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Mathematical Problems in Engineering
Volume 2018, Article ID 3124182, 10 pages
Research Article

Scheduling Batch Processing Machine Using Max–Min Ant System Algorithm Improved by a Local Search Method

1School of Mines, China University of Mining and Technology, Xuzhou 221116, China
2School of Management, University of Science and Technology of China, Hefei 230026, China

Correspondence should be addressed to Yu Wang; moc.621@CTSUgnaWuY

Received 4 September 2017; Revised 13 December 2017; Accepted 1 January 2018; Published 28 January 2018

Academic Editor: Fiorenzo A. Fazzolari

Copyright © 2018 XiaoLin Li and Yu Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of minimizing the makespan on single batch processing machine is studied in this paper. Both job sizes and processing time are nonidentical and the processing time of each batch is determined by the job with the longest processing time in the batch. Max–Min Ant System (MMAS) algorithm is developed to solve the problem. A local search method MJE (Multiple Jobs Exchange) is proposed to improve the performance of the algorithm by adjusting jobs between batches. Preliminary experiment is conducted to determine the parameters of MMAS. The performance of the proposed MMAS algorithm is compared with CPLEX as well as several other algorithms including ant cycle (AC) algorithm, genetic algorithm (GA), and two heuristics, First Fit Longest Processing Time (FFLPT) and Best Fit Longest Processing Time (BFLPT), through numerical experiment. The experiment results show that MMAS outperformed others especially for large population size.