  We describe in this paper a new method for building an efficient algorithm
for scheduling jobs in a cluster. Jobs are considered as parallel tasks (PT)
which can be scheduled on any number of processors. The main feature is to
consider two criteria that are optimized together. These criteria are the
makespan and the weighted minimal average completion time (minsum). They are
chosen for their complementarity, to be able to represent both user-oriented
objectives and system administrator objectives. We propose an algorithm based
on a batch policy with increasing batch sizes, with a smart selection of jobs
in each batch. This algorithm is assessed by intensive simulation results,
compared to a new lower bound (obtained by a relaxation of ILP) of the optimal
schedules for both criteria separately. It is currently implemented in an
actual real-size cluster platform.
