In this sstudy, we considered a single-machine scheduling problem with release times and the objective is to minimize the total weighted completion time. Two new heuristics were proposed with the use of decision indexes that assign the priorities to jobs in the sequence. The former decision index is based on the rearrangement of the objective function whereas the latter is based on a decomposition procedure to generate a better lower bound. A dominance rule was also developed to eliminate the node in which its partially scheduled sequence is dominated by a simple heuristic developed in this study. Experimental results showed that both heuristics yielded near-optimal solutions in a very short time.