Online heuristic for the preemptive single machine scheduling problem to minimize the total weighted tardiness

Abstract

In this paper, we refine the ties within decision rules of the Total Weighted Tardiness (TWT) heuristic from Jaramillo and Erkoc (2017) applied by the authors to solving the preemptive single machine scheduling problem with arbitrary release and due dates, priority factors (weights), and equal processing times of a finite number of jobs. The TWT heuristic is intended to minimize the total weighted tardiness of schedules. Our refinements allow to extend equal processing times to arbitrary ones such that we are able to solve benchmark instances online with up to 200 jobs and 20 units of processing times within 47 ms and essentially decrease TWT of returned schedules. The time and space complexities of returned schedules outperform the state of the art for the cases of arbitrary release dates, weighted and unweighted total tardiness, with equal and arbitrary processing times.