Three parallel task assignment problems with shared resources

We study three optimization problems in which non-renewable resources are used to execute tasks in parallel. Problems differentiate by the assumptions of whether a resource can be shared between several tasks or not, or whether resource sharing between the tasks is limited. We present very efficient solution procedures for two of these problems and prove that the third problem is NP-hard in the strong sense and that it can be solved efficiently for special cases. Applications include optimal resource allocation problems in labor-intensive cellular manufacturing and in parallel task computing.