3.3 Step 3: calculation of the parameters needed for the mathematical model

The intercellular transport costs are shown in Table 5. The rest of the parameters to be used in the mathematical model were the following: average cycle time C ¼ 0:15 gives a value of Smin = 6, and a value of Smax = 10 was also considered. The number of cells obtained from the combined precedence diagram gave values of Kmin = 4 and Kmax = 6, which are adequate for the groups of machines that can be visualized previously, giving values of Mmax = 8 and Mmin = 5, respectively. All this information is presented in Tables 6–8.


Figure 6.

53

Table 4.

Extended combined precedence diagram for the industrial problem.

16 16 52–55

Results of the assignment of machines and products.

i m j im j 1 11–4, 10–19, and 60–67 17 17 60–67 2 2 60–67 18 1 5–9 and 20–34 3 3 30–38 19 1 35–51 4 4 15–23 20 3 39–47 5 5 30–34 21 4 22–29 66 5–9 and 20–23 22 5 43–51 7 7 60–67 23 6 22–29 8 8 52–55 24 8 56–59 9 9 30–34 25 9 43–51 10 10 30–38 26 10 39–51 11 11 1–4 and 10–23 27 11 5–9 and 22–29 12 12 52–59 28 13 39–51 13 13 30–38 29 14 5–9 and 22–29 14 14 10–23 30 15 43 and 44 15 15 45–47 31 16 56–59

A Methodology to Design and Balance Multiple Cell Manufacturing Systems

DOI: http://dx.doi.org/10.5772/intechopen.89463

Table 3. Values of qm obtained for the industrial problem.


A Methodology to Design and Balance Multiple Cell Manufacturing Systems DOI: http://dx.doi.org/10.5772/intechopen.89463

#### Table 4.

planning horizon of T = 1296 h. Tables 1 and 2 present general information with respect to the types of machines and the different product models, respectively.

Applying Eq. (1) to determine the number of machines of type (qm) needed to

Comparing these results with the actual values of the number of machines of a given type present in the plant, we get that they are equal for almost all the values of

a. m = 3, which means that one more machine must be bought to fulfill the

Case (a) explains in some way why machine 3 punching machine has become a bottleneck in the plant when "accessory"-type products are made. Maintain, in this study use will be made of the current excess capacity produced by the two type 15 machines (connector welder) reflected in case (b), assigning products to both

Applying the proposed assignment procedure of Figure 2, we get the assignment of machines (i) to the (m) machine types and of products (j), which are presented in Table 4, where the fact that machine 12 will function as a "virtual machine" in

With the determination of the number of types of machines, and the assignment of products to machines obtained in the previous stage, the precedence restrictions deliver the extended combined precedence diagram shown in Figure 6, where the virtual machine 12 differs from the rest because in it the two benders with the largest capacity operate simultaneously in the production of pillar-type products. These products have a larger size, so it is advisable to use both benders one next to the other to mechanize the product and, in this way, reduce the processing time of

3.3 Step 3: calculation of the parameters needed for the mathematical model

The intercellular transport costs are shown in Table 5. The rest of the parameters to be used in the mathematical model were the following: average cycle time C ¼ 0:15 gives a value of Smin = 6, and a value of Smax = 10 was also considered. The number of cells obtained from the combined precedence diagram gave values of Kmin = 4 and Kmax = 6, which are adequate for the groups of machines that can be visualized previously, giving values of Mmax = 8 and Mmin = 5, respectively. All this

m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 qm 312222122 2 2 2 2 2 1 2 1

satisfy the capacity restrictions, the values presented in Table 3 are obtained.

3.1 Step 1: calculating and assigning the required machines

required capacity of this type of machine.

b. m = 15, where there is currently one extra machine.

which two machines will operate simultaneously is pointed out.

3.2 Step 2: preparation of the extended combined precedence diagram

m, except in the following two cases:

Mass Production Processes

machines.

this operation.

Table 3.

52

information is presented in Tables 6–8.

Values of qm obtained for the industrial problem.

Results of the assignment of machines and products.

Figure 6. Extended combined precedence diagram for the industrial problem.


i<sup>0</sup>

55

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A Methodology to Design and Balance Multiple Cell Manufacturing Systems

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DOI: http://dx.doi.org/10.5772/intechopen.89463

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#### A Methodology to Design and Balance Multiple Cell Manufacturing Systems DOI: http://dx.doi.org/10.5772/intechopen.89463

i

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Mass Production Processes

0

54


Table 5.

Intercellular transport costs between machines i and i´ (Cii´). 3.4 Step 4: statement and solution of the mathematical model

Weighted average processing times (ti) for each machine i.

DOI: http://dx.doi.org/10.5772/intechopen.89463

process exceptional products. This solution is represented in Figure 7.

uct models were assigned to each of these production cells. This solution is

the methodology shows the resultant cells and the product families assigned to them, where it is seen that cell 1 processes products of the beam and slotted angle type, cells 2 and 3 process only accessories, cell 4 processes only beams, and cell 5 processes only pillars. In this way, it is easier to improve the obtained balance by sequencing mixed product models, because in a cell there are no different types of products that compete for the same resources (machines), but they rather process the same types of products, grouped in families. Only work stations 1, 2, and 8 turn out being multicellular, because they process exceptional products that undergo intercellular movements, most of which are associated with the operation of the cutter type machines, since they are those that are mostly shared by the different

To analyze the results, it is necessary to have performance measures of the solution, but since the present study has taken up a new problem that is part of the manufactured cell formation problem (MCFP) and the general assembly line balancing problem (GALBP), we must use measures of performance commonly employed for both problems separately, such as group capability index (GCI), for

3.5 Step 5: assigning the product models to the production cells

represented in Table 9.

products.

57

Table 6.

Table 7.

Table 8.

Parameters to be used in the model.

Set of precedence relations between machines.

With the parameters calculated above, we state the mathematical model. The model was then solved using the Extended LINGO© version 8.0 software, getting an optimal global solution in 2 h and 32 min, after 121 iterations, giving as a result 5 manufacturing cells and 9 work stations, 3 of them multicellular, because they

i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ti 0.033 0.03 0.03 0.031 0.033 0.034 0.031 0.021 0.02 0.031 0.034 0.028 0.029 0.03 0.014 i 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ti 0.022 0.031 0.034 0.028 0.023 0.034 0.034 0.034 0.014 0.02 0.034 0.034 0.026 0.033 0.011

A Methodology to Design and Balance Multiple Cell Manufacturing Systems

Kmin Kmax θ Mmax Mmin M C A ⌈Smin⌉ Smax cs (MM\$) cb (MM\$) 4 6 4 8 5 31 0.15 0.005 6 10 0.45 0.05

E (8,12), (24,12), (12,16), (12,31), (1,2), (1,4), (2,7), (4,11), (7,17), (11,14), (18,4), (18,6), (18,21), (18,23), (18,5), (6,11), (6,27), (21,27), (23,27), (27,29), (5,10), (3,10), (3,9), (10,13), (9,13), (19,3), (19,22), (19,20), (22,26), (20,26), (20,25), (25,30), (25,15), (26,28), (30,28), (15,28)

With the groups of machines obtained thanks to the model's solution, the prod-

The proposed cellular manufacturing system that results from the application of

### A Methodology to Design and Balance Multiple Cell Manufacturing Systems DOI: http://dx.doi.org/10.5772/intechopen.89463


Table 6.

Weighted average processing times (ti) for each machine i.


Table 7.

Parameters to be used in the model.


Table 8.

Set of precedence relations between machines.
