Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility
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 pap...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/319281 |
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| _version_ | 1832556150874177536 |
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| author | Lida Dong Tianyang Chi Chengcheng Zhu Jun Yin |
| author_facet | Lida Dong Tianyang Chi Chengcheng Zhu Jun Yin |
| author_sort | Lida Dong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a4dd5f5461304c00a2894420f23c56d1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a4dd5f5461304c00a2894420f23c56d12025-02-03T05:46:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/319281319281Mixed Integer Programming-Based Liveness Test for FMS with Full Routing FlexibilityLida Dong0Tianyang Chi1Chengcheng Zhu2Jun Yin3Hangzhou Institution of Service Engineering, Hangzhou Normal University, Hangzhou 310027, ChinaHangzhou Institution of Service Engineering, Hangzhou Normal University, Hangzhou 310027, ChinaInstitution of Electronic Circuit & Information Systems, Zhejiang University, Hangzhou 310027, ChinaInstitution of Electronic Circuit & Information Systems, Zhejiang University, Hangzhou 310027, ChinaMixed 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.http://dx.doi.org/10.1155/2014/319281 |
| spellingShingle | Lida Dong Tianyang Chi Chengcheng Zhu Jun Yin Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility Journal of Applied Mathematics |
| title | Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility |
| title_full | Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility |
| title_fullStr | Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility |
| title_full_unstemmed | Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility |
| title_short | Mixed Integer Programming-Based Liveness Test for FMS with Full Routing Flexibility |
| title_sort | mixed integer programming based liveness test for fms with full routing flexibility |
| url | http://dx.doi.org/10.1155/2014/319281 |
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