A novel priority rule heuristic: learning from justification

The Resource Constrained Project Scheduling Problem consists of finding start times for precedence-constrained activities which compete over renewable resources, with the goal to produce the shortest schedule. The method of Justification is a very popular post-processing schedule optimization technique which, although it is not clear exactly why, has been shown to work very well, even improving randomly generated schedules over those produced by advanced heuristics. In this paper, we set out to investigate why Justification works so well, and, with this understanding, to bypass the need for Justification by computing a priori the priorities Justification implicitly employs. We perform an exploratory study to investigate the effectiveness of Justification on a novel test set which varies the RCPSP phase-transition parameters across a larger range than existing test sets. We propose several hypotheses to explain the behavior of Justification, which we test by deriving from them several predictions, and a new priority rule. We show that this rule matches the priorities used by Justification more closely than existing rules, making it outperform the most successful priority rule heuristic.