Bicriteria scheduling on an unbounded parallel-batch machine for minimizing makespan and maximum cost

This paper studies the bicriteria problem of scheduling n jobs on an unbounded parallel-batch machine. The goal is to minimize makespan and maximum cost simultaneously. When the jobs have arbitrary processing times and equal release dates, we obtain an O(n3)-time algorithm, improving the previously best known O(n4)-time algorithm. When the jobs have equal processing times and arbitrary release dates with a precedence relation, we also obtain an O(n3)-time algorithm, which is the first polynomial time algorithm for this problem. •Study unbounded parallel-batch scheduling to minimize makespan and maximum cost simultaneously.•Obtain a faster algorithm when the jobs have arbitrary processing times and equal release dates.•Obtain the first polynomial time algorithm when the jobs have equal processing times and arbitrary release dates with a precedence relation.