover, we assume that information can be related to operations as well as to unavailability periods. Consequently an unavailability period can make possible or not the interruption of an operation. As an application to this new problem, the single machine problem with heads and tails and the job-shop scheduling problem are tackled. All combinations of possible cases are studied and after a review of the state-of-the-art, branch-and-bound algorithms are proposed to solve these problems. Finally, computational experiments are conducted and discussed.