1. Petri Nets: Their Development and Use in Production Planning Jeffrey E. Short, P.E. December 6, 2000

2. Slide 2 Advanced Manufacturing System Design Acknowledgements Librarians at Al Harris Library where I ordered an enormous amount of interlibrary loan material and kept it until several weeks overdueLibrarians at Al Harris Library where I ordered an enormous amount of interlibrary loan material and kept it until several weeks overdue

3. Slide 3 Advanced Manufacturing System Design Petri Nets History First suggested by C. Petri in 1962First suggested by C. Petri in 1962 –Described communication among automated machines Work expanded by othersWork expanded by others –Information System Theory Project of Applied Data Research, Inc. –Project MAC at MIT Many definitions followed to serve particular purposesMany definitions followed to serve particular purposes

4. Slide 4 Advanced Manufacturing System Design Petri Nets Definition Powerful modeling tool for manufacturingPowerful modeling tool for manufacturing A Petri net is a four-tuple:A Petri net is a four-tuple: –Places –Transitions –Input functions –Output functions

5. Slide 5 Advanced Manufacturing System Design The Petri Graph Places -Places -  Transitions -Transitions - | Directed Arcs (input & output functions) -Directed Arcs (input & output functions) -  Tokens -Tokens -

6. Slide 6 Advanced Manufacturing System Design The Petri Graph

7. Slide 7 Advanced Manufacturing System Design The Petri Graph Place

8. Slide 8 Advanced Manufacturing System Design The Petri Graph Place Transition

9. Slide 9 Advanced Manufacturing System Design The Petri Graph Place Transition Output & Input Functions

10. Slide 10 Advanced Manufacturing System Design The Petri Graph Place Transition Output & Input Functions Token

11. Slide 11 Advanced Manufacturing System Design Petri Net Execution Marking - determined by the placement of tokensMarking - determined by the placement of tokens Transition FiringTransition Firing –Enabled when # of tokens in each the input places = # of directed input arcs to the transitions –Firing occurs in zero time and is non-deterministic (randomly determined)

12. Slide 12 Advanced Manufacturing System Design Petri Net Execution t 1 is enabled since p 1 has one token

13. Slide 13 Advanced Manufacturing System Design Petri Net Execution t 1 is enabled since p 1 has one token t 3 is enabled

14. Slide 14 Advanced Manufacturing System Design Petri Net Execution t 1 is enabled since p 1 has one token t 3 is enabled t 2 is not enabled

15. Slide 15 Advanced Manufacturing System Design Petri Net Execution FiringFiring –Removes from the input places the number of tokens equal to the number of input arcs –Places in the output places the number of tokens equal to the number of output arcs –Thereby, tokens can be created and removed from the graph by execution

16. Slide 16 Advanced Manufacturing System Design Petri Net Execution To begin, t 1 or t 3 may fire. Chance determines which will.

17. Slide 17 Advanced Manufacturing System Design Petri Net Execution t 3 has fired

18. Slide 18 Advanced Manufacturing System Design Petri Net Execution t 1 has fired

19. Slide 19 Advanced Manufacturing System Design Petri Net Execution t 4 has fired and the net is dead

20. Slide 20 Advanced Manufacturing System Design Petri Net Execution Machine Shop Example

21. Slide 21 Advanced Manufacturing System Design Extended Petri Nets TimedTimed –Add time requirements to the transitions –Add time to requirements to the tokens in places Generalized StochasticGeneralized Stochastic –Randomly distribute time throughout the net

22. Slide 22 Advanced Manufacturing System Design Extended Petri Nets ColoredColored –Add coded (colored) tokens –Use selective firing rules for filtering or changing the token color FuzzyFuzzy –Add fuzzy rules to the transitions –Add fuzzy value to places or tokens –Fuzzy variables are things like high, medium, or low

23. Slide 23 Advanced Manufacturing System Design Current Uses of Petri Nets in Production Planning Project ManagementProject Management –Modeling resource constraints Traditional ManufacturingTraditional Manufacturing –Production Scheduling –Process determination

24. Slide 24 Advanced Manufacturing System Design Current Uses of Petri Nets in Production Planning FMSFMS –Modeling resource constraints like machine loading –Modeling schedules –Monitoring machine efficacy PLCPLC –Possible replacement to ladder logic particularly for fuzzy rules

25. Slide 25 Advanced Manufacturing System Design Future of Petri Nets ISO JT1/SC1/WG11 working on a standard with impact on the Petri netISO JT1/SC1/WG11 working on a standard with impact on the Petri net Several experts are advocating a separate committee within the working group just for Petri netsSeveral experts are advocating a separate committee within the working group just for Petri nets

26. Advanced Manufacturing Systems Design Jeffrey E. Short, P.E. Petri Nets: Their Development and Use in Production Planning December 6, 2000