**4.3. Simulation, inventory and lead time calculations**

To test and refine the model was chosen a plan already done, two weeks and nine production orders. It was informed the load for each place, resulting from earlier orders, at the moment of the first evaluated order will enter the system. A new order is queued of previous processing orders, which explains why the lead time in manufacturing is much higher than the standard manufacturing time. The queuing discipline adopted was FIFO (First-In-First-Out). Table 1 shows data from nine manufacturing orders contained in the production plan (dates are considering working days – 8h40m/day = 3.200s/day). In the last column, there is the order lead time, calculated by simulation, and their average.



Wiendahl (1995) presents a method that considers the size of the order Qi. By this method, TLm = [ ΣQi x TLorder I ] / ΣQi = 2.73 days, close to the calculated 2.63 days. The correlation between real and simulated outputs (column 5 and 6) is 0.99 and the absolute error | real simulated | average is 9,821s (2.27% of the largest real value). Figure 3 shows the comparison of information from real and simulated outputs, order to order.

> Number of Pairs in Manufacturing N(t)

Accumulated Outputs O(t)

0 1,000 - - 25 1,000 - - 50 1,500 - - 75 3,000 1,000 2,000 100 3,000 1,000 2,000 125 3,800 1,500 2,300 150 3,800 1,500 2,300 175 4,600 3,000 1,600 200 4,600 3,000 1,600 225 5,000 3,000 2,000 250 5,000 3,800 1,200 275 5,000 3,800 1,200 300 5,000 4,600 400 325 6,000 5,000 1,000 350 6,500 5,000 1,500 375 7,000 6,000 1,000 400 - 6,500 - 425 - 6,500 - 450 - 7,000 - AVERAGE: 1,546 Pairs

**Table 2.** Accumulated inputs and outputs of each order presented in Table 1 (at the same interval)

The simulation can generate data for all processes, individually. For instance, Figure 5 shows the results in place INPUT Sewing Process – m44, the operator at this place is overloaded, also observed in the real process. An alternative would be a redistribution of

A different situation is shown in Figure 6, the time that the operator is idle in this place is low, and there are no accumulations of tasks over time. This represents that, for this place,

Other screens allow similar analyzes in all manufacturing places. It is important to analyze the changes in the manufacturing and the impacts that an action causes in each process (for

**5. Applications in manufacturing management – results discussion** 

tasks, adopting parallelisms, without overloading the following posts.

instance, allocate more operators to develop a specific task).

the tasks are well distributed.

Time x 10³ (s)

Accumulated Inputs I(t)

**Figure 3.** Comparison of information from real and simulated outputs

The simulated mean performance is Pm = 31,200 x [ 7,000 / (428,504 – 66,480 ) ] = 583 pairs of shoes per day. The calculation basis is: in (428,504 - 66,480) seconds, were delivered 7,000 pairs. The real mean performance is Pm = 31,200 x [ 7,000 / (428,504 – 78,000 ) ] = 608 pairs of shoes per day.

The time interval between simulated outputs is Δt = [(428,504 – 66,480) / 7,000] = 51.7s and the real is Δt = [(436,800 – 78,000) / 7,000] = 51,25s. The expected mean inventory is Im =Pm.TLm = 583 pairs / day x 2.627 days = 1,531 pairs.

**Figure 4.** Throughput diagram for real inputs and simulated outputs (at intervals of 25,000s)

The instantaneous numbers of pairs in the system is N(t) = I(t) – O(t). The average, an indicator of mean inventory, calculated by this method is close than the one calculated by the funnel method (1,546 and 1,531 pairs respectively).


100 Petri Nets – Manufacturing and Computer Science

shoes per day.

**Figure 3.** Comparison of information from real and simulated outputs

=Pm.TLm = 583 pairs / day x 2.627 days = 1,531 pairs.

the funnel method (1,546 and 1,531 pairs respectively).

The simulated mean performance is Pm = 31,200 x [ 7,000 / (428,504 – 66,480 ) ] = 583 pairs of shoes per day. The calculation basis is: in (428,504 - 66,480) seconds, were delivered 7,000 pairs. The real mean performance is Pm = 31,200 x [ 7,000 / (428,504 – 78,000 ) ] = 608 pairs of

The time interval between simulated outputs is Δt = [(428,504 – 66,480) / 7,000] = 51.7s and the real is Δt = [(436,800 – 78,000) / 7,000] = 51,25s. The expected mean inventory is Im

**Figure 4.** Throughput diagram for real inputs and simulated outputs (at intervals of 25,000s)

The instantaneous numbers of pairs in the system is N(t) = I(t) – O(t). The average, an indicator of mean inventory, calculated by this method is close than the one calculated by **Table 2.** Accumulated inputs and outputs of each order presented in Table 1 (at the same interval)
