A DP algorithm for minimizing makespan and total completion time on a series-batching machine

Authors:
Cheng He;Yixun Lin;Jinjiang Yuan
Affiliations:
Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China and Institute of Science, Information Engineering University of PLA, Zhengzhou, Henan 450001, P ...;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China
Venue:
Information Processing Letters
Year:
2009

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Abstract

This paper studies a bicriteria scheduling problem on a series-batching machine with objective of minimizing makespan and total completion time simultaneously. A series-batching machine is a machine that can handle up to b jobs in a batch and the completion time of all jobs in a batch is equal to the finishing time of the last job in the batch and the processing time of a batch is the sum of the processing times of jobs in the batch. In addition, there is a constant setup time s for each batch. For the problem we can find all Pareto optimal solutions in O(n^2) time by a dynamic programming algorithm, where n denotes the number of jobs.