A Flow - Based Approach to Solving Resource - Constrained Scheduling

A novel integer linear programming (ILP) formulation for resource-constrained scheduling problems is presented. Existing ILP-based methods for the same problem typically have a complexity (measured in terms of the number of unknown integer variables) that is proportional to the latency bound of the problem. Hence, they are restricted in scope (e.g., high-level synthesis). Our approach consists in (1) overlaying a ow graph to a given problem graphG(V;E) (i.e., task, precedence graph) which allows to model the impact of resource and scheduling constraints in a single graph model. (2) Based on this model, we formulate a number of resource-constrained scheduling problems as problems of optimal resource ow. The complexity of the model can be measured in terms of O(jV j2) binary variables that model the ow of resources from node to node, and, in case there is a non-zero ow, activate serialization constraints of allowed schedules. (3) We analyze the polyhedral structure of this ILP model and prove that only a subset of ow variables have to be declared integer. (4) Also, we explain how to eliminate ow variables. Procedures for optimizing the polyhedral structure are outlined including the addition of facet de ning inequalities and the optimization of constant parameters of the model. (5) Finally, we present strategies for e ciently solving the ILP-model. Chapter