Virtual resources team up to create a computational grid, which is used in computation-intensive problem solving. A majority of these problems require high performance resources to compute and generate results, making grid computation another type of high performance computing. The optimization in computational grids relates to resource utilization which in turn is achieved by the proper distribution of loads among participating resources. This research takes up an adaptive resource ranking approach, and improves the effectiveness of NDFS algorithm by scheduling jobs in those ranked resources, thereby increasing the number of job deadlines met and service quality agreements met. Moreover, resource failure is taken care of by introducing a partial backup approach. The benchmark codes of Fast Fourier Transform and Matrix Multiplication are executed in a real test bed of a computational grid, set up by Globus Toolkit 5.2 for the justification of propositions made in this article.