Abstract : In the context of grid scheduling we consider a scheduling scenario, where parallel jobs have to be scheduled non-preemptively on heterogeneous computational platforms of processors. The speed of the processors may differ among the platforms and the jobs are submitted si- multaneously or over the time and cannot run across multiple platforms. We focus on the target of minimizing the total makespan, i.e. the global latest finishing time of a job. In this paper we present an AFPTAS for the problem without release times and show how to generalize our result to malleable jobs and jobs with release times.