Grid computing facilitates the resource sharing through the administrative domains which are geographically distributed. Scheduling in a distributed heterogeneous environment is intrinsically very hard because of the heterogeneous nature of resource collection. Makespan and tardiness are two different measures of scheduling, and many of the previous researches concentrated much on reduction of makespan, which measures the machine utilization. In this paper, we propose a hybrid scheduling algorithm for scheduling independent grid tasks with the objective of reducing total weighted tardiness of grid tasks. Tardiness is to measure the due date performance, which has a direct impact on cost for executing the jobs. In this paper we propose BG_ATC algorithm which is a combination of best gap (BG) search and Apparent Tardiness Cost (ATC) indexing algorithm. Furthermore, we implemented these two algorithms in two different phases of the scheduling process. In addition to that, the comparison was made on results with various benchmark algorithms and the experimental results show that our algorithm outperforms the benchmark algorithms.
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