Parallelism on heterogeneous machines brings cost effectiveness, but also raises a new set of complex and challenging problems. This paper addresses the problem of estimating the minimum time taken to execute a program on a fine-grained parallel machine composed of different types of processors. In an earlier publication, we took the first step in this direction by presenting a graph-construction method which partitions a given program into several homogeneous parts and incorporates timing constraints due to heterogeneous parallelism into each part. In this paper, to make the method easier to be applied in a scheduling framework and to demonstrate its practical utility, we present an efficient implementation method and compare the results of its use to the optimal schedule lengths obtained by enumerating all possible solutions. Experimental results for several different machine models indicate that this method can be effectively used to estimate a program's minimum execution time.