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Finding an optimal solution to the problem of scheduling an application modeled by a directed acyclic graph (DAG) onto a set of heterogeneous machines is known to be an NP-hard problem. In this study, we present a duplication based scheduling algorithm, namely the levelized duplication based scheduling (LDBS) algorithm, which solves this problem efficiently. The primary goal of LDBS is to minimize the schedule length of applications. LDBS can accommodate different duplication heuristics, thanks to its modular design. Specifically, we have designed two different duplication heuristics with different time complexities. The simulation studies confirm that LDBS is a very competitive scheduling algorithm in terms of minimizing the schedule length of applications.