Experimental analysis of tardiness in preemptive single machine scheduling

Abstract

This paper studies the scheduling of a finite set of jobs on a single machine. Jobs can be preempted. They are associated with respective release and due dates. In a more general case, each job has a priority weight. The objective is to minimize the total weighted tardiness. An optimal schedule providing the minimal total weighted tardiness can be found by our Boolean linear programming model, but it becomes computationally intractable as the problem size grows. Thus, we analyze the recently designed heuristic to minimize total weighted tardiness based on using the remaining available time and remaining processing time. It is a rapid online scheduling algorithm but the heuristic may return schedules whose tardiness deviates from an optimal value by 50% and more. We extend the heuristic into four branches with a purpose to improve it by excluding options of job selection uncertainty. Depending on the scheduling problem type, we render the metaheuristic to a single branch which is run after the main heuristic algorithm. This allows building schedules online. Our extensive computational study shows that our online metaheuristic returns high quality schedules.