Pareto-scheduling with family jobs or ND-agent on a parallel-batch machine to minimize the makespan and maximum cost

We study Pareto-scheduling on an unbounded parallel-batch machine that can process any number of jobs simultaneously in a batch. The processing time batch is equal to the maximum consider two problems. In one problem, are partitioned into families and from different cannot be processed together same assume constant. objective minimize makespan cost. other we have agents A B, where each agent $$E\in \{A,B\}$$ has its job set $${{\mathcal {J}}}_{E}$$ , called E-jobs. Assuming sets {J}}}_{A}$$ {J}}}_{B}$$ not necessarily disjoint, call $$\text {ND}$$ agents. A-jobs cost B-jobs. provide polynomial-time algorithms solve