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2014 Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility
Lida Dong, Tianyang Chi, Chengcheng Zhu, Jun Yin
J. Appl. Math. 2014: 1-12 (2014). DOI: 10.1155/2014/319281


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.


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Lida Dong. Tianyang Chi. Chengcheng Zhu. Jun Yin. "Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility." J. Appl. Math. 2014 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131514
Digital Object Identifier: 10.1155/2014/319281

Rights: Copyright © 2014 Hindawi


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