Enumeration of Circuits and Minimal Forbidden Sets

In resource-constrained scheduling, it is sometimes important to know all inclusion-minimal subsets of jobs that must not be scheduled simultaneously. These so-called minimal forbidden sets are given implicitly by a linear inequality system, and can be interpreted more generally as the circuits of a particular independence system. We present several complexity results related to computation, enumeration, and counting of the circuits of an independence system. On this account, we also propose a backtracking algorithm that enumerates all minimal forbidden sets for resource constrained scheduling problems

When Greediness Fails: Examples from Stochastic Scheduling

The purpose of this paper is to present examples for the sometimes surprisingly different behavior of deterministic and stochastic scheduling problems. In particular, it demonstrates some seemingly counterintuitive properties of optimal scheduling policies for stochastic machine scheduling problems