performance analysis of cellular manufacturing … · performance analysis of cellular...

PERFORMANCE ANALYSIS OF

CELLULAR MANUFACTURING SYSTEMS USING COLORED PETRI NETS

Hilano José Rocha de Carvalho (USP-EESC) [email protected]

Arthur José Vieira Por to (USP-EESC) [email protected]

The need for flexibility due to the global competitiveness is influencing the way companies are organized. There are several ways of organizing a manufacturing system directly dependent on the volume and on the variability of the products ddemanded. In order to reduce material handling and production scrap costs, cellular manufacturing systems (CMS) have emerged. Concerning a CMS study, the building of simulation models capable of handling complex simultaneity of processes and multifunctional work policies motivates the use of more efficient programming and simulation techniques. Hence, the aim of this paper is focused on proposing the use of colored Petri net formalism to develop a simulation model for the analysis of cellular manufacturing systems with multifunctional workforce in order to overcome the former limitations. The CPN Tools was used for the CPN edition and simulation analysis. The resultant colored Petri net based cellular manufacturing system simulation model (CPNCMSSM) was successfully used for the practical investigation of a three-working-cell CMS. Three scenarios were studied for which the number of family parts was the factor altered, converging to adequate and expected results about multifunctional work performance and work in process magnitude. Hence, the CPNCMSSM can be used to the study of bigger and more complex arrangements as an alternative to conventional programming and simulation languages and tools available. Keywords: Colored Petri nets, Cellular Manufacturing Systems, Simulation

�� !"�� #%$'&��(�� &&�" � � ( #�� )� *�&"�#�!� � �� ,+-#%��#�( &�+.&��!/1032547698�:�;9<=:%>@?9AB2DCFE94�?9G9H3IJ:LK ?909M9<@G9K <DN ?969H32O<D>P?9036QK 0R:L25694�<=:�K ?903S1E947?UT725IJ:V<W03G@CDH9CX:X<DK 03<WY9K N K :�8

Iguassu Falls, PR, Brazil, 09 - 11 October 2007

Z [\[\[][\^`_�a`b�^dc_�[�eV^dc�fPg�eV^%h1a1b�a1^%g]aPi�j.k j�l�m�n�o9p�k q�rP/1j�s�k jV/1/1p�k j�s.q�j�l.iVt]/`pVq�o9k i�j�n'uQq�j�q�s�/`uQ/1j�ovDwBxUy zX{�|�}B~�|d��9xR�%�Dy �5��B��|�� BwB�B~��B� ~U� �5zB�Bx�~U��BwBz � wX|�xRz5y ~�|�� DwB�B�By\��\xU��|d~UwB��J�B��|�~U� w�~U�B� � � | {


2

1. Introduction

The need for flexibility due to the global competitiveness is influencing the way

companies are organized. There are several ways of organizing a manufacturing system directly

dependent on the volume and on the variability of the products demanded (ASKIN, 1993). In

order to reduce material handling and production scrap costs, cellular manufacturing systems

(CMS) have emerged. As a matter of fact, such a system is defined by the concept of part family

about which different types of machines and products (or parts) are grouped according to a

predefined similarity index, e.g., the sequence of production operations, in order to form working

cells (SINGH & RAJAMANI, 2004).

Computer tools to model and simulate cellular or any kind of production system already

exist (LAW & KELTON, 2000). However, the time taken by the modeler using conventional

simulation programming languages to adapt a primary model for different scenarios may be a

costly constraint. In addition, an attempt to generalize a simulation model may yield modeling

loss of expressiveness, especially considering complex simultaneity of processes and material

handling.

Hence, the main objective of this paper is focused on the proposal of using a colored Petri

net simulation model to model and to simulate cellular manufacturing systems in order to reduce

complexity and modeling time without loss of expressiveness.

As a related work, Carvalho et al. (2005) demonstrated the potentiality of Petri nets to

model and to analyze the performance of the multifunctional workforce in a U-shaped production

line compared to other simulation languages. However, due to the low level Petri nets

limitations, especially in terms of the huge number of modeling elements, different levels of

complexity inherently present in real and large manufacturing systems demand a more

sophisticated approach. In this sense, the investigation herein tries to overcome the drawbacks

and to keep the positive aspects evidenced by Carvalho et al. (2005) using a high level Petri net

formalism.

The remainder of this paper is organized as follows. In Section 2, the theory of colored

Petri nets formalism is focused, concerning its main concepts and modeling and simulation

elements, the CPN tools for academic purposes. In Section 3, a colored Petri net based cellular



3

manufacturing system simulation model (CPNCMSSM) is presented. Section 4 is dedicated to

the practical use of CPNCMSSM using simulation. Finally, Section 5 is focused on the

conclusions and final considerations.

2. Colored Petr i nets

The theory of colored Petri nets (CPN) was developed as an extension to the basic Petri

nets theory (JENSEN, 1997). The prime objective of CPN is to make feasible the modeling and

formal analysis of large, concurrent and distributed systems using Petri nets. A detailed definition

and discusson about the CPN formalism can be found in Jensen (1997).

The CPN tools as defined in Jensen et al. (2007), in turn, comprise two components: a

graphical user interface (GUI) and CPN ML. These ones are directly related to three integrated

tools: the CPN editor, the CPN simulator and the CPN state space tool. The CPN ML is a

functional programming language implemented on top of a SML/NJ compiler. Herein used, the

CPN tools 2.2.0 academic version was obtained from CPNTools (2006).

Based on the CPN formalism and the CPN tools as defined above, the token primitive and

compound types are defined by the color sets associated with each place and their type

modifications are accomplished by the functions defined on the arcs. In order to do that, the

corresponding transition must be enabled to fire. This happens when the number and the type of

the input place tokens to the transition agrees with the conditions of transition’s enablement

defined by the transition guard. Figure 1 shows the CPN basic modeling elements, their graphical

representation and an example of how to deal with the CPN formalism.

As can be seen in Figure 1, the initial state of the CPN model is represented by three

tokens in “Place P1” . The number and the type of those tokens are defined by the initial place

marking of P1 (in this case, a five integer token and two ten integer tokens). They are three true

firing conditions to “Transition T1” since they are in agreement with the transition guard. The

firing of T1 initialize the function “FUN(X)”. “FUN(X)” captures the token data by the arc

variable “X” and transforms them into one string token in number and in type following the “ if-

then-else” structure of the CPN ML code of Figure 1. Finally, “Place P2” receives the one string

token from “FUN(X)” .



4

colset INT = integer; colset STRING = string; val X : INT; FUN(X) = If (X >= 5) andalso (X < 10)

then 1`¨YES else 1`¨NO¨;

Figure 1 – CPN basic modeling elements, their graphical representation and a CPN model example with its CPN ML code.

The prior conceptual discussion and the example depicted in Figure 1 is actually restricted

to a non-hierarchical colored Petri net. Herein, a hierarchical colored Petri net is proposed which

may incorporate two fundamental elements of modularization:

• Substitution transitions – permits the derivation of simpler submodels by others already

defined using a hierarchy approach of pages;

• Fusion places – permits a faster mechanism of distribution of token data along the entire

model linking submodels that may not be hierarchically associated.

In the light of simulation principles present in Law & Kelton (2000), the Petri net basic

modeling elements can be classified into static and dynamic elements. The static elements are the

places, the transitions and the arcs. The dynamic element that goes through the different

constituent nodes of a model is the token which may suffer several types of modifications in

number or in type. As discussed above, the presence of a token or a set of tokens in a determined

place defines the marking. As a matter of fact, the latter may be associated with the state of an

object, the value of a variable or any kind of content that might be relevant at the modeling stage.

Besides, the CPN editor and the CPN simulator with the CPN ML may provide the corresponding

characters for the requirements of discrete event simulation programming language (DESPL) as

defined by Law & Kelton (2000) and evidenced by Jensen et al. (2007). Moreover, the CPN state

space tool constitutes the main differentiation from a conventional DESPL, once it provides a

stable and formal manner for the verification of the so-called Petri nets model property analysis.

FUN(X)

INT STRING

X

1`5 ++ 2`10

[X > 0]

Color Type

Place P1 Place

Marking

Arc Var iable

Transition T1

Function

Arc Guard

Place P2

Name



5

3. A colored Petr i net simulation model for cellular manufactur ing system analysis

Hence, based on these last concepts and on those of Section 2 and Section 1, the intended

colored Petri net simulation model prime and highest page is depicted in Figure 2.

Figure 2 – CPN Tools editor interface: the prime page of the colored Petri net simulation model for a cellular manufacturing system.

In Figure 2, alongside the “ManufacturingSpecifications” prime page, the main CPN

modeling parts, the “Values Initialization” , the “Color Set Definitions” , the “Arc Variables” and

the “CPN ML Code Function Definitions” , are evidenced. Particularly, the “Values

Initializations” part define the automatic initialization of the number and the type of the products,

machines, workers, stations and production operations in consonance with the specifications of

the manufacturing system under study. The “Color Set Definitions” and the “Arc variables” parts

define, respectively, the necessary color sets associated with the resultant places and the direct

related arc variables of the model building. The main part which definitely differentiates the CPN

based CPN Tools from any other extension to Petri nets and establishes its modeling potentiality

is the “CPN ML Code Function Definitions” . The latter is responsible for the definition of the

Values Initialization

Color Set Definitions

Arc Variables

CPN ML Code Function Definitions

CPN Subpages



6

methods defined by the manufacturing system processes which will act directly on the token

modifications in number and in type.

The CPN subpages which derived from the prime page are also depicted in Figure 2. The

way each subpage was conceived followed a functional fashion for which different submodels

with specific purposes were constructed. Their hierarchy of pages is depicted in Figure 3.

Figure 3 – The hierarchy of pages (prime page and its derived subpages) of the CPNCMSSM. The “Workstation” subpage is presented separately.

In Figure 3, the “DefineProcesses” subpage is in charge of generating and controlling the

initial and the subsequent process tokens, concerning the type of products, workers, production

operations, machines and their corresponding stations. The worker resource dynamic property has

to do with the motions inside the working cells due to multifunctional work. At this present

paper, the workforce motion control is accomplished in the “DefineOperTravel” subpage, only

taking into account the time taken by the worker to go from one workstation to another. Hence, if

the same worker is demanded by more than one process information token at the same time (a

conflict situation), the former will be allocated to execute one production operation arbitrarily.

Consecutively, the “Processes” subpage was conceived to coordinate the above cited subpages

providing to the subsequent level, that is, the “Workstations” subpage, the necessary process and

worker motion information by means of colored tokens.

The place “Workplace” in Figure 3 constitutes the core of the CPN modeling herein

conceived. If the conditions for the start of a determined process become true, that is, the

ManufacturingSpecifications

Workstations

DefineProcesses DefineOperTravel

Processes Workplace



7

resources tokens demanded by the process information tokens are all simultaneously available, a

job token with a time stamp corresponding to the process time (based on the type of the

operation, product and machine) is put into the place “Workplace” . In this sense, the

simultaneous presence of different job tokens in place “Workplace” represents a condensed form

of modeling the simultaneity of several workstations carrying out different production operations

which correspond to the wholly function of the entire cellular manufacturing system.

4. A practical use of CPNCMSSM with simulation results

The cellular manufacturing system investigated comprises three working cells. It is

considered, at this present work, that a prior layout design was successfully done resulting in the

layout structure of Figure 4 in accordance with the production sequence similarities of the

different products.

Figure 4 – The cellular manufacturing system consisting of three working cells.

In Figure 4, each working cell is depicted with the replicate of each necessary machine

and the multifunctional workers. For example, in working cell 1, “M1_1” means one replicate of

a machine of type 1. Each machine, in turn, is located in a place called “StatType(i)” , where i

ranges from 1 to 15, that is, the total number of replicates of each machine. In addition, each of

the ten different types of machines is dedicated to the accomplishment of one type of operation

while all workers can do more than one operation due to the multifunctional work control policy,



8

as evidenced in Figure 4. Hence, the CPNCMSSM as defined in Section 3 was adapted to the

CMS of Figure 4. The distance among the fifteen machine replicates were approximately

considered in order to calculate the delay times associated with the multifunctional workforce

motion. The different process times of each machine were also taken into account. For the

generation of all types of initial process information tokens, an exponential distribution with

average rate of 100 was defined. Concerning this, for the maximum statistical confidence of

analysis, twenty replications of 48000 steps each were considered for the three scenarios

analyzed. These three different scenarios were defined varying the number of products: six

products for the first one, twelve products for the second one and eighteen products for the last

one. In this sense, the main objective of the experimental investigation herein is simply to verify

the use of CPNCMSSM on the performance analysis of the multifunctional workforce due to the

increase of the number of family parts.

Productive Indicators Scenar io 1 Scenar io 2 Scenar io 3

Average workforce usage* 4.21 (60,1%) 5.95 (85 %) 5.95 (85 %)

Average process queue length* 5.39 518.54 1149.12

Average workforce usage** - - 7.46 (83 %)

Average process queue length** - - 756.83

Table 1 – A comparative of productive indicators for three different scenarios. * Results for the initial multifunctional work control policy; * * Results for the new multifunctional work control

policy.

Table 1 presents a piece of the CPN Tools simulation reports for the average workforce

usage and processes in queue (work in process) in each of the three scenarios simulated. In Table

1, the average number of busy workers has increased from Scenario 1 to Scenario 2, being stable

from Scenario 2 to Scenario 3. The lesser change from Scenario 2 to Scenario 3 was due to the

fact that in the former the multifunctional work have already been fully executed which

influenced directly the increase in the average work in process from Scenario 2 to Scenario 3.

Hence, a new multifunctional workforce control policy was applied with the addition of two

workers to working cells 1 and 2 and a redefinition of the operations each one was supposed to



9

perform. Due to the latter modifications, as can be seen in Table 1, the average work in process

has considerably decreased for Scenario 3, but the average workforce usage remained

approximately the same from the one obtained by the former multifunctional work control policy

in percentage terms.

5. Conclusions

The performance analysis of multifunctional work in manufacturing system using Petri

nets was already evidenced by Carvalho et al. (2005). However, only by means of a CPN model

and CPN Tools, an effective cellular manufacturing system can be analyzed, as demonstrated by

a practical case in Section 4. The resultant colored Petri net based cellular manufacturing system

simulation model (CPNCMSSM) of Section 3 is general enough to be used to any kind of CMS,

since the modeler has only the task to change the possible machine distance alterations due to

layout re-designs and to consider or not multifunctional workforce. Even the addition of new

productive resources, such as workers and machines, can be easily done. Without a doubt,

CPNCMSSM is an alternative technique from conventional simulation languages and packages,

especially owing to multifunctional work and process simultaneity modeling power. For further

works, a user-friendly interface and an automatic code generator (CPNCMSSM´s CPN ML)

could be implemented by means of CPN Tools external communication with other programming

techniques.

References

ASKIN, R.G. & STANDRIDGE, C.R. Modeling and Analysis of Manufacturing Systems. New York: John Wiley & Sons, 1993.

CARVALHO, H. J. R. & YOSHIZAWA, A. R. & PONTES, H. L. J., & PORTO, A. J. V. Modelagem e Simulação de Linhas de Produção em Forma de U com Operadores Polivalentes por Redes de Petri Temporizadas, Anais do XXV Encontro Nacional de Engenharia de Produção, 2005.

CPNTools. Available via <http://wiki.daimi.au.dk/cpntools/cpntools.wiki> accessed in November, 2006.

DESROCHERS, A. & AL-JAAR, R. Applications of Petri Nets in Manufacturing Systems: modeling, control, and performance analysis, New York: IEEE Press, 1995.

JENSEN, K. Colored Petri Nets: Basic Concepts. 2. ed. New York: Springer, 1997.

JENSEN, K. & KRISTENSEN, L.R. & WELLS, L. Coloured Petri Nets and CPN Tools for Modeling and Validation of Concurrent Systems. International Journal on Software Tools for Technology Transfer. Special Section CPN 04/05, p.1-42, 2007.

LAW, A.M., & KELTON, W.D. Simulation modeling & analysis. 3. ed. New York: McGraw Hill



10

Inc., 2000.

SINGH, N. & RAJAMANI, D. Cellular Manufacturing Systems: Design, Planning and Control. Chapman & Hall: John Wiley & Sons, 1993.

performance analysis of cellular manufacturing … · performance analysis of cellular...

Documents