**1. Introduction**

94 Petri Nets – Manufacturing and Computer Science

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*International Conference on Production Research*, pp. 445-449

A proper planning and the search for better results in the production processes are important for the competitiveness that manufacturing can add to business operations. However, changes in manufacturing involve risks and uncertainties that may affect the company's operations. In this case, modeling and simulation of the production line can assist the decision-making process, avoiding unnecessary expenses and risks before making a decision. A model that can be simulated in the computer is a mechanism that turns input parameters, known and associated requirements of the process, into output parameters and performance metrics that have not yet happened in the real world (Law; Kelton, 1991).

Thereby, a line production model, which can be used in a computer simulation, can be a tool for decision support, because, before the results will crystallize in the real world manufacturing, it can be predicted, with a given reliability, in virtual simulation.

Inventory in process and throughput time that a production plan will generate are quantities that may be useful in decision making in manufacturing and can be predicted by computer simulation. The inventory process (work in process or WIP) consists of materials that have already been released for manufacture (have already left the warehouse or have been received from suppliers), but their orders still not been completed. Lead time is the time between release manufacture order and the product availability for shipment to the customer (Antunes et al., 2007). Some decisions in internal logistics of manufacturing may be related to these quantities: choosing alternatives for compliance with scheduled delivery dates, intermediate storage areas for processing of applications, equipment for internal movement; resources for tool changes and machinery preparation. The most important decision that can be supported by the proposed method is the definition of in-process

© 2012 Facchin and Sellitto, licensee InTech. This is an open access chapter 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. © 2012 Facchin and Sellitto, licensee InTech. This is a paper 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.

inventory level that will be allowed in manufacturing. This should not be so low as to generate idle nor so high as to increase the throughput time.

Measurement of Work-in-Process and Manufacturing Lead Time by Petri Nets Modeling and Throughput Diagram 97

**Figure 1.** Symbolic representation of Petri Nets

**3. Throughput diagram in manufacturing** 

materials (Silva; Morabito, 2007; Papadopoulos et al., 1993).

represents a significant manufacturing effort (Sellitto, 2005).

**Figure 2.** Throughput diagram of a work center

In manufacturing, a queue arises when, for variability, at a given instant, the number of orders to be implemented is greater than the available job centers. The manufacturing arrives at the work position (or center), waiting its turn, is processed and proceeds. The sequence is subject to change priorities and interruptions for maintenance or lack of

A work center (machine, production line or manufacturing plant) can be compared to a funnel, in which orders arrive (input), waiting for service (inventory) and leave the system (output). When the work center is observed for a continuous period, the reference period, the cumulative results can be plotted. In Figure 2, it is possible to observe strokes representing the accumulated input and output, measured in amount of work (Wiendahl, 1995). This quantity may be in parts, numbers of hours or another unit value which

To obtain the line that represents input is necessary knowing the amount of work waiting in the initial inventory at the beginning of the reference period and the output is plotted summing the completed work orders. Wiendahl (1995) presents an analytical development related to the throughput diagram and calculates various quantities of

In the first two chapters will be presented basic concepts for modelling the proposed system using Petri Nets and throughput diagram, these methods will be applied in a real manufacturing and the results compared with the real manufacturing outputs.

The aim of this paper is to measure in advance in-process inventory and lead time in manufacturing that a production plan will generate. Knowing the magnitudes of the plan prior to release, a manager can predict and possibly prevent problems, changing the plan. The specific objectives were: i) mapping manufacturing, ii) model building for PN, refining and validated by field data, iii) with the results simulated by throughput diagram, calculate the inventory in process and expected lead time; and iv) discuss the application. Computer simulation is the research method. Delimitation is that made in a single application in shoe manufacturing, in a period of two weeks. The working method includes two operations research techniques, Petri nets (PN) and the throughput diagram and was tested in a production plan already performed, whose results served to refine and validate the model, which can be used in plans not yet released for manufacturing.

The main contribution of this paper is the method of working, replicable to other applications: simulation PN, validated by data field and use the throughput diagram results to calculate the performance metric. The method can be useful in ill-structured problems, as may occur in manufacturing.
