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.