  The problem considered is the non-preemptive scheduling of independent jobs
that consume a resource (which is non-renewable and replenished regularly) on
parallel uniformly related machines. The input defines the speed of machines,
size of jobs, the quantity of resource required by the jobs, the replenished
quantities, and replenishment dates of the resource. Every job can start
processing only after the required quantity of the resource is allocated to the
job. The objective function is the minimization of the convex combination of
the makespan and an objective that is equivalent to the $l_p$-norm of the
vector of loads of the machines. We present an EPTAS for this problem. Prior to
our work only a PTAS was known in this non-renewable resource settings and this
PTAS was only for the special case of our problem of makespan minimization on
identical machines.
