This research considers the problem of schedulingjobs on parallel machines with an unrestricted due date and additional resources. The objective is to minimize the total absolute deviation ofjobcompletion times about the common due date. This problem is motivated by restrictions that occur in the handling and processing of jobs in certain phases of semiconductor manufacturing and other production systems. It is shown that the problem is polynomial when there exists one single typeofadditional resource and the resource requirements per job are zero or one.