In project scheduling, resource constraints are usually defined via
resource consumption and -availability. Many algorithmic
approaches, however, are based on the concept of minimal forbidden
sets to represent the resource constraints. Jobs of a forbidden
set can be scheduled simultaneously with respect to the precedence
constraints, however, they consume more resources than available.
Forbidden sets are usually not given explicitly, and by definition
even the number of inclusion-minimal forbidden sets may be
exponential in the number of jobs. In this paper, we propose a simple
branch-and-bound type algorithm to efficiently compute and represent
all minimal forbidden sets for a given instance.
We evaluate the algorithm on well established
test sets of the project scheduling problem library PSPLIB. In
addition, we exhibit intimite relations between the different
representations of resource constraints and threshold hypergraphs.
