The problem of minimizing the total deviation of ending times of performing task for common due date by parallel machines

The article presents the problem of scheduling theory, in which it is necessary to schedule the tasks with a common due date on several parallel machines by the criterion of minimizing the total deviation of the completion of tasks from the due date. Problem's main feature is that there are no restrictions on the beginning of the tasks execution (at the schedule's launch time). Two cases are considered in the article: in the first device are identical, and in the second - are proportional, that is, those that differ in the speed of work. Servicing system with only one device is considered as a corner case. Optimal scheduling algorithm has been developed for all considered problems. Algorithm usage examples are provided.