This paper presents a novel heuristic approach, named JDS-HNN, to simultaneously schedule jobs and replicate data files to different entities of a grid system so that the overall makespan of executing all jobs as well as the overall delivery time of all data files to their dependent jobs is concurrently minimized. JDS-HNN is inspired by a natural distribution of a variety of stones among different jars and utilizes a Hopfield Neural Network in one of its optimization stages to achieve its goals. The performance of JDS-HNN has been measured by using several benchmarks varying from medium- to very-large-sized systems. JDS-HNN's results are compared against the performance of other algorithms to show its superiority under different working conditions. These results also provide invaluable insights into scheduling and replicating dependent jobs and data files as well as their performance related issues for various grid environments.