This paper presents a new algorithm for finding efficient schedules with respect to total flowtime and maximum tardiness. A detailed comparison is made between this algorithm and the well‐known Van Wassenhove and Gelders’ algorithm (VGA) on a variety of problem sizes, up to 100 jobs. Computational results show that the proposed algorithm is of considerable value, especially for large problems. In particular, for the 10‐job problem the proposed algorithm requires roughly one‐half the computation time of VGA, and for the 100‐job problem the ratio reduces to one to sixteen.