The Test Laboratory Scheduling Problem (TLSP) is an extension of the Resource-Constrained Project Scheduling Problem (RCPSP). Besides several additional constraints, it includes a grouping phase where the jobs to be scheduled have to be assembled from smaller tasks and derive their properties from this grouping. Previous solution approaches for TLSP have focused primarily on the scheduling subproblem (TLSP-S), for which it is assumed that a suitable grouping is already given as part of the input. In this paper, we provide for the first time a solution approach that encompasses the full problem including grouping. We propose both a Constraint Programming model for TLSP and a Very Large Neighborhood Search algorithm based on that model. Furthermore, we apply our algorithms to real-world instances as well as randomly generated ones and compare our results to the best existing solutions. Experimental results show that our solution methods consistently outperform those for TLSP-S when both are initialised with a good grouping and in many cases even when this grouping is provided only to the latter.