Modeling of a Manufacturing Process Using
Petri Nets and Fuzzy Logic
Emmanuelle de Gentili, Ange de Cicco, Jean-Francois Santucci
University of Corsica, UMR CNRS 6134
Corsica, FRANCE
Email: gentili, decicco, santucci@univ-corse.fr
Abstract—This paper describes the modeling of a manufacturing
process using Petri Nets [Silva et al., 1998],
[Peterson, 1982]. Thanks to this approach, we could structure
and separate the order model from the data model,
and hence assure the modeling’s adaptability and portability.
Due to the data types and uncertainty of some, we apply
the theory of fuzzy subsets developed by Zadeh in 1970
[Zadeh, 1975] to model the system’s ”uncertainty” parameters
[Cardoso et al., 1993]. In addition, we present a brief
summary of the basic concepts of fuzzy linear programming
used in the decidability of our problem, allowing us to
model one of the links in the production system, which the
manufacturing process represents.
I. INTRODUCTION
This paper addresses a problematic and the subsequent
study we carried out on an agro-alimentary production
system aimed at controlling the quality of the products
using appropriate mathematical concepts and adapted
computer tools [Agioux, 2003]. This production system
involved a process for making cheese from raw milk.
Our goal was to model the global cheese making process.
The difficulty we encountered in this study was due
to the fact that the ”accepted” data were not ”frozen”
data. On the other hand, the pasteurized cheese making
process as a whole and its various phases and work times
were controlled [Jeanson, 2000]. Similarly, the objective
to attain in production was also an ”uncertain” data (i.e.,
got the product).
We proposed a computer modeling of the
production system [Valette, 1997] using Petri nets
[Silva et al., 1998], [Peterson, 1982] and fuzzy logic
[Zadeh, 1975]. Petri nets allowed us to sequentially
model the production system. Fuzzy logic gave us
a representation of the ”uncertain” parameters in the
production system together with the acceptance of
subjective elements dependent on factors capable of
varying.
The modeling tools we used were analysis and prediction
tools indispensable not only for coping with the
consequences of human actions or natural changes, but
also for evaluating and taking into account the inaccuracy
in the model’s parameters, so that a bracket of values
and not a unique value could be provided as a simulation
result.
Throughout this article we describe the concepts and
methods which allowed us to model a production system.
In section 1 we summarize the various concepts and
theories used in our models : (1) Petri nets, which
gave us a modular and portable representation of the
production systems ; (2) fuzzy subset theory, which
allowed us to model the system’s ”uncertain” parameters
[Cardoso et al., 1993] ; and (3) linear programming,
which allowed us to solve our system. In section 2
we describe the concept of ”got”, which conditions the
perception that we have a product of quality. In section
3, we detail the modeling of the variables by fuzzy
logic as well as one of the links in the production
system representing the cheese making process. Finally,
in the conclusion, we evaluate the results obtained with
these premiere initiatives and propose some approaches
to follow in future work.
II. STATE OF THE ART
A. Petri Nets
Petri nets were defined by Carl Adam Petri in 1962
[Petri, 1962], [Petri, 1966], [Petri, 1977]. They allow
modeling and displaying behaviors comprising parallelism
[Diaz, 2001], synchronization and sharing of resources.
In addition, they have furnished abundant theoretical
results.
According to Peterson, the modeling of production
systems [Peterson, 1981], [Peterson, 1984] using the formalism
of Petri nets, which are powerful tools, allows
specifying, modeling, evaluating and managing dynamic
systems. It also fosters the understanding, defining and
analyzing of the global behavior of the systems from their
inception and all along through their design process. This
expansion process is carried out in phases, each validated
before the next phase is started [David and Alla, 1997].
States are denoted here by pi, pi, p and
transitions by ti, ti, t, for simplicity according to
the case [Vidal-Naquet and Choquet-Geniet, 1992],
[Reisig, 1985]. By convention an arc has a weight with
the integer value 1. More generally, an arc weight may
be an integer greater than 1, but such a value should be
indicated explicitly on the corresponding arc. A Petri net
can be represented formally by a quadruplet R = (P, T,
W, mo) where :
• P = {p1, p2, . . . , pn} is a set of states ;
• T = {t1, t2, . . . , tn} is a set of transitions ;
• W : (P × T) [ (T × P) -! N is the weight function
;
• m : P -! N is a marking function.
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