Due dates assignment and JiT scheduling with equal-size jobs

Abstract : 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(n^4) time. We first show that this complexity can be reduced to O(n^3) 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.