Task scheduling is a fundamental issue in achieving high performance in grid computing systems. However, it is a big challenge for efficient scheduling algorithm design and implementation. In this paper, the problem of scheduling independent tasks on tree-based grid computing platforms, where resources have different speeds of computation and communication, is discussed. In contrast to minimizing the total execution time, which is NP-hard in most formulations, an integer linear programming model for this problem is presented. Using the model, the optimal scheduling scheme that determines the optimal number of tasks assigned to each computing node is obtained. With the optimal scheduling scheme, two demand-driven and dynamic heuristic algorithms for task allocation are proposed: OPCHATA (optimization-based priority-computation heuristic algorithm for task allocation) and OPBHATA(optimization-based priority-bandwidth heuristic algorithm for task allocation). The experimental results show that the proposed algorithms for the scheduling problem obtain better performance than other algorithms.