PERFORMANCE ANALYSIS OF CELLULAR MANUFACTURING SYSTEMS USING COLORED PETRI NETS

!" #%$'&( &&" ( #)* &"#!,+-#% #(&+.&! /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 PERFORMANCE ANALYSIS OF CELLULAR MANUFACTURING SYSTEMS USING COLORED PETRI NETS Hilano José Rocha de Carvalho (USP-EESC) hilanorc@sc.usp.br Arthur José Vieira Porto (USP-EESC) ajvporto@sc.usp.br 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

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 2

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 Petri 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 ifthen-else structure of the CPN ML code of Figure 1. Finally, Place P2 receives the one string token from FUN(X). 3

colset INT = integer; colset STRING = string; val X : INT; FUN(X) = If (X >= 5) andalso (X < 10) then 1` YES else 1` NO ; Place Marking Color Type Name 1`5 ++ 2`10 Place P1 Arc Variable Transition T1 X Place P2 FUN(X) INT [X > 0] Arc Guard Function STRING 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. 4

3. A colored Petri net simulation model for cellular manufacturing 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. CPN Subpages Values Initialization Color Set Definitions Arc Variables CPN ML Code Function Definitions 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 5

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. ManufacturingSpecifications Workstations Processes Workplace DefineProcesses DefineOperTravel 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 6

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, 7

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 Scenario 1 Scenario 2 Scenario 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 8

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 9

Inc., 2000. SINGH, N. & RAJAMANI, D. Cellular Manufacturing Systems: Design, Planning and Control. Chapman & Hall: John Wiley & Sons, 1993. 10