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Journal of Applied Mathematics
Volume 2014, Article ID 319281, 12 pages
Research Article

Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility

1Hangzhou Institution of Service Engineering, Hangzhou Normal University, Hangzhou 310027, China
2Institution of Electronic Circuit & Information Systems, Zhejiang University, Hangzhou 310027, China

Received 31 December 2013; Revised 20 June 2014; Accepted 2 July 2014; Published 7 August 2014

Academic Editor: Javier Oliver

Copyright © 2014 Lida Dong et al. 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.


Mixed integer programming (MIP) is an important technique to verify the liveness property of sequential flexible manufacturing systems (FMS) modeled by Petri nets. When there are some fully flexible routings in FMS, the existing MIP-based methods are not suitable for testing their liveness. This paper defines a subclass of S*PR nets firstly, namely, OSC-S*PR nets, and concludes that an OSC-S*PR net is live if there exist no non-max′-controlled siphons. Accordingly, determining whether or not an OSC-S*PR net is live can also be realized by using standardized mixed integer programming (MIP) tools. Furthermore, the liveness property of S*PR nets can be tested in two steps: first, for a given S*PR net, constructing an OSC-S*PR net to ensure that if the latter is live then the former must be live; second, testing liveness of the constructed OSC-S*PR net by the aforementioned MIP-based algorithm. In the end, the performance of the method is demonstrated by an application of FMS.