Assessing the quality of heuristic solutions to parallel machines min-max scheduling problems

In this paper, we propose a tool for testing the quality of heuristic solutions for scheduling problems with a min-max objective function, such as, for example, the minimization of maximum tardiness or makespan. We present a bounding scheme which is powerful enough to allow an accurate quality assessment of the available solutions in most cases of practical relevance. In order to validate the effectiveness of our assessment approach, we discuss a real-life application and perform experimental tests on the actual applicative scenario and on possible future scenarios.