Summary form only given. We examine several heuristic algorithms for the maximum allowable workload (MAW) problem for real-time systems with tasks having variable workloads. Briefly, the problem concerns the allocation of tasks to m processors, where each task t is characterized by a function t.r(w) that gives the running time of the task in terms of its workload (or input size) w. The objective of the maximum allowable workload problem is to find an allocation of tasks to processors so that the allocation is feasible (no task misses its deadline) when each task is given a workload of w or smaller and w is maximized. This optimization problem uses a robustness measure that is closely related to the MAIL (maximum allowable increase in load) metric recently proposed by Gertphol et al. The main contribution of this paper is the comparison of several heuristic algorithms for the MAW-RMS problem. Hillclimbing, random search, simulated annealing, and first-fit heuristics are presented and evaluated via simulation. As we show here, the first-fit greedy heuristic produces solutions of a reasonable quality compared to the other algorithms. In addition, we demonstrate the applicability of our model in air defense systems.