1. A dispersion compensation design system, comprising: a changing unit configured to set a changed value for an amount of dispersion compensation for at least one of spans connecting nodes constituting an optical network; a path classification unit configured to determine whether respective paths in the optical network are capable of transmission on an assumption that the amount of dispersion compensation is updated with the changed value, and classify one or more of the paths as second category paths based on the determination results, wherein a path is classified as the second category path if the path itself is incapable of transmission but there is a longer path that includes the path and is capable of transmission; an updating unit configured to compare a retained previous classification result with a latest classification result of the path classification unit, and update the amount of dispersion compensation for the at least one of spans with the changed value and retain the latest classification result if a number of the second category paths in the latest classification result is less than a number of the second category paths in the retained previous classification result; and a repeating unit configured, if not all of the paths in the optical network are capable of transmission, to prevent use of combinations of amounts of dispersion compensation applied to the spans in the second category paths in the latest classification result, and cause the changing unit, the path classification unit, and the updating unit to repeat the setting of the changed value, the classification of the paths, and the updating of the amount of dispersion compensation.