Due dates assignment and JIT scheduling with equal-size jobs

This paper deals with due date assignment and just-in-time scheduling for single machine and parallel machine problems with equal-size jobs where the objective is to minimize the total weighted earliness-tardiness and due date cost. These two problems, but with a common due date to be calculated, were shown to be polynomially solvable in O(n4) time. We first show that this complexity can be reduced to O(n3) by modeling the single machine scheduling problem as an assignment problem without necessary due date enumeration. We next prove that the general case with identical parallel machines and a given set of assignable due dates where the cardinality of this set is bounded by a constant number is still polynomially solvable.