Sensitivity bounds for machine scheduling with uncertain communication delays

The paper deals with the scheduling of tasks on a set of parallel machines subject to precedence constraints and communication delays, that are not fully known before the execution. This is usual in parallel computing (message passing) and in production workshops (part transportation). The goal is to give a priori information on the behavior of different schedules computed before the execution. This sensitivity analysis helps to choose among different available algorithms. It also provides tools to decide whether it is justified to change the schedule structure at execution time (run-time scheduling). By hypothesis, the communication delays are within a given interval. Worst case sensitivity bounds are proposed that give the maximum loss of performance. These bounds hold for algorithms which are optimal in the deterministic case, but can be easily adapted to arbitrary algorithms. Some applications to specific problems are presented, namely two identical machines, and unbounded number of machines, for tree-like precedence constraints.