Scheduling is a fundamental issue in achieving high performance on metacomputers and computational grids. For the first time, the job scheduling problem for grid computing on metacomputers is studied as a combinatorial optimization problem. The efforts to construct a national scale grid computing environment have brought unprecedented computing capacity. Exploiting this complex infrastructure requires efficient middleware to support the execution of a distributed application, composed of a set of subtasks, for best performance. The main idea of the proposed algorithms is to execute jobs optimally, i.e. with minimum average waiting, turnaround and response times. An extensive performance comparison is presented using real workload traces to evaluate the efficiency of scheduling algorithms.