This paper studies a scheduling problem involving two agents E and F with \(n_1\) and \(n_2\) jobs respectively on a serial-batch processor. The aim is to Pareto optimize the criteria of agent E’s maximum completion time (makespan) and agent F’s maximum cost. The two agents are compatible (meaning that their jobs can be batched together) and non-disjoint (meaning that their job sets may overlap). The unlimited serial-batch processor can handle an unlimited number of jobs jointly and sequentially in a batch, with the batch’s processing time being the sum of the individual jobs contained within it. Additionally, initiating each new batch necessitates a predetermined amount of setup time before the processing begins. An \(O(n_1+{n_2}^3)\) -time Pareto optimal algorithm is presented which is the first polynomial time algorithm for this problem. For the special case with maximum lateness instead of maximum cost, the obtained algorithm has a better time complexity of \(O(n_1+{n_2}^2\log n_2\) ).
