Two-agent bounded parallel-batching scheduling for minimizing maximum cost and makespan

This paper considers the bounded parallel-batching scheduling with two agents to minimize maximum cost of agent $A$ and makespan of agent $B$ simultaneously, in which all jobs of agent $A$ have equal processing time, the jobs from different agents can be processed in a common batch and the cost function of each agent is only determined by its own jobs. In the paper, we present a polynomial-time algorithm to generate all Pareto optimal points for the problem and determine a corresponding Pareto optimal schedule for each Pareto optimal point.