The Structure of Assignment, Precedence, and Resource Constraints in the ILP Approach to the Scheduling Problem

This paper presents a general treatment of the combinatorial approach to the scheduling problem, enhancing previous formulations in the literature. The focus of this paper is a formal analysis of the ILP approach, which we use to evaluate the structure of our formulation. Polyhedral theory and duality theory are used to demonstrate that efficient solutions of the scheduling problem can be expected from a carefully formulated integer linear program (ILP). Furthermore, we use the theory of valid inequalities to tighten the constraints and make the formulation more efficient