This paper considers a single machine scheduling problem with release dates, due dates,precedence constraints and aiming for the minimization of the maximum lateness or the sumof completion times over a sampled set of release dates scenarios, either in a stochastic orrobust setting. The standard 2-stage approach for stochastic and robust scheduling on a singlemachine considers first-stage decisions that output a full ordering (sequence) of the jobs (J-SEQ) on the machine and second-stage decisions that set the job start times in accordancewith the information of a given scenario.. In this paper, we study the performances of analternative 2-stage solution method based on groups of permutable jobs. The method, initiallypresented in [1], considers first-stage decisions that output only a partial ordering in the formof a sequence of groups of permutable jobs (G-SEQ). Given a scenario, the second stage policyorders the jobs inside each group according to the earliest realized release date first heuristic.We introduce a constraint programming approach to compute an optimal G-SEQ solutionbut show that in a limited time, it provides poor quality solutions on the largest instancescompared to a standard J-SEQ solution approach. We then design several heuristics that usea portion of the time limit to obtain good quality J-SEQ starting solutions and then switch toG-SEQ solutions via greedy or local search. The best G-SEQ heuristics outperform all of thestandard J-SEQ approaches under the same time limit.