Abstract
Ordinary t-timed modular Petri Nets are used for modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems. Each system is first decomposed into production line, assembly, disassembly and parallel machine modules followed by derivation of their modular Petri Net models. Two sets of modules, generic and generalized respectively, are derived corresponding to the simplest and most general cases. Overall system Petri Net model is obtained via synthesis of the individual modules satisfying system features (production rates, buffer capacities, machine expected up, down or idle times). Detailed mathematical expressions are derived for modules P-invariants (and T-invariants when exist); they are further generalized for a random topology and complexity dedicated production system. Total number of the individual Petri Net module nodes as well as of the combined system Petri Net model is also calculated. Results show the applicability of the proposed methodology and justify its modeling power and generality.
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References
M. Allam H. Alla (1998) ArticleTitleModeling and simulation of an electronic component manufacturing system using hybrid Petri Nets IEEE Transactions on Semiconductor Manufacturing 11 IssueID3 374–383
R. Akella P. R. Kumar (1986) ArticleTitleOptimal control of production rate in a failure prone manufacturing system IEEE Transactions on Automatic Control 31 116–126
Anschuetz, Henryk (2001) HPSIM, http://home.t-online.de/home/henryk.a/petrinet/e/hpsim_e.htm
F. Balduzzi A. Giua G. Menga (2000) ArticleTitleFirst – Order Hybrid Petri Nets: A model for Optimization and Control IEEE Transactions on Robotics and Automation 16 IssueID4 382–399
Bai, S. X. and Gershwin, S. B. (1990) Scheduling manufacturing systems with work-in-process inventory control: formulation of single part type systems. in Proceedings of the 29th IEEE CDC, pp 557–564
S. X. Bai S. B. Gershwin (1994) ArticleTitleScheduling manufacturing systems with work-in-process inventory control: multiple-part-type systems International Journal of Production Research 32 365–386
Boel, R. and Stremersch, G. (1999) VHS Case Study 5: Semantics of Timed Petri nets, equivalence and model reduction, Technical Report for VHS (Verification of Hybrid Systems), Systems Group University Ghent
J. A. Buzacott J. G. Shanthikumar (1993) Stochastic Models of Manufacturing Systems Englewood Cliffs Prentice Hall, NJ
S. Christensen L. Petrucci (2000) ArticleTitleModular Analysis of Petri Nets The Computer Journal 43 IssueID3 224–242
R. Conway W. Maxwell J. O. McClain Thomas L. Joseph (1988) ArticleTitleThe role of work-in-process inventory in serial production lines Operations Research 36 229–241
L. Custodio J. Senteiro C. Bispo (1994) ArticleTitleProduction Planning and Scheduling using a fuzzy decision system IEEE Transactions on Robotics and Automation 10 160–168
R. David H. Alla (1992) Petri Nets & Grafcet – Tools for Modeling Discrete Event Systems Prentice Hall ␣
A. A. Desrochers R. Al–Jaar (1995) Applications of Petri Nets in Manufacturing Systems – Modeling, Control and Performance Analysis IEEE Press ␣
M. Domg F. F. Chen (2001) ArticleTitleProcess modelling and analysis of manufacturing supply chain networks using object-oriented Petri nets Robotics and Computer Integrated Manufacturing 17 121–129
K. Feldmann C. Schnur W. Colombo (1996) ArticleTitleModularised, distributed real-time control of flexible production cells, using petri nets Control Engineering Practice 4 IssueID8 1067–1078
G. Frey (2000) ArticleTitleAssembly line sequencing based on Petri-net T-invariants Control Engineering Practice 8 63–69
S. B. Gershwin (1994) Manufacturing Systems Engineering Prentice Hall New Jersey
S. B. Gershwin (2000) ArticleTitleDesign and operation of manufacturing systems: the control-point policy IIE Transactions 32 891–906
T. Gu P. Bahri (2002) ArticleTitleA survey of Petri net applications in batch processes Computers in Industry 47 99–111
Ioannidis, S., Tsourveloudis, N. and Valavanis, K. (2002) Supervisory control of multiple-part-type production networks, CD-ROM Proceedings, 10th IEEE Mediterranean Conference on Control and Automation, Lisbon, Portugal
Wern-Kueir. Jehng (2002) ArticleTitlePetri net models applied to analyze automatic sequential pressing syst ems Journal of Materials Processing Technology 120 115–125
M. D. Jeng X. Xie (2001) ArticleTitleModeling and analysis of Semiconductor Manufacturing Systems with Degraded Behaviour Using Petri Nets and Siphons IEEE Transactions on Robotics and Automation 17 IssueID5 ␣–␣
J. Martinez M. Silva (1982) ArticleTitleA Simple and fast algorithm to obtain all invariants of generalized Petri net Application and Theory of Petri Nets 52 301–311
E. L. Mellado (2002) ArticleTitleAnalysis of discrete event systems by simulation of timed Petri net models Mathematics and Computers in Simulation 61 53–59
J. Moody P. Antsaklis (1998) Supervisory Control of Discrete Event Systems Using Petri Nets Kluwer Academic Publications ␣
T. Murata (1989) ArticleTitlePetri Nets: properties, analysis and applications Proceedings of the IEEE 77 IssueID4 541–580
A. Nketsa R. Valette (2001) ArticleTitleRapid and modular prototyping-based Petri nets and distributed simulation for manufacturing systems Applied Mathematics and Computation 120 265–278
J. Peterson (1981) Petri Net Theory And The Modeling of Systems Prentice Hall Inc ␣
J.M. Proth N. Sauer (1998) ArticleTitleScheduling of piecewise constant product flows: a Petri net approach European Journal of Operational Research 106 45–56
J.M. Proth X. Xiaolan (1996) Petri Nets, A Tool for Design and Management of Manufacturing Systems John Wiley & Sons ␣
W. Reisig (1992) A Primer in Petri Net Design Springer Verlag Germany
G. Rogers L. Bottaci (1997) ArticleTitleModular production systems: a new manufacturing paradigm Journal of Intelligent Manufacturing 8 147–156
Y. Tang M. C. Zhou R. Caudill (2001) ArticleTitleAn integrated approach to disassembly planning and demanufacturing operation IEEE Transactions on Robotics and Automation 17 IssueID6 773–784
L. Thevenon J. M. Flaus (2000) ArticleTitleModular representation of complex hybrid systems: application to the simulation of batch processes Simulation Practice and Theory 8 IssueID5 283–306
J. Thomas N. Nissanke K. Baker (1996) ArticleTitleA hierarchical Petri Net framework for the representation and analysis of assembly IEEE Transactions on Robotics and Automation 12 IssueID2 248–279
Torn, A. Petri nets – Calculating invariants, online at www.abo.fi/∼atorn/Petri/P53.html
Tsinarakis, G. (2002) Modeling Synthesis and Analysis of Production Systems with use of Petri Nets Master Thesis (in Greek), Technical University of Crete, Department of Production Engineering and Management
N. Tsourveloudis E. Dretoulakis S. Ioannidis (2000) ArticleTitleFuzzy work-in-process inventory control of unreliable manufacturing systems Information Sciences 27 69–83
K. Valavanis (1990) ArticleTitleOn the Hierarchical Modeling Analysis and Simulation of Flexible Manufacturing Systems with Extended Petri Nets IEEE Transactions on Systems, Man and Cybernetics 20 IssueID1 23–23
R. Valette B. Chezalviel-Pradin (1999) An Introduction to Petri net theory Fuzziness in Petri nets J. Cardoso H. Carmago (Eds) Studies in fuzziness and soft computing Physica Verlag ␣ 3–24
Veltsos, C. (1998) Automated Petri Net Synthesis for the Modeling and Analysis of Complex Dynamic Systems, Dissertation presented to the Graduate Faculty of The University of Southwestern Louisiana
K. Venkatesh M. Ilyas (1995) ArticleTitleReal-time Petri nets for modelling controlling and simulation of local area networks in flexible manufacturing systems Computers in Engineering 28 IssueID2 147–162
L. C. Wang (1996) ArticleTitleObject-oriented Petri nets for modeling and analysis of automated manufacturing systems Computer Integrated Manufacturing Systems 26 IssueID2 111–125
L. C. Wang S. Y. Wu (1998) ArticleTitleModeling with colored timed object-oriented petri nets for automated manufacturing systems Computers in Engineering 34 IssueID2 463–480
L. Wein (1988) ArticleTitleScheduling semiconductor wafer fabrication IEEE Transactions on Semiconductor Manufacturing 1 115–130
Y. Xue R. M. Kieckhafer F. F. Choobineh (1998) ArticleTitleAutomated construction of GSPN models for flexible manufacturing systems Computers in Industry 37 17–25
M. C. Zhou F. DiCesare (1993) Petri Net Synthesis for Discrete Event Control of Manufacturing Systems Kluwer Academic Publishers ␣
Zuberek, W. (1998) TPN-tools – tools for modeling and performance analysis using Timed Petri nets, online at web.cs.mun.ca/∼wlodek/tpntools/tpntools-i nvar.html
W. Zuberek (2001) ArticleTitleTimed Petri nets in modeling and analysis of cluster tools IEEE Transactions on Robotics and Automation 17 IssueID5 562–575
W. Zuberek W. Kubiak (1999) ArticleTitleTimed Petri Nets in Modeling and Analysis of Simple Schedules for Manufacturing Cells Computers and Mathematics with Applications 37 191–206
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Tsinarakis, G.J., Tsourveloudis, N.C. & Valavanis, K.P. Modular Petri Net based modeling, analysis, synthesis and performance evaluation of random topology dedicated production systems. J Intell Manuf 16, 67–92 (2005). https://doi.org/10.1007/s10845-005-4825-5
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DOI: https://doi.org/10.1007/s10845-005-4825-5