Grid system consists of heterogeneous resources, so the major challenge of task scheduling is effectively by using the whole grid power to minimize the task makespan.

In grid computing, a good algorithm for tasks scheduling should not only decrease the makespan of all tasks but also balance the load among the resources in the grid system.

The algorithm adopts a mechanism of the measuring value that considers the completion time and the execution time between tasks and processors as the parameters together,and it adjusts the proportions of both to achieve a better performance.

We consider a problem of scheduling n jobs with random processing times on a single machine in order to minimize the expected total weighted absolute deviations of completion times about a common due date.