A heuristic algorithm for two-stage flexible flow shop scheduling with head group constraint

Abstract

On the background of the shops in the mould manufacturers, in this paper, a two-stage flexible flow shop scheduling problem is first described to minimise the makespan with head group constraint and released time, where the first stage consists of unrelated parallel work centres. Next, this problem is proved to be NP-hard. After that, a constructive heuristic algorithm, named as H′, is proposed and then both its time complexity and worst-case bound are analysed in detail. In addition, three classical heuristics are improved for the solution of this problem and their time complexity is also given. In order to test the efficiency of the H′ algorithm, sets of instances are designed. Compared with the three improved heuristics by means of these sets of examples, the performance of the H′ algorithm is superior. Furthermore, the H′ algorithm can even solve large-size practical problems in a reasonable solution time, which is significant to the application in the shops of mould makers.

Keywords:

• heuristic
• flow shop
• head group constraint
• worst-case analysis

Acknowledgements

This work was financially supported by the National Natural Science Foundations of China (50675039, 51175094) and Production and Research Project of Guangdong Province of China (2010A090200054). We would like to thank the anonymous reviewers whose comments helped to improve the manuscript considerably.