Scheduling Dependent Batching Tasks

We formulate and analyze the following problem of scheduling dependent batching tasks on a common resource. Each task is associated with an execution time window. Some can be executed simultaneously in batch, while others need exclusively use of the resource. A task may depend on a set of tasks such that it becomes executable only if all its ancestor tasks are completed. We look for a task scheduling policy maximizing the system reward. We investigate both the offline and online settings by focusing on a typical scenario where the task dependency forms a tree or a forest. In both settings, we formally establish the hardness of the scheduling problem by showing that the offline scheduling is NP-hard and the online counterpart admits no scheduling policy with finite competitive ratio. We then develop approximation scheduling algorithms for both cases with deterministic worst-case performance guarantee in terms of system utility. We further conduct numeric experiments to evaluate our algorithms under a variety of parameter settings to demonstrate the effectiveness of our scheduling algorithms.