The Ranked Positional Weight Method is a technique used for assembly line balancing that takes into account precedence relationships and task processing times. It involves calculating a Ranked Positional Weight for each work element based on duration and precedence, arranging them in descending order, and then assigning them to workstations to optimize time, machinery, labor and output. The example shows the steps of constructing a precedence diagram, calculating RPW values, ordering by RPW, and assigning elements to six workstations with the goal of minimizing idle time.