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1 Introduction

Modern manufacturing systems are intelligent, complex, large, and expensive. For modeling these sophisticated systems, we need advanced tools. This paper focuses on discrete manufacturing systems and presents a new approach that is based on Petri nets.

Petri nets, because of its graphical nature, are self-documenting and easy to understand. The mathematics behind Petri nets is also easy to grasp. Hence, Petri nets are a suitable framework for modeling discrete event systems [1]. However, there is indeterminism in Petri nets, and it has a tendency to become huge when many resources are involved in the system.

This paper introduces a new approach known as the Activity-Oriented Petri Nets (AOPN) that provides a solution by developing discrete models in two phases: in the first phase, a simpler static Petri net model (“skeleton”) is developed, and in the second phase, the run-time details are added. This approach, while keeping the Petri net model size to a minimum allows implementation of sufficient logic on the model so that advanced discrete manufacturing systems can also be modeled.

In this paper: A short literature review is given in Section 2. Section 3 presents the classical approach for modeling manufacturing systems with Petri nets. Section 4 presents the new approach AOPN. Finally, Section 5 presents some discussions.

2 Literature Review: The Subsystems of a Manufacturing System

According to [1], a manufacturing system is composed of two main parts: The physical system and the decision-making system (DMS).

2.1 The Physical System

The physical system can be divided into subsystems [2]:

  • The active systems (e.g. machines).

  • The passive systems (e.g. buffers).

Some of the physical systems can be active or passive (e.g. robots) depending on the situation. For instance, a robot can be used as an active system (machining an input material), whereas in some other situations, it can be used as a passive system (handling). Since this paper focuses only on modeling with Petri nets, the physical system is modeled as a decision-free Petri net, consisting of many modules that represent the functional entities (e.g. the machines, transportation systems, buffers, etc.). When modeling manufacturing systems with Petri nets, there is a degree of indeterminism involved in the model. For example, which transition is to fire if there are several transitions enabled by the same enabling tokens? In addition, Petri nets are incapable of realizing all the modeling logic of real-life manufacturing systems, despite some Petri nets extensions can do so at the expense of the analytical power [3].

2.2 The Decision-Making System (DMS)

The decision-making system (DMS) is to cope with the incapability of the physical system to make decisions on its own and to manage the indeterminism in the Petri net model. The DMS can be further divided into two subsystems: Physical System State-based DMS (P-DMS) and Environment State-based DMS (E-DMS) [1].

  • P-DMS is the subsystem that computes the decisions based on the input from the physical system; for example, the control decisions that are made based on the sensor data from the machines.

  • E-DMS is the subsystem that computes the decisions based on the inputs from the external environment. For example, the decisions that are made based on the market conditions, and unplanned stoppage of production due to unavailability of transportation of products.

The P-DMS is further partitioned into two subsystems: iP-DMS and oP-DMS:

  • The iP-DMS includes all the P-DMS decision processes that can be modeled as a decision-free Petri net (iP stands for inside Petri net).

  • The oP-DMS includes all the P-DMS decision processes that cannot be modeled as a decision-free Petri net (oP stands for outside Petri net).

Since we are primarily interested in modeling manufacturing system with Petri nets, we group the set of decision processes belonging E-DMS and oP-DMS into the subsystem called Outside-DMS (O-DMS). Thus, O-DMS = (E-DMS) U (oP-DMS) [1].

For practical modeling of a manufacturing system, not all the subsystems that are shown in the Fig. 1 are needed. The most needed and often used subsystems are the active and passive physical systems, and the iP-DMS and the O-DMS.

Fig. 1.
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The subsystems of a manufacturing system

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2.3 Interaction Between O-DMS and iP-DMS

A Petri net model of a large manufacturing system consists of several modules that represent functional entities of the manufacturing systems. These Petri net modules makeup the iP-DMS; O-DMS is the decisions that are made outside the Petri net modules. The interaction between the iP-DMS and O-DMS subsystems happens through the control places [4], as shown in the Fig. 2.

Fig. 2.
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Classical approach: the interaction between the iP-DMS and O-DMS subsystems happens through the control places

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In the Fig. 2, the Petri net model consists of two subsystems, the iP-DMS and the O-DMS. The iP-DMS consists of six Petri net modules, representing the arrival of raw materials, two machines, one robot for handling, a testing station, and a unit for transportation of products out of the manufacturing facility. The Petri net modules are controlled (enabled) by the control places (represented by two concentric circles), which are under the complete control of the O-DMS. Unlike ordinary places in a Petri net, the control places do not loose tokens when the input transitions (that are connected to the control places) fire. The tokens in the control places are only for enabling the respective transitions. The tokens are deposited into and removed from the control places by the O-DMS.

3 The Classical Approaches for Developing Petri Net Models of Manufacturing Systems

We start this section with an example to illustrate the classical approach for modeling a manufacturing system with the subsystems O-DMS and iP-DMS. Then, we show how the new approach can provide more expressive and yet compact Petri net models.

3.1 Modeling by the Classical Approach: An Example

Figure 3 shows the Petri net model of a simple Flexible Manufacturing System (FMS). This FMS consists of an input conveyor belt, an output conveyor belt, a horizontal CNC machine (H-CNC), a vertical CNC machine (V-CNC), and a testing station. The FMS also has a robot to move raw material and parts between the elements mentioned above. Since the model is so simple, the transitions and places are not grouped into modules as shown in the Fig. 3.

Fig. 3.
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The model of a simple Flexible Manufacturing System.

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When the input material arrives (represented by the transition tIM), the robot picks them from the conveyor belt (tR1) and places into the H-CNC machine. The FMS performs a simple job with two operations: the first operation (tH) is performed by the H-CNC machine and the second one (tV) is performed by the V-CNC machine. After these two operations, the robot put the product into the testing station (tR3). If the product passes the quality test (tTS), it goes into (tPT) the output conveyor belt; otherwise, it will be discarded automatically (tPR).

Table 1 lists the transitions and the places involved in the Petri net model. In the Petri net model, the control place cR and the place pR are shown three times, in order to avoid cluttering of connections.

Table 1. The elements of the Petri net model.
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3.2 The Control Places

In the classical approaches, control places are the main mechanism for interfacing iP-DMS and O-DMS, as shown in the Figs. 2 and 3 [1, 3, 4]. A control place contains at most one token, where the token is deposited into and removed from by O-DMS. However, the implementation of the token addition and removal is not defined in any works. Also, the control places can only offer Boolean ON/OFF control, which is very limited in scope when it comes to modeling present day intelligent, complicated, and large-scale manufacturing systems.

4 A New Approach

In the previous section, the control place based mechanism was introduced for Petri nets based modeling of manufacturing systems. This mechanism has the following limitations:

  1. 1.

    The control places have to be treated as special places, as they do not behave like normal places. Thus, the mathematical tools that are so useful for analysis of Petri net models (such as reachability tree) become useless.

  2. 2.

    As stated earlier, for large Petri net model, the O-DMS has to control a large number of control places.

  3. 3.

    Most importantly, the control place based mechanism offers a very primitive control power, namely Boolean ON/OFF type control.

In the new approach proposed in this section, the control places are eliminated altogether. Instead, the transitions are controlled by the O-DMS. To allow O-DMS directly control the transitions inside the iP-DMS, each transition is equipped with pre- and post-processors. The new approach is known as the Activity-Oriented Petri Nets (AOPN) [5]. The software tool General purpose Petri net simulator (GPenSIM) is a realization of AOPN on the MATLAB platform; GPenSIM is freely available from the website [6]. Both the AOPN methodology and the software GPenSIM are developed by the author of this paper [2, 7].

4.1 Activity-Oriented Petri Nets (AOPN)

In the AOPN approach:

  1. 1.

    There are no control places. A Petri net model or module only consists of ordinary places, transitions, and arcs.

  2. 2.

    Every transition in the Petri net module can have a pre-processor. The pre-processor of a transition will be executed whenever the transition becomes enabled. Only if the conditions coded in the pre-processor are satisfied, then the transition is allowed to start firing.

  3. 3.

    Every transition in the Petri net module can have a post-processor. The post-processor of a transition will be run immediately after the transition completes firing.

  4. 4.

    The O-DMS control every transition through the pre-processors and post-processors.

  5. 5.

    The transitions in a Petri net model usually represent active physical systems only (e.g. CNC machines). The passive physical systems (e.g. AGVs transporting materials), referred to as ‘resources’ in AOPN terminology, are not usually represented by transitions in the Petri net model.

  6. 6.

    When an active system (represented by a transition) needs a resource to perform an operation, the active system requests the O-DMS for the resource. If the resource is available, the O-DMS allocates the required resource to the transition so that the transition can start firing. When the transition finishes firing, it releases the resource back to O-DMS.

  7. 7.

    O-DMS also computes details about the resource usage: how many resources were used, their efficiency of utilization (line efficiency), the costs involved in the resource usage, etc.

The pre-processor and the post-processor are MATLAB files (M-files). Since these are M-files, we can write any code, as much as we want, for bidirectional information flow and control flow between O-DMS and the Petri net model (iP-DMS) (Fig. 4).

Fig. 4.
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Firing of a transition: the pre- and post-processor files.

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Modeling a discrete event system by the AOPN approach consists of two phases [5]:

  • Phase-I: Developing the static Petri net model

  • Phase-II: Developing the run-time model

4.2 Phase-I: Developing the Static Petri Net Model

In the Phase-I, the static Petri Net model is developed. In this phase, mainly the activities are considered and they are represented by transitions interleaved with buffering places (e.g. places p10–p15 in the Fig. 5). The resources (passive physical systems) are grouped into two groups such as ‘focal’ resources and ‘utility’ resources. Only the focal resources are included in the static Petri Net model; the utility resources will be considered later in the phase-II (the run-time model). Thus, a compact Petri Net model is obtained with only the transitions representing the activities and, if there are any focal resources, they will be represented by places. Using the tool GPenSIM, coding the static Petri net in phase-I will result in the Petri net definition file (PDF).

Fig. 5.
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The static Petri net model resulting after phase-I of the AOPN modeling approach.

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Figure 5 shows the static Petri net model. In this model, the robot is assumed as a utility resource thus not shown in the model. The active physical systems such as H-CNC, V-CNC, and the testing station are represented by the transitions tH, tV, and tTS, respectively. Also, the arrival of raw materials is represented by tIM and the outflow of the testing station, namely accepted and rejected parts are represented by tPT and tPR, respectively.

The Petri net definition file (PDF) is the GPenSIM code for implementing (programming) the static Petri net model in GPenSIM software. The PDF for the static Petri net shown in the Fig. 5 is given in the Fig. 6.

Fig. 6.
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PDF for the static Petri net model shown in the Fig. 5

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4.3 Phase-II: Developing the Run-Time Model

In the phase-II of the AOPN approach, the run-time details that are not considered in the phase-I are added to the Petri Net model; e.g. transitions (activities) requesting, using, and releasing of the utility resources are coded in the run-time model (Fig. 7). Using the tool GPenSIM, the run-time details in the phase-II will result in the pre-processor file COMMON_PRE.m and the post-processor file COMMON_POST.m.

Fig. 7.
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The run-time Petri net model obtained after the Phase-II of the AOPN approach. The run-time details are coded in the M-files COMMON_PRE and COMMON_POST

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In the COMMON_PRE file (Fig. 8), the following two conditions are coded:

Fig. 8.
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The COMMON_PRE file.

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  • The transitions tH, tV, and tTS will be requesting the robot to load the part into the respective machine.

  • About 2% of the products are rejected by the testing station.

In the COMMON_POST file shown in the Fig. 9, the transitions tH, tV, and tTS will be releasing the robot after usage.

Fig. 9.
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The COMMON_POST file.

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4.4 GPenSIM Code for Simulations

For simulation of the FMS problem with GPenSIM, four M-files are needed:

  • Petri Net Definition File (PDF): this is the GPenSIM code of the static Petri net. For example, the PDF given in the Fig. 6 is the GPenSIM code for the static Petri net model shown in the Fig. 5.

  • Main Simulation File (MSF): In this file, the initial dynamics (e.g. initial tokens in the places: none in this example), the firing times of transitions, and the availability of the resource ‘Robot’ are declared. The MSF is shown in the Fig. 10.

    Fig. 10.
    figure 10

    The main simulation file.

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  • COMMON_PRE: In this file, the conditions for the enabled transitions to start firing are coded, mainly about reservation of the required resource ‘Robot’ by a transition, and using the resource if it is allocated.

  • COMMON_POST: the post-firing actions of the transitions are coded here, usually releasing the resource ‘Robot’ after usage.

For reproducibility, the complete code for simulation (the four files mentioned above) is given on the web page [8]; interested readers are encouraged to visit the web page for downloading the codes and experimenting with them.

4.5 Simulation Results

Simulation results show that some products with the probability of 10% get rejected by the testing station. The rejected parts end up in the buffer p15, whereas the quality products are placed in the buffer p14 (Fig. 11).

Fig. 11.
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Simulation results.

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5 Discussion

The FMS example shows that the AOPN approach provides a simple two-way information and control flow between the Petri net model (iP-DMS) and the surrounding decision-making system (O-DMS) via the pre- and post-processors. The classical approaches that use control places for interfacing the iP-DMS and O-DMS provide only primitive Boolean ON/OFF control, whereas with the AOPN approach any control algorithm can be coded into the pre-processors and post-processors. The FMS example also shows that implementation of the Petri net models using GPenSIM usually results in compact code as none of the files (PDF, MSF, and the pre- and post-processors) is more than half page long.

In summary, the duality – the compact Petri net models because of the activity-oriented view and the powerful and flexible resource management by the O-DMS, enables modeling, simulation, performance analysis, and control of any discrete event system.

6 Conclusion

GPenSIM is the software realization of the new AOPN approach. Though AOPN approach and the software GPenSIM are new, there are Doctoral dissertations, and many Master theses are done based on AOPN/GPenSIM. GPenSIM is used to solve many industrial and research problems in diverse fields of engineering. For example, in discrete manufacturing systems and production planning, airport capacity modeling, fish supply chain, Speech recognition, computer gaming, Marine-Diesel Engine Control, Service-Oriented Architecture, Grid-Computing, E-commerce, and Bluetooth Devices, to name a few [9, 10].