As Grid computing continues to make inroads into different spheres of our lives and multicore computers become ubiquitous, the need to leverage the gains of multicore computers for the scheduling of Grid jobs becomes a necessity. Most Grid schedulers remain sequential in nature and are inadequate in meeting up with the growing data and processing need of the Grid. Also, the leakage of Moore’s dividend continues as most computing platforms still depend on the underlying hardware for increased performance. Leveraging the Grid for the data challenge of the future requires a shift away from the traditional sequential method. This work extends the work of [1] on a quadcore system. A random method was used to group machines and the total processing power of machines in each group was computed, a size proportional to speed method is then used to estimates the size of jobs for allocation to machine groups. The MinMin scheduling algorithm was implemented within the groups to schedule a range of jobs while varying the number of groups and threads. The experiment was executed on a single processor system and on a quadcore system. Significant improvement was achieved using the group method on the quadcore system compared to the ordinary MinMin on the quadcore. We also find significant performance improvement with increasing groups. Thirdly, we find that the MinMin algorithm also gained marginally from the quadcore system meaning that it is also scalable.