We propose a framework to control the search for solutions by relaxation, reduction, and decomposition of scheduling problems. Scheduling problems are regarded as constraint satisfaction problems (CSPs) which are represented by sets of constraints. We introduce the notion of subquadrangle and show how to represent any constraint by intersections and unions of subquadrangles. This allows us to connect all three aspects of search control in the same framework, and to determine the maximum search time needed for a given problem. We derive a new tractable class of scheduling problems in this framework and show how to efficiently combine and generate scheduling heuristics. Finally, we present some experimental results.