Some new polynomial cases in just-in-time scheduling problems with multiple due dates

Coming from the ldquojust-in-timerdquo philosophy in management and production theory, minimizing total weighted earliness-tardiness on machine scheduling problems has wide industrial applications. In the case of a single machine with a given common due date, the problem is known NP-hard. In this paper, n jobs with identical processing times should be scheduled on m uniform machines. The objective is to minimize the total weighted earliness-tardiness penalties. In this study, we consider l given due dates (l<n). We show that the scheduling problem on m uniform machines is polynomially solvable.