An improved algorithm on unbounded parallel-batching scheduling to minimize maximum cost and makespan

Abstract

This paper studies the bicriteria problem of scheduling n jobs on a parallel-batching machine to minimize maximum cost and makespan simultaneously. A parallel-batching machine is a machine that can handle up to b jobs in a batch. The jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the largest processing time of jobs in the batch. We consider the unbounded case. For the above bicriteria scheduling problem, we present an O(n3)-time algorithm, which improved the best known O(n4)-time algorithm, and the time complexity is the same as the special case in which maximum cost is maximum lateness. Meanwhile, our algorithm can also solve the single-criterion unbounded parallel-batching scheduling problem to minimize maximum cost in O(n3) time, which improved the best known O(n4)-time algorithm.