In this paper, we propose a neuro-genetic artificial neural network framework to achieve certain targeted productivity measures/ performance values in a flow shop with parallel processors (resources) at each stage. The performance measures that we consider are flow time, number of tardy jobs, total tardiness and machine utilizations. In order to achieve these goals, the management has to make decisions on the availability of resources, in our setting, the number of identical machines in each work station and the dispatching rule to be utilized in the shop floor to achieve performance values as close as to the targeted ones.