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 ( n 3 )-time algorithm, improving the previously best known O ( n 4 )-time algorithm. When the jobs have equal processing times and arbitrary release dates with precedence relation, we also obtain an O ( n 3 )-time algorithm, which is the first polynomial time algorithm for this problem