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DAG scheduling is a process that plans and supervises the execution of interdependent tasks on heterogeneous computing resources. Efficient task scheduling is one of the important factors to improve the performance of heterogeneous computing systems. In this paper, an investigation on implementing Variable Neighborhood Search (VNS) algorithm for scheduling dependent jobs on heterogeneous computing and grid environments is carried out. Hybrid Two PHase VNS (HTPHVNS) DAG scheduling algorithm has been proposed. The performance of the VNS and HTPHVNS algorithm has been evaluated with Genetic Algorithm and Heterogeneous Earliest Finish Time algorithm. Simulation results show that VNS and HTPHVNS algorithm generally perform better than other meta-heuristics methods.