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

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  • Lida Dong
  • Tianyang Chi
  • Chengcheng Zhu
  • Jun Yin

Abstract

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.

Suggested Citation

  • Lida Dong & Tianyang Chi & Chengcheng Zhu & Jun Yin, 2014. "Mixed Integer Programming‐Based Liveness Test for FMS with Full Routing Flexibility," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:319281
    DOI: 10.1155/2014/319281
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    References listed on IDEAS

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    1. Byrne, M. D. & Chutima, P., 1997. "Real-time operational control of an FMS with full routing flexibility," International Journal of Production Economics, Elsevier, vol. 51(1-2), pages 109-113, August.
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