**4.2. Transition time assignments**

98 Petri Nets – Manufacturing and Computer Science

Pm = mean performance (parts per day).

**4. Research - characterization** 

manufacturing management.

(assembling and dispatching).

**4.1. Manufacturing process mapping** 

will be applied:

manufacturing.

interest to workload control (WLC) such as: lead time, average performance, autonomy, work progress and delays in delivery of orders. For this study case, the funnel formula

TLm = Im / Pm (1)

Where, TLm = simple mean lead time of orders (days); Im = mean inventory (parts); and

For the demonstration, the author uses the figure and considers steady state, i.e., the balance between input and outputs (α1 = α2) and tan α1 = Im / TLm e tan α2 = Pm. Wiendahl (1995) suggests that the equation can be used for measurement and control of

The research method was a computer simulation. Simplifications have been admitted, but

process mapping and data collection; ii) model construction by Petri Nets; iii) feeding the model with the initial situation of load in a production plan already executed, run and use the results to fit the model; iv) with the results, calculate the mean lead time of orders; and v) discussing and refining the method, analysis of the implications of its use in

The production process consists of modeling, cutting, sewing, assembling, packing and delivery (dispatching process). Some works use multitasking labour, that moves between closer stages. The manufacturing was divided in three different process: i) Process 1 (cutting, splitting and chamfer); ii) Process 2 (preparation and sewing); and iii) Process 3

Basically, the first process consists in cutting operations of the pre-fabricated (insole and sole) and the upper part of the shoes (leather upper). In pre-fabricated, the model was simplified grouping sequential operations. The input of the system is the place "INPUT – m1", all the orders should be loaded in this place, the transition Separation Table (after place m41) is only enabled when all the parts arrive at the place "Separation Table – m41", and is guaranteed by the auxiliary places (m78, m82, m79, m28, m83, m84, m85). The cutting of leather upper was detailed, this process is sequential because the parts should be cutted in different parts of the leather. The input of this process is the place "m42", observe that some operations are performed by the same operators, which explains the use of inhibitor arcs. The third process includes the assembling and dispatching, after this, the shoe process will be finished and ready to leave the factory.

The output of the system is the place "BOX OUTPUT – m16".

without losing the replicability. The work method was: i) choice of manufacturing,

To assign time to the transitions, all the processes were timed. With the orientation of the production supervisor, the start/end time of each task was defined. It was considered a confidence level of 95% and used the calculation model suggested by Vaz (1993) and AEP (2003). As an example, for the sole cutting operation the average time was 18.13 seconds and the standard deviation was 2 seconds. The minimum number of samples to ensure the confidence level was 19.5, adopting 20 samples. The time for each transition is the average values collected.
