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It has been demonstrated that the performance of scheduling heuristics for the Resource Constrained Project Scheduling Problem (RCPSP) can be affected by the use of alternative project execution strategies. This current work seeks to expand our understanding of the relationship between planning (scheduling) and execution procedures. The relative performance of a selected group of “high performing” scheduling heuristics on project total duration, Net Present Value (NPV), and a new class of stability measures under four different execution strategies is examined. A benchmark set of RCPSP cases were scheduled and then simulated through execution and the results are compared. The research findings indicate that relative performance is affected by the execution strategy in some cases but not in others; and that these relative standings are sensitive to the presence of variability in task duration. A new heuristic is also proposed and evaluated.