Abstract-- Scheduling problems are already difficult on traditional parallel machines, and they become extremely challenging on heterogeneous clusters. In this paper we deal with the problem of scheduling multiple applications, made of collections of independent and identical tasks, on a heterogeneous masterworker platform. The applications are submitted online, which means that there is no a priori (static) knowledge of the workload distribution at the beginning of the execution. The objective is to minimize the maximum stretch, i.e., the maximum ratio between the actual time an application has spent in the system and the time this application would have spent if executed alone. On the theoretical side, we design an optimal algorithm for the offline version of the problem (when all release dates and application characteristics are known beforehand). We also introduce a heuristic for the general case of online applications. On the practical side, we have conducted extensive simulations...