Blazewicz, Pesch, Sterna and Werner (2004) proposed an algorithm for scheduling the two- machine open shop with common due dates and minimize the number of late jobs. Their solution used a makespan minimizing process first proposed by Gonzalez and Sahni (1976) to construct an initial schedule, then modify it by shifting some jobs in order to minimize the idle time before the common due date and, consequently, to minimize the late work in the system. As this benchmark algorithm is only for two-machines open shops, the proposed heuristic may seem incommensurate for the general purpose application for the latter. But the number of computational steps can be compared to determine the level of complexity between the two.