Is a unit-time job shop not easier than identical parallel machines?

AbstractThis paper gives the positive answer to the question posed in the title for a wide class of minimization criteria including the maximum completion time, maximum lateness, total completion time, total weighted completion time, total tardiness, total weighted tardiness, number of late jobs and the weighted number of late jobs. That is any scheduling problem for m identical parallel machines to minimize a criterion of the class reduces to a scheduling problem for an m-machine unit-time job shop to minimize the same criterion. Employing this general reduction we prove the NP-hardness of unit-time job-shop scheduling problems which had unknown complexity status before. The paper also presents a comprehensive picture of complexity results attained in unit-time job-shop scheduling and related open problems