In this study, a model for scheduling projects with the aim of minimizing the total weight of earliness and tardiness costs of works, a situation where prerequisite work and rate of correction of activities and their depreciation is allowed in unrelated parallel machine. Completion of activities earlier and later sometimes imposes heavy costs on the organization, which, if completed earlier, incurs maintenance costs and penalties for tardiness. To receive feedback and appropriate decisions on any project, project management must use a system that has the ability to integrate between the scope of work, cost, and time. In the real world, zeroing the total cost of tardiness and earliness is somewhat impossible, and pre-work is one of the most important issues in scheduling theory. The project's scheduling issues seem to have received less attention with criteria such as earliness and tardiness, in which pre-work permitting is allowed and depreciation is involved, as well as activity correction rates. This scheduling is one of the NP-hard issues that will be discussed below.
