Heterogeneous computing (HC) systems composed of interconnected machines with varied computational capabilities often operate in environments where there may be inaccuracies in the estimation of task execution times. Makespan (defined as the completion time for an entire set of tasks) is often the performance feature that needs to be optimized in such systems. Resource allocation is typically performed based on estimates of the computation time of each task on each class of machines. Hence, it is important that makespan be robust against errors in computation time estimates. In this research, the problem of finding a static mapping of tasks to maximize the robustness of makespan against the errors in task execution time estimates given an overall makespan constraint is studied. Two variations of this basic problem are considered: (1) where there is a given, fixed set of machines, (2) where an HC system is to be constructed from a set of machines within a dollar cost constraint. Six heuristic techniques for each of these variations of the problem are presented and evaluated. © 2006.