Precedence Constraint Posting for Cyclic Scheduling Problems

Resource constrained cyclic scheduling problems consist in planning the execution over limited resources of a set of activities, to be indefinitely repeated. In such a context, the iteration period (i.e. the difference between the completion time of consecutive iterations) naturally replaces the makespan as a quality measure; exploiting inter-iteration overlapping is the primary method to obtain high quality schedules. Classical approaches for cyclic scheduling rely on the fact that, by fixing the iteration period, the problem admits an integer linear model. The optimal solution is then usually obtained iteratively, via linear or binary search on the possible iteration period values. In this paper we follow an alternative approach and provide a port of the key Precedence Constraint Posting ideas in a cyclic scheduling context; the value of the iteration period is not a-priori fixed, but results from conflict resolution decisions. A heuristic search method based on Iterative Flattening is used as a practical demonstrator; this was tested over instances from an industrial problem obtaining encouraging results.