In many scheduling applications it is required that the processing of
some job must be postponed until some other job, which can be chosen
from a pre-given set of alternatives, has been completed. The
traditional concept of precedence constraints fails to model such
restrictions. Therefore, the concept has been generalized to
so-called AND/OR precedence constraints which can cope with this
kind of requirement.
In the context of traditional precedence constraints, feasibility,
transitivity, as well as the computation of earliest start times for
jobs are fundamental, well-studied problems. The purpose of this
paper is to provide efficient algorithms for these tasks for the more
general and complex model of AND/OR precedence constraints. We show
that feasibility as well as many questions related to transitivity can
be solved by applying essentially the same linear-time algorithm. In
order to compute earliest start times we propose two polynomial-time
algorithms to cope with different classes of time distances between
jobs.
