Petri Nets: Their Development and
Use in Production Planning
Jeffrey E. Short, P.E.
December 6, 2000
Acknowledgements
• Librarians at Al
Harris Library
where I ordered
an enormous
amount of
interlibrary loan
material and
kept it until
several weeks
overdue
Slide 2
Advanced Manufacturing
System Design
Petri Nets History
• First suggested by C. Petri in 1962
– Described communication among
automated machines
• Work expanded by others
– Information System Theory Project of
Applied Data Research, Inc.
– Project MAC at MIT
• Many definitions followed to serve
particular purposes
Slide 3
Advanced Manufacturing
System Design
Petri Nets Definition
• Powerful modeling tool for
manufacturing
• A Petri net is a four-tuple:
–
–
–
–
Slide 4
Places
Transitions
Input functions
Output functions
Advanced Manufacturing
System Design
The Petri Graph
• Places -

• Transitions -
|
• Directed Arcs (input & output
functions) • Tokens Slide 5

l
Advanced Manufacturing
System Design
The Petri Graph
Slide 6
Advanced Manufacturing
System Design
The Petri Graph
Place
Slide 7
Advanced Manufacturing
System Design
The Petri Graph
Transition
Place
Slide 8
Advanced Manufacturing
System Design
The Petri Graph
Transition
Output &
Input Functions
Slide 9
Place
Advanced Manufacturing
System Design
The Petri Graph
Transition
Token
Output &
Input Functions
Slide 10
Place
Advanced Manufacturing
System Design
Petri Net Execution
• Marking - determined by the
placement of tokens
• Transition 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)
Slide 11
Advanced Manufacturing
System Design
Petri Net Execution
t1 is enabled
since p1 has one
token
Slide 12
Advanced Manufacturing
System Design
Petri Net Execution
t1 is enabled
since p1 has one
token
Slide 13
t3 is enabled
Advanced Manufacturing
System Design
Petri Net Execution
t2 is not enabled
t1 is enabled
since p1 has one
token
Slide 14
t3 is enabled
Advanced Manufacturing
System Design
Petri Net Execution
• Firing
– 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
Slide 15
Advanced Manufacturing
System Design
Petri Net Execution
To begin, t1 or t3 may fire. Chance
determines which will.
Slide 16
Advanced Manufacturing
System Design
Petri Net Execution
t3 has fired
Slide 17
Advanced Manufacturing
System Design
Petri Net Execution
t1 has fired
Slide 18
Advanced Manufacturing
System Design
Petri Net Execution
t4 has fired and the
net is dead
Slide 19
Advanced Manufacturing
System Design
Petri Net Execution
Machine Shop
Example
Slide 20
Advanced Manufacturing
System Design
Extended Petri Nets
• Timed
– Add time
requirements to
the transitions
– Add time to
requirements to
the tokens in
places
Slide 21
• Generalized
Stochastic
– Randomly
distribute time
throughout the
net
Advanced Manufacturing
System Design
Extended Petri Nets
• Colored
• Fuzzy
– Add coded
(colored) tokens
– Use selective
firing rules for
filtering or
changing the
token color
Slide 22
– Add fuzzy rules
to the
transitions
– Add fuzzy value
to places or
tokens
– Fuzzy variables
are things like
high, medium,
or low
Advanced Manufacturing
System Design
Current Uses of Petri
Nets in Production
Planning
• Project
Management
– Modeling
resource
constraints
Slide 23
• Traditional
Manufacturing
– Production
Scheduling
– Process
determination
Advanced Manufacturing
System Design
Current Uses of Petri
Nets in Production
Planning
• FMS
• PLC
– Modeling resource
constraints like
machine loading
– Modeling
schedules
– Monitoring
machine efficacy
Slide 24
– Possible
replacement to
ladder logic
particularly for
fuzzy rules
Advanced Manufacturing
System Design
Future of Petri Nets
• ISO 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
nets
Slide 25
Advanced Manufacturing
System Design
Advanced Manufacturing Systems
Design
Jeffrey E. Short, P.E.
Petri Nets: Their Development and
Use in Production Planning
December 6, 2000