The Complexity of a Cyclic Scheduling Problem With Identical Machines and Precedence Constraints

Abstract We consider a set T of tasks with unit processing times. Each of them must be executed in nitely often. A uniform constraint is de ned between two tasks and induces a set of precedence constraints on their successive executions. We limit our study to a subset of uniform constraints corresponding to two hypotheses often veri ed in practice : each execution of T must end by a special task f , and uniform constraints between executions from di erent iterations start from f . We have a xed number of identical machines. The problem is to nd a periodic schedule of T which maximizes the throughput. We prove that this problem is NP-hard and show that it is polynomial for two machines. We also present another non trivial polynomial subcase which is a restriction of uniform precedence constraints.