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In this paper, we present an efficient method to solve unrelated parallel machine total weighted tardiness (TWT) scheduling problems. We apply an ant colony optimization (ACO) approach as a heuristic to solve this NP-hard problem. A colony of artificial ants is used to construct iteratively solutions of the scheduling problem using artificial pheromone trails and heuristic information. For the computation of the heuristic information, we use the apparent tardiness cost (ATC) dispatching rule. We additionally improve the TWT value by applying a decomposition heuristic that solves a sequence of smaller scheduling problems optimally. We report on computational experiments based on stochastically generated test instances. Problems of this type arise in semiconductor manufacturing and have great practical relevance.