Abstract: For the single machine scheduling problem with number of tardy jobs and controllable processing times, Daniels and Sarin gave some results for con-trucking the tradeoff curve between the number of tardy jobs and the total crashing times, but they had not developed such an algorithm. Under the condition of all w_j equal to one, this paper analyses some results given in their paper, proves the number of efficient values in the tradeoff curve. Basing on considering only on the number of tardy jobs and the method given by Daniela and Sarin, the peper develops also an algorithm for constracting such a tradeoff curve.

Key words: scheduling, multiple objective, number of tardy jobs, controllableprocessing times.