In this paper, we present a formal analysis of the constraints of the scheduling problem, and evaluate the structure of the scheduling polytope described by those constraints. Polyhedral theory and duality theory are used to demonstrate that e cient solutions of the scheduling problem can be expected from a carefully formulated integer linear program ILP. Furthermore, we present an algorithm to lower bound the resource requirement of the time-constrained scheduling problem that enables us to solve the ILP more e ciently.
Samit Chaudhuri, Robert A. Walker