Tardiness

Abstract: We consider the problem of scheduling n jobs to minimize the total earliness and tardiness penalty. We review the literature on this topic, providing a framework to show how results have been generalized starting with a basic model that contains symmetric penalties, one machine and a common due date. To this base we add such features as parallel machines, complex penalty functions and distinct due dates. We also consolidate many of the existing results by proving general forms of two key properties of earliness/tardiness models.

Abstract: The problem of minimizing the total tardiness for a set of independent jobs on one machine is considered. Lawler has given a pseudo-polynomial-time algorithm to solve this problem. In spite of extensive research efforts for more than a decade, the question of whether it can be solved in polynomial time or it is NP-hard in the ordinary sense remained open. In this paper the problem is shown to be NP-hard in the ordinary sense.

Abstract: Suppose n jobs are to be processed by a single machine. Associated with each job j are a fixed integer processing time pi, a due date di, and a positive weight wj. The weighted tardiness of job j in a given sequence is wj, max (O, Ci, - di), where Ci is the completion time of job j. Assume that the weighting of jobs is “agreeable”, in the sense that pi

Abstract: Mainstream research in priority dispatching has considered jobs with equal delay penalties, thereby ruling out strategic differentiation of customer orders. We develop and test efficient dispatchin...