**1. Introduction**

The objective of modeling a manufacturing process is mostly utilitarian with aspects such as support of its planning, ensuring optimizing or providing environment for automation of its planning. Its cognitive aspect is also of importance as building a model forces a planner to track the entire issue of generating a process plan. The main components of a production process description include: a description of the stereo-metric structure (stereo-structure), a description of the time structure (chrono-structure), a specification of processing conditions and a description of the factors of ensuring reliability of processing. Stereo-structure involves characteristics related to dimensional production chains, spatial arrangement and connection

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

with movement of working units of the machine tool. Chrono-structure involves characteristics related to structural components of operation time and the sequence of these components. Chrono-structure of a complex, multi-tool machining processes involves the following components: specification of simple operations completed on individual features; assigning simple operations to complex operations; distribution of operations into complex operations and defining a reasonable sequence of complex operations.

This period was followed by a range of significant applications of Petri networks in modeling discrete manufacturing processes. The team of Kiritsis has showed particular interest in this issue [3–10]. The published works analyzed the opportunities of classifying operations in the process of production, representation of alternative courses of manufacturing process and dynamic planning of processes. The complete approach in the 1990s has also been put forward by the duo of Horvát and Rudas [11–14]. It involved both acquisition of knowledge and modeling the structure of the manufacturing process as well as evaluation of the generated Petri network. The authors aimed at developing a knowledge-based manufacturing process modeling methodology. In the same period, the use of Petri networks was forecast for two purposes: modeling knowledge related to selection and classifying operations and flexible

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Today, it might be stated that this modeling technique has become the most popular one in FMS modeling, scheduling production [17], controlling and management of manufacturing processes in FMS. Stochastic Petri networks are used for considering the random nature of some events [18]. Preventive detection of locks is one of the FMS model's main functions [19]. The issue of flow of objects through the manufacturing process remains in between planning of the manufacturing process and the measures necessary to implement it. The Petri networks methodology is also used here. The work [10] considering the issue of estimating the upper and lower limit of time and cost of completing a production series of a given part in certain workshop conditions is essential here. An opportunity of variant course of individual processes for individual parts of a production batch is assumed. A more efficient model was obtained—compared to the traditional approach based on determining critical path—with

The most expanded Petri network classes in manufacturing are used in the work [20] for the purpose of loading machinery in FMS. Based on of hybrid Petri networks [21], which are fuzzy neural Petri networks, their language was expanded by adding color attributes, inhibitory arcs and time function. According to the authors, the ENhanced Fuzzy Neural Petri Net (ENFNPN) gives extraordinary opportunities of flexible modeling perfectly corresponding to

Multi-axis machine tools with a larger number of machine units currently play an increasingly significant role in machine processing. The effective use of such machine tools is strictly determined with maximizing concurrency, which is reflected by an optimum chrono-structure of operations. In order to optimize the chrono-structure of a concurrent operation, it is necessary to define subsets of operations that might be conducted simultaneously and to define the optimum relation of preferences, taking into account the division along with a range of various conditions and limitations. It is not a trivial task; hence, it is preferable to use a correctly adapted computer aided process planning (CAPP) class system and planning

Process specification language (PSL) is the most complex project in modeling and analysis of manufacturing processes using the Petri network technique. The works on this project, which were coordinated by the National Institute of Standards and Technology (NIST) aimed at developing an international standard of a description language for all aspects of manufacturing

FMS, allowing for modeling and processing knowledge at the expert system level.

representation of the sequence of operations [15, 16].

regard to the availability of production tools and machinery.

methodology.

A simple operation understood as processing one feature with one tool is a basic component of the operations chrono-structure. A complex operation means a group of simple operations completed using one tool without replacing it, changing the position of the processed part and without re-mounting, even a partial one. Complex operations are combined in sequences on rising hierarchy levels. Borders of these sequences are set by: change of a tool, change of the parts processing position within the reference frame of the machine tool, re-mounting, change of reference frame and, on a higher level of production process, division into roughing and precise processing.

A manufacturing operation might be defined as a cause-and-effect process including three basic subgroups:


A description of the chrono-structure might be made by defining organization and concurrency relations on sets of components of the aforementioned subgroups. If the first of the subgroups is treated as a set of conditions and the other two as a set of events, and flow relation is described on these two sets, the result is a directed bipartite graph structure—a base of the Petri network.

Topological characteristics of a bipartite directed graph that the Petri network is allowed for modeling various logical, cause and effect, time, attribute, linguistic, semantic, geometrical and other relations. Such relations are considered both at the stage of planning a production process and at the stage of implementing it. Therefore, an interest in the methodology of Petri networks for the purpose of planning manufacturing processes grew as early as in the second half of the 1980s [1]. The first attempts to use the Petri network in planning manufacturing processes were related to connecting the production process plan to conditions resulting from the production department's potential. Therefore, their basic use in construction of machines consisted of modeling of production systems, mostly the flexible manufacturing system (FMS). A comprehensive review of use of Petri networks in planning manufacturing processes by 1992 is put forward in this work [2].

This period was followed by a range of significant applications of Petri networks in modeling discrete manufacturing processes. The team of Kiritsis has showed particular interest in this issue [3–10]. The published works analyzed the opportunities of classifying operations in the process of production, representation of alternative courses of manufacturing process and dynamic planning of processes. The complete approach in the 1990s has also been put forward by the duo of Horvát and Rudas [11–14]. It involved both acquisition of knowledge and modeling the structure of the manufacturing process as well as evaluation of the generated Petri network. The authors aimed at developing a knowledge-based manufacturing process modeling methodology. In the same period, the use of Petri networks was forecast for two purposes: modeling knowledge related to selection and classifying operations and flexible representation of the sequence of operations [15, 16].

with movement of working units of the machine tool. Chrono-structure involves characteristics related to structural components of operation time and the sequence of these components. Chrono-structure of a complex, multi-tool machining processes involves the following components: specification of simple operations completed on individual features; assigning simple operations to complex operations; distribution of operations into complex operations

A simple operation understood as processing one feature with one tool is a basic component of the operations chrono-structure. A complex operation means a group of simple operations completed using one tool without replacing it, changing the position of the processed part and without re-mounting, even a partial one. Complex operations are combined in sequences on rising hierarchy levels. Borders of these sequences are set by: change of a tool, change of the parts processing position within the reference frame of the machine tool, re-mounting, change of reference frame and, on a higher level of production process, division into roughing

A manufacturing operation might be defined as a cause-and-effect process including three

**1.** Passive (static) including current statuses of features, tools, status of the machine tool's auxiliary assemblies such as tailstock sleeve, steady rest, turntable, pallet changer, position

**2.** Active (dynamic) including operations, changes of tools, movement of auxiliary units, re-

**3.** Decision-making, including events, the nature of which is not temporary, but informative such as releasing the opportunity of changing a tool, forcing a change in the table's posi-

A description of the chrono-structure might be made by defining organization and concurrency relations on sets of components of the aforementioned subgroups. If the first of the subgroups is treated as a set of conditions and the other two as a set of events, and flow relation is described on these two sets, the result is a directed bipartite graph structure—a base of the

Topological characteristics of a bipartite directed graph that the Petri network is allowed for modeling various logical, cause and effect, time, attribute, linguistic, semantic, geometrical and other relations. Such relations are considered both at the stage of planning a production process and at the stage of implementing it. Therefore, an interest in the methodology of Petri networks for the purpose of planning manufacturing processes grew as early as in the second half of the 1980s [1]. The first attempts to use the Petri network in planning manufacturing processes were related to connecting the production process plan to conditions resulting from the production department's potential. Therefore, their basic use in construction of machines consisted of modeling of production systems, mostly the flexible manufacturing system (FMS). A comprehensive review of use of Petri networks in planning manufacturing

of tool head as well as selected manufacturing datum and clamping methods;

and defining a reasonable sequence of complex operations.

and precise processing.

38 Petri Nets in Science and Engineering

clamping, and so on;

processes by 1992 is put forward in this work [2].

tion, and so on.

Petri network.

basic subgroups:

Today, it might be stated that this modeling technique has become the most popular one in FMS modeling, scheduling production [17], controlling and management of manufacturing processes in FMS. Stochastic Petri networks are used for considering the random nature of some events [18]. Preventive detection of locks is one of the FMS model's main functions [19].

The issue of flow of objects through the manufacturing process remains in between planning of the manufacturing process and the measures necessary to implement it. The Petri networks methodology is also used here. The work [10] considering the issue of estimating the upper and lower limit of time and cost of completing a production series of a given part in certain workshop conditions is essential here. An opportunity of variant course of individual processes for individual parts of a production batch is assumed. A more efficient model was obtained—compared to the traditional approach based on determining critical path—with regard to the availability of production tools and machinery.

The most expanded Petri network classes in manufacturing are used in the work [20] for the purpose of loading machinery in FMS. Based on of hybrid Petri networks [21], which are fuzzy neural Petri networks, their language was expanded by adding color attributes, inhibitory arcs and time function. According to the authors, the ENhanced Fuzzy Neural Petri Net (ENFNPN) gives extraordinary opportunities of flexible modeling perfectly corresponding to FMS, allowing for modeling and processing knowledge at the expert system level.

Multi-axis machine tools with a larger number of machine units currently play an increasingly significant role in machine processing. The effective use of such machine tools is strictly determined with maximizing concurrency, which is reflected by an optimum chrono-structure of operations. In order to optimize the chrono-structure of a concurrent operation, it is necessary to define subsets of operations that might be conducted simultaneously and to define the optimum relation of preferences, taking into account the division along with a range of various conditions and limitations. It is not a trivial task; hence, it is preferable to use a correctly adapted computer aided process planning (CAPP) class system and planning methodology.

Process specification language (PSL) is the most complex project in modeling and analysis of manufacturing processes using the Petri network technique. The works on this project, which were coordinated by the National Institute of Standards and Technology (NIST) aimed at developing an international standard of a description language for all aspects of manufacturing process completion [6]. Petri network class called the Compact Process Planning net (CPP-net) is the technical representation of PSL concept. Formally, CPP-net is an organized set of four components (P, T, E, M0); it is therefore a base Petri network. A set of P locations in CPP-net includes three subsets: control locations, input locations and locations representing limits. Components of T set represent tasks to be performed, conditioned by the E flow relation. A feasibility graph is developed based on the Petri network. It presents all the possible transition sequences in CPP-net corresponding to possible courses of the process. A large proportion of this course is irrational. Therefore, the subsequent stage includes a heuristic method to eliminate the courses that are not compliant with certain assumptions resulting from correctness of the production process [5]. It allows to significantly reduce the number of possible variants of the course of the process.

#### **2. Generative process planning**

Basically, there are two various approaches to plan a process in CAPP systems: generative (GCAPP) and variant (VCAPP). Differences are significant and are also reflected in models of manufacturing processes. An intermediate approach, also called a hybrid one, is also customary, but its description cannot be easily formalized. Generative planning consists of drawing up the process using individual features, to synthesis of tasks on an increasingly higher level: a complex operation, mounting, operation, processing stage, manufacturing process. The generative approach is used if manufactured machine parts significantly differ from each other and groups of parts with manufacturing similarities cannot be identified. The process model in GCAPP is generated gradually as progress is made in planning it. A generated model has a dispersed nature; however, it includes modules with a previously defined structure. It is then necessary to determine the number of modules of a certain type and classify them. **Figure 1** presents the general structure of such models.

The Petri network language class used for building the model has the following form:

$$\text{PN}\_1 = \{P, T, E, I, S, R, M\_0\} \tag{1}$$

where *P*: a nonempty, finite set of places, *T*: a nonempty, finite, disjointed of P set of transitions, *E* ⊂ (P × T) ∪ (T × P): a flow relation, *I*: a set of inhibitor arcs, *S*: *T* → *N0* , a function of time, *R*: *T* → [0, 1], a priority function, and *M0* : *P* → (0, 1), an initial marking.

The conditions of preparing transition *t* for firing have the following form:

$$M\!\!\!\!p\!/\!p\!/\!\!\/=\begin{cases}1,\forall p\ \in\!\!\!\/(p,\!t)\in\!\!\/(p,\!t)\in\!\!\/(p,\!\!\/),\tag{2}$$

The interdependence between M current status and M' status directly resulting from it has

0 *if p* ∈ .

*M*(*p*) *otherwise*

*t and p* ∉ *t*. <sup>1</sup> *if <sup>p</sup>* <sup>∈</sup> *<sup>t</sup>* .

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(3)

⎧ ⎪ ⎨ ⎪ ⎩

been defined as follows:

where *t*.

*M*(*p*) =

—*t* transition output places set.

**Figure 1.** General (partial) multi-tool processing operation model.

where *M* (*p*)—a current marking for *p* place, ∙ *t*–*t* transition input places set, *i*(*p*, *t*)—inhibitor arc from *p* place to *t* transition.

Eq. (2) applies in cases where only one transition meets the feasibility conditions. If two or more transitions meet the feasibility conditions, only one of them—the highest priority one is completed. Other transitions are ranked in next iteration of the simulations process.

**Figure 1.** General (partial) multi-tool processing operation model.

The interdependence between M current status and M' status directly resulting from it has been defined as follows:

$$M(p) = \begin{cases} 0 \text{ if } p \in \cdot \land \text{ and } p \notin \cdot \\\ 1 \text{ if } p \in \cdot \land \\\ \quad M(p) \text{ otherwise} \end{cases} \tag{3}$$

where *t*. —*t* transition output places set.

process completion [6]. Petri network class called the Compact Process Planning net (CPP-net) is the technical representation of PSL concept. Formally, CPP-net is an organized set of four components (P, T, E, M0); it is therefore a base Petri network. A set of P locations in CPP-net includes three subsets: control locations, input locations and locations representing limits. Components of T set represent tasks to be performed, conditioned by the E flow relation. A feasibility graph is developed based on the Petri network. It presents all the possible transition sequences in CPP-net corresponding to possible courses of the process. A large proportion of this course is irrational. Therefore, the subsequent stage includes a heuristic method to eliminate the courses that are not compliant with certain assumptions resulting from correctness of the production process [5]. It allows to significantly reduce the number of possible variants of

Basically, there are two various approaches to plan a process in CAPP systems: generative (GCAPP) and variant (VCAPP). Differences are significant and are also reflected in models of manufacturing processes. An intermediate approach, also called a hybrid one, is also customary, but its description cannot be easily formalized. Generative planning consists of drawing up the process using individual features, to synthesis of tasks on an increasingly higher level: a complex operation, mounting, operation, processing stage, manufacturing process. The generative approach is used if manufactured machine parts significantly differ from each other and groups of parts with manufacturing similarities cannot be identified. The process model in GCAPP is generated gradually as progress is made in planning it. A generated model has a dispersed nature; however, it includes modules with a previously defined structure. It is then necessary to determine the number of modules of a certain type and classify them. **Figure 1**

The Petri network language class used for building the model has the following form:

tions, *E* ⊂ (P × T) ∪ (T × P): a flow relation, *I*: a set of inhibitor arcs, *S*: *T* → *N0*

The conditions of preparing transition *t* for firing have the following form:

*PN*<sup>1</sup> = (*P*, *T*, *E*, *I*, *S*, *R*, *M*0), (1)

where *P*: a nonempty, finite set of places, *T*: a nonempty, finite, disjointed of P set of transi-

1, ∀*p* ∈ .

Eq. (2) applies in cases where only one transition meets the feasibility conditions. If two or more transitions meet the feasibility conditions, only one of them—the highest priority one is completed. Other transitions are ranked in next iteration of the simulations process.

: *P* → (0, 1), an initial marking.

*<sup>t</sup>* 0, <sup>∀</sup>*i*(*p*, *<sup>t</sup>*) <sup>∈</sup> <sup>I</sup> (2)

*t*–*t* transition input places set, *i*(*p*, *t*)—inhibitor

, a function of time,

the course of the process.

40 Petri Nets in Science and Engineering

**2. Generative process planning**

presents the general structure of such models.

*R*: *T* → [0, 1], a priority function, and *M0*

*<sup>M</sup>*(*p*) <sup>=</sup> {

where *M* (*p*)—a current marking for *p* place, ∙

arc from *p* place to *t* transition.

The aforementioned class is therefore a temporary Petri network with a binary marking function and inhibitor arcs. Inhibitor arcs make the model simpler, more transparent, therefore, easier to build and analyze. The suggested module structure allows for automation in generating the model. Modules for replacement of tools in the number of tools used for the process control the need to replace a tool. Topologically identical modules of control of calling the Workpiece Coordinate System (WCS) should be identified as the position required by the production process and the orientation of a processed object in a machine coordinate system. A module of complex operations is the core of the model. Each transition in the module calls a tool and WCS for the subsequent complex operation. A subsequent module is a sequence of operations conducted using the same tool on subsequent features. The modules is an area for structural optimization of the process by way of minimizing the number of tool changes. The model is supplemented by modules classifying simple operations for individual features. A marker on the last item of a module means ending processing of a given feature.

purpose of processing machine parts with similar features in order to achieve a high level of production reproducibility and artificially extend the size of a production batch. GT is related to the cellular production [24] concept, which means production both in flexible manufacturing cells and in autonomous flex-cell. GT therefore involves a range of various operations of a design, production and organizational nature, which requires coherence and synchronization. Many of them, such as determining production similarity of machine parts, grouping and classification of machine parts, variant design, parametric programming of computer numerical control (CNC) machine tools, developing group manufacturing processes, designing group processing equipment, configuration of manufacturing cells [25] and the issue of planning and controlling the manufacturing process are still readily raised subject of development works. Technical implementations of VCAPP systems most frequently include one of the two solutions: building a system based on finding a similar part of a previously manufactured machine part and adopting its production process plan or developing a group production process for the so-called synthetic representative of the group. In both cases, it is possible to use a process model developed in the Petri network technique; however, the second method is more natural in using its potential. Feature precedence network (FPN) defined as a directed graph representing precedences that result from limitations imposed by the features is a precondition for designing a correct manufacturing operation. For complex parts, with a large number of processed features and relations between them, FPN might be very complex and very difficult to manually process. In [26, 27] has developed a system generating FPN based on the analysis of interactions between the features and verification of FPN using the Petri network model. The developed structure involves generating features by way of mapping from CAD system, analysis of interactions between the features and an algorithm automatically creating a Petri network corresponding to a given FPN. An analysis of interaction between the features involves comparing each pair of features with reference to the defined set of rules. These rules include heuristic preferences of processing sequence, which guarantee its effectiveness. The rules take geometric, production and economic

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In case of variant approach to production process design FPN represents a model developed for the synthetic representative of a given group of machines. The synthetic representative represents an abstract object that includes all types of features that can be found in the group of parts with production similarities. The process model should allow for an explicit definition of

of processing individual features is defined based on the FPN. Subsequent, structurally unified modules of the model supplement the remaining functions of the model. The work [28] elaborates on this issue and gives an example of the variant approach for axially symmetrical parts.

As it has been mentioned in Section 1, modeling, simulation and controlling the production process in automated, robotized, discrete production systems is the main area of using the Petri network technique in production. The systems are typical examples of asynchronous concurrent systems. The problem of management of limited resources, classifying tasks and autodiagnosis in such systems is a very complex issue and requires optimizing procedures both at

. The sequence

a processing task only by way of correct positioning of initial marking vector M0

**4. Modeling and optimizing production systems**

factors into account.

The aforementioned issue of optimizing the structure of multi-tool production operations might be solved using two simple heuristics: give preference to the tool that might currently process the largest possible number of areas and give preference to the tool that might currently complete all the operations that have been assigned to it. The suggested approach allows for a satisfying sequence of simple operations with a small number or iterations equal to the number of tools used. It is an optimal sequence in more than 95% cases. In order to appreciate the benefits of this method, one can compare it to the full browsing algorithm. The advantages of this method also include a very simple method of transferring its results in the form of an organized sequence of complex operations to a formal network model.

The sequence of processing individual features might be conditional on their technological nature. An opportunity to automatically classify the conducted operations then requires initiating the optimizing procedure. A function of priorities assigned to each transition is used for this purpose. Example use of this method based on genetic algorithm is shown in the work [22].
