In this paper, we focus on the problem of scheduling batches of identical task graphs on a heterogeneous platform, when the task graph consists in a tree. We rely on steady-state scheduling, and aim at reaching the optimal throughput of the system. Contrarily to previous studies, we concentrate upon the scheduling of batches of limited size. We try to reduce the processing time of each instance, thus making steady-state scheduling applicable to smaller batches. The problem is proven NP-complete, and a mixed integer program is presented to solve it. Then, different solutions, using steady-state scheduling or not, are evaluated through comprehensive simulations.